tag:blogger.com,1999:blog-22104970642073783862024-03-11T12:58:38.702-07:00Teacher Educator BjørnI am a teacher educator in mathematics. In this blog I will write about mathematics, teacher education and topics connected to this.Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.comBlogger119125tag:blogger.com,1999:blog-2210497064207378386.post-16201036224229779232024-03-11T12:58:00.000-07:002024-03-11T12:58:02.905-07:00Diversity in Norwegian mathematics examinations, 1962-2020<p>Yesterday, the article «<a href="https://www.tandfonline.com/doi/full/10.1080/00313831.2024.2322950" target="_blank">Diversity in Norwegian mathematics examinations, 1962-2020</a>» was published in the journal Scandinavian Journal of Educational Research. It is open access and written by my colleague Aina Fossum and me. </p><p>As far as I can remember, this project started in the spring of 2020. We got the idea that we could study all the Norwegian national mathematics exams for «grunnskolen» to see how diversity had changed throughout the years. I remember that we sat in an early meeting and discussed - only half jokingly - that we wanted to have a way of analysing the exams that was simple enough to be done on the beach. After all, with the work hours that are typical among researchers, it is not healthy if they all have to be indoors, next to a computer screen.</p><div style="text-align: left;">The findings of the article can of course best be read in the article. The abstract includes this short summary: «<span style="-webkit-text-size-adjust: 100%; caret-color: rgb(51, 51, 51); color: #333333; font-family: "Open Sans", sans-serif;">Representation in Norwegian examination tasks has improved gradually over the past half century. While representation of girls approached 50% in the 1980s, people with non-stereotypical Scandinavian names or appearances (non-white) were in the single digits until the 2000s. However, it appears that inclusion has been selective, and that some groups are still invisible. There are no clear examples of homosexuality and only two of explicitly disabled people in our material.</span>» The article is unique (as far as I know) in studying many identity markers through a period of almost 60 years, and gives results that are worth pondering for anyone interested in representation in exams and other materials, in my opinion.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Thinking back, it is amazing how many people have had input that has influenced the final article. We have discussed the ideas and later the provisional findings in many different conferences and research groups, and peer reviewers have given a lot of constructive feedback.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">I challenge anyone to do similar research in their own country. If such a series of annual exam does not exist, perhaps different series of textbooks could do the trick. It would be very interesting to see how such change has occured in different countries, and which patterns are the same or different. Are there any countries in which disabled people take part in mathematics tasks? Or where there exist both same-sex couples and different-sex couples? And so on.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">In the mean time: enjoy the article. It was fun to plan, research and write, but it was a particular pleasure to see it published online…</div>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-40451082922879806542022-07-24T07:37:00.004-07:002022-07-24T07:37:39.978-07:00Official language: Broken English<p><span style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">This week, I've been to another conference (ESU9 in Salerno, Italy, for people who want to know. I will blog about it later). It was a wonderful conference, both in terms of ideas shared and in terms of a pleasant and friendly atmosphere. The kind and clever people presenting came from all over Europe (and beyond) and can read and speak brilliantly in French, German, Spanish, Norwegian, Greek and so on - these capabilities are useful, by the way, when doing historical research. However, even in this context, I heard people apologize for their bad English when presenting in English. I hear these apologies in all conferences I go to where English is the official language.</span></p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">I have, however, also been to a conference (was it Mathematics Education and Society?) which states specifically that the official language of the conference is Broken English. Broken English is, according to Wikipedia, "non-standard, non-traditionally spoken or alternatively-written versions of the English language". The whole point of having English as an official language of a conference, is that everybody - even those who do not learn English when they were children - do their very best to speak some version of English, and that everybody, obviously, do their best to understand. There is no reason to apologize.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Having Broken English as official language has at least two consequences: </p><ul style="-webkit-text-size-adjust: auto; direction: ltr; margin-bottom: 0in; margin-top: 0in; unicode-bidi: embed;" type="disc"><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">People do not have to apologize for speaking English in the very best way they are able.</span></li><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">People should be prepared to do an effort to understand, and also know that some points may be lost in translation. </span></li><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">People who do not speak Broken English (that is, people who have English as their first language, for instance), should not pretend they are in a conference where Perfect English is the official language. For instance, they should not try to get a 30-minute presentation into their 10-minute timeslot by speaking so fast that only native listeners can understand... (I have experienced that, although not recently).</span></li></ul><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Having your first language the official language of a conference is a privilege, as it is so much easier to present your ideas and formulate your questions and comments. We need to work to make this privilege less than it has to be.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">(By the way, there is of course differences of privilege in the group using Broken English as well - I am so lucky that one of the languages that we use at home, is (Broken) English, which has given me some training in formulating thoughs into Broken English...) </p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-5761087012289795542022-06-03T05:59:00.004-07:002022-06-03T05:59:47.051-07:00NERA 2022 Day 3<p> <span lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">The third day of NERA 2022 consisted solely of plenaries. The first one was the second sociologist plenary speaker at this conference;: </span><span lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; font-weight: bold;">Guy Standing</span><span lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">: "</span><span lang="en-GB" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">The Precariat: Recovering the Soul of Education". He claimed that we are living in a period of constant uncertainty, with "unknown unknowns". (Already, I guessed that I would need Hans Rosling here on my shoulder to keep a balance.) He blamed "neo-liberal" capitalism for leading to a new class structure, where both economic goods and security are concentrated among those who possess assets. The "salariat" (those with secure salaries) are shrinking. The precariat is growing. He defined the precariat with three dimensions: 1) a status of unsecure labor, they don't have a occupational narrative (which in Skovsmose's words would be part of their foreground), they have an education above the level demanded of the jobs they are getting (while the education demanded to </span><span lang="en-GB" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; font-style: italic;">get</span><span lang="en-GB" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;"> a job is increasing). The precariat do not know what is needed to change their situations. 2) The precariat gets wages but not the extras that the salariat gets (such as paid holidays, health care...) and are "systematically exploited by debt". (It would be fun to do a discourse analysis of how he talks... It feels like he is pointing to important issues in a language that is so out-there that it gets in the way of the message.) 3) They are systematically losing rights of citizenship - not seeing political parties that can address their position. </span></p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Three factions of the precariat: 1) those not having much education, and feel that the present is worse than the past - voting for Trump, Urban, Putin...) 2) the nostalgics, have no current time, mostly don't vote at all. 3) the progressives, who have been promised a future if they do their studies, coming out of college with debt and jobs that will lead nowhere. These are looking for a new sense of the future. </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Finally, he got to the role of education (which happens to be the theme of this conference). He claims there has been a commodification of education, which used to be viewed as a common good. He rallied against relevance, employability, human capital, arguing that education is not about that. He claimed that education is failing to teach history, to prepare for democracy and so on. (Really?!)</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The lack of nuance in this lecture is astounding. He talks about a "disease" and the importance of curing it, but curing a disease usually depends on an understanding of the disease, not just slogans. If his "diagnosis" is right, we might just as well just close down the entire educational system and start again, as nothing good gets out of it at the moment. (To his credit, in one of his last sentences, he recognized that his picture is less accurate in some countries than in others.) I miss Hans Rosling.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">To summarize, I did enjoy parts of Standing's discussion of the precariate - I see that the growth of short-terms jobs is a problem in the rich world. But his discussion of education was painted with an enormously broad brush. Moreover, such plenaries tend to occur regularly in education conferences. It is a bit surprising that organizers do not invite people who can say something a bit new about education, rather than some sociologist who can only offer an often-repeated, caricatured image of education policy. </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The third plenary was by <span style="font-weight: bold;">Dennis A Francis</span>, talking about "Precarious bodies, affect and education". This was yet another sociologist. They started by story-telling about an incident in a Durban classroom, with sexuality education, homophobia, CIS-normativity interweaved. Vulnerability is not an individual characteristic, but a result of societal factors. COVID-19 shows how the rich and the poorer world are interdependent, but not more than there is a huge vaccine inequality. (That is, even when vaccinating everyone is of interest to the rich world, it is not enough to actually provide vaccines.) Even COVID-19 has not been an equalizer.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Images from the war in Ukraine is shown in African newspapers, as was the Charlie Hebdo terrorist attack - supporting the long-standing impression that lives of white European are more valuable and news-worthy than lives in other parts of the world. How can anti-oppressive education respond to injustice and precariousness to those both in proximity and at a distance? How can educators be actors in addressing precarity, inequality and social action?</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">They noted that there has been an explosion of reported hate crimes due to homophobic or transphobic hate crime in the UK and the US. The pandemic has been bad in this regard. Transgender women of color are especially hard hit. The same can be seen in South Africa. They also gave examples of schools explicitly condoning homophobia and forbidding the support of pride.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">They argued that education has to understand the mechanism of inequality, and that all people are grievable. We need a critical analysis of precariousness and oppression. We need to disrupt the hyper-individualisation of education. "You are because we are" (Ubuntu). (I feel a need to stress to our students that their task is not to study and get their individual qualifications, but to work together so that the group learns as much as possible.) Maybe knowledge is not the answer - rather questioning "How did I learn racism?", "Where did my attitudes towards LGBT come from?".</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">(Why do I appreciate this talk so much more than the previous one? Francis also paints a dire picture of the situation. However, it is filled with concrete data and examples, and the intersectional references makes it more nuanced.)</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">This marked the end of the NERA 2022 conference on my part. There was a plenary panel as well as a closing ceremony left, but I did not feel a need for more intellectual input at the time, wanting rather to spend some quality time with my notes from the conference to summarize a little.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Conferences are about content and people. In terms of content, I have of course attended a lot of presentations, and some of them have included interesting food for thought which I will take with me. In terms of people, I have spent most of the "free time" with people I already knew, strengthening existing relationships. Most of the scheduled time has been spent in various networks, where discussions go on for three or four minutes before the next presentation meets. The format of CERME, for instance, in which you spend most of the day for several days in a room with a limited number of people, is much more conductive to establishing contacts that may lead to friendships, collaborations, research stays and so on. But I must also admit that I'm not of the strategic kind - I do not draw up a list of people I want to get in touch with beforehand, and then seek them out. There are probably quite a lot of people I should have tried to meet in that way. For instance, I could have read up on Jón Ingvar Kjaran's work, approached him in the conference and tried to make him interested in collaborating on something LGBTQ-related in the future (as I know his name as an important figure in the field). But that is so far out of my comfort zone that I'll just add this to the already long list of opportunities missed...</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">On the fringe of the conference, however, I have had meetings with Icelandic colleagues in mathematics education, so I do have some bright moments. </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">As to NERA 2022 as a conference, I think it has delivered on its promises - for me, it has not been any major flaws when comparing to the programme posted. I do have some issues with the organization of the conference, though. I think the plenaries should provide new perspectives for many participants, and that they should be earlier in the conference, making it possible to refer back to them in discussions throughout the conference. I also think the networks should be strengthened and people being encouraged to stick to a network.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Finally, some random reflections at the end of the conference: </p><ul style="-webkit-text-size-adjust: auto; direction: ltr; margin-bottom: 0in; margin-top: 0in; unicode-bidi: embed;" type="disc"><li lang="nb-NO" style="color: #191919; margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">"Reading a paper" is, these days, not meant to be taken literally.</span></li><li lang="nb-NO" style="color: #191919; margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">Some people seem to think that not using Powerpoint is a wonderfully creative practice and a subversion of the norm. It is, rather, a practice of exclusion when the oral presentation is partly inaudible. When a presentation is given in a monotonous voice, a Powerpoint presentation can give welcome ideas of what are the headings and key points of the presentation.</span></li><li lang="nb-NO" style="color: #191919; margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">"As mentioned above" has a wonderfully surreal quality when uttered in an oral presentation - especially when we are on the top floor of the building.</span></li><li lang="nb-NO" style="color: #191919; margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">Braun & Clarke is often mentioned, but more rarely used. (As Braun & Clarke are the first to point out.)</span></li><li lang="nb-NO" style="color: #191919; margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">For people asking questions: the fact that you have fallen in love with a particular theoretical viewpoint, does not mean that it is a weakness when others do not use it. </span></li></ul>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-8636881695599320812022-06-03T05:59:00.000-07:002022-06-03T05:59:00.151-07:00NERA 2022 Day 2<p> <span style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">The second (and second to last) day of NERA was made into a full network session day, with no less than four 90-minute network sessions (each with a number of smaller talks) and no plenaries. The first one started at the unusual time of 8 AM. (I am happy that I was not talking at this time, as it would be difficult to get breakfast (starting at 7 AM), have half an hour's walk and then be there in good time to get things ready on the computer.)</span></p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">I attended network 4's session first. Network 4 is "Justice through Education" (as may be apparent already, the networks' themes are rather overlapping, which helps to explain why people do not stick to one network throughout the conference).</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Revealing the invisible: studies of Whiteness in the Nordic Educational Research" by <span style="font-weight: bold;">Maïmouna Jagne-Soreau, Gunilla Holm and Jenni Helakorpi </span>was the first talk. She started by discussing the concept of whiteness, which is a social construction related to power positions and privileges. She also said a few words about critical whiteness theory and critical race theory, as well as the difference between racialization and racification. The research, however, is a qualitative study of Nordic publications (so far 36) and their use of "white" and "whiteness". (She noted her problem that researchers may write about this without using these words, of course.) She found four stages (?): </p><ul style="-webkit-text-size-adjust: auto; direction: ltr; margin-bottom: 0in; margin-top: 0in; unicode-bidi: embed;" type="disc"><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">white supremacy and nationalists; research on neo-nazi youth etc.</span></li><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">from colorblindness to problematizing color-evasiveness; concluding that whiteness should be studied.</span></li><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">critical whiteness beyond colorblindness: for instance critical whiteness theory as a critical framework when analyzing.</span></li><li lang="nb-NO" style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11pt;">doing whiteness in the classroom: Habel (2012), about being a black teacher in a white classroom. Also discussions of tolerance, whiteness as performative, positionality.</span></li></ul><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">She concluded by, among other things, noting that whiteness is almost uniquely observed through negative manifestations, which was rather interesting.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">There was also a rather interesting discussion starting with the question about whether the authors of the studied papers are white or non-white, whereafter it was pointed out that it is not sufficient to look at a person's skin colour to see whether they are white or not in this understanding. People may have white skin but still not being included in the "white". Therefore, it is impossible from the articles themselves to see whether there is a majority of "white" authors or not.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"“I wasn’t Black until I came to Iceland”: Perspectives from middle-class parents of color with children in Icelandic schools" (<span style="font-weight: bold;">Berglind Rós Magnúsdóttir and Elizabeth B Lay</span>) followed. She started by telling about a recent increase in the percentage of immigrants in Iceland (after having been at 100 % a little more than 1000 years ago, it has steadily declined until just a few years ago, I guess). In educational research, there has been a focus on the vulnerable position of immigrants. She stated that she used an intersectional approach, with ideas from Bourdieu, critical race theory and the interplay between the two. </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">While this is an ongoing project, she presented some preliminary results, but most did not directly concern the parent-school-relationship.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"What Racism? A Content Analysis of The Norwegian Curriculum" (<span style="font-weight: bold;">Sara Blikstad Nyegaard</span>). She wanted to study whether racism is prioritized in the making of policy documents, and in particular in the new curriculum LK20. She has studied the subjects Norwegian, Social Science and KRLE as well as the general part of LK20. She looked for four approaches: intercultural (a focus on representation and respect), relational (relation building etc), democratic (citizenship, democracy) and norm-critical approaches to antiracism. The relational approach is the one that is most frequent in the curriculum, while intercultural appraoches are mostly seen in connection with particular minorities. However, racism is not a concept used in the curriculum, and racism seem to be seen as an individual problem, not an inherent part of our system and democracy. (Seeing racism as the opposite of democracy is rather troubling, as there are of course plenty of examples of democracies having racist policies and practices.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">In the discussion, there were questions of whether the non-mention of racism can in itself being seen as institutionalized racism. (To me, that is perhaps going a bit far - it all depends on the context. If - hypothetically - everyone knows that racism is important based on the general formulation in the law and regulations, it may not be necessary to mention it explicitly in all the parts of the curriculum that can be related to it. Or even worse: it may be that teachers read racism into every sentence which could equally well be interpreted to concern homophobia etc.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">After a quick break, I was back to Network 19, where there were four talks in 90 minutes:</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"The third space: Teaching collaboration as a pivot for knowledge development and coherence in teacher education" by (<span style="font-weight: bold;">Åshild Vassend Holm and Marianne Martinsen</span>) was the first talk. Her context is teacher education and school-teacher education partnership, in particular partner schools (lærerutdanningsskoler). She stressed the importance of "third space", being "equal" and "shared" goals. Other key concepts were "boundary crossing". There was a case study - a pilot - done in the 7th semester at the teacher education at Hamar, in PE studies. One of the activities was to have a professional conversation about a scientific paper. (I wonder what the definition of "equal" is, as they seem to have as an ideal that the student, the teacher mentor and the teacher educator are "equal" in the discussion about a scientific paper, even though scientific papers are, in my mind, clearly on the teacher educators' "home turf", inviting the other participants to the teacher educators' space.) The preliminary results are that it helps, but that it is time consuming. (And it is often a problem to know whether it is scalable.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Preparing student teachers to teach in diverse classrooms: A comparative case study of two teacher education programmes" (<span style="font-weight: bold;">Britt Oda Fosse</span>) She presented a paper that is already published in Acta Didactica, comparing two teacher education programs, one in Norway and one in Greece. Two central concepts are differentiated instruction (DI) and intercultural education (IE). (It does seem to me that intercultural education is more focused on one particular kind of diversity (cultural diversity), while differentiated instruction is often connected to another kind of diversity, mostly connected to ability or performance. And that many other kinds of diversity are not included?) Among findings was that special needs pupils were more prominent in the minds of Norwegian students, while Greece have more special schools making it less prominent in "ordinary" students. Greek students were more interested in immigrants and their knowledge of Greek. Greek TEP seemed more occupied with assimilation into Greek culture.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Based on realities and meeting challenges. Teacher students’ master projects in collaboration with the field of practice" (<span style="font-weight: bold;">Lennart Jølle, Leiv Inge Aa and Randi Solheim</span>). Students' master project themes were developed (in this pilot with just 16 students) through discussions between students, practice teachers and teacher educators. Students master's projects were anchored in field practice based on teaching methods (literary conversation in this case), on pupils' backgrounds and group characteristics (language and linguistic diversity) and on curriculum/teaching projects (on L1 writing and life skills). Students, in groups of 4, had their individual projects around a common theme, with different foci. It was stressed that the collaboration did change the roles, making it easier to see each other as teacher educators.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Crossing Boundaries within Work-integrated Teacher Education" (<span style="font-weight: bold;">Sandra Jederud</span>). (At this time, I had to give my hands a break, so no notes from the last talk. Sorry.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">After lunch, I attended Network 4 again, for a symposium on "Diverse Diversity; contradictions and challenges in education". There were supposed to be three presentations. In addition, there was a discussant (Gunilla Holm), that could not attend the conference and had to be a discussant on Skype, which is, of course, far from ideal (the usual time spent on technical problems as well as low sound quality which in effect is an exclutionary practice towards people without perfect hearing).</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"To be a participant but still not belong" (<span style="font-weight: bold;">Hermína Gunnþórsdóttir</span>) was based on a paper published in Icelandic (and with an extended abstract in English), studying students (4 boys and 4 girls) of foreign origin in Icelandic compulsory schools (grades 6-10, in fact) in a rural village. While students treasured their native language (which was used with parents/grandparents and friends), it was absent in school. The students had good relations to teachers, but still hesitated to ask for help when they failed to understand tasks. They felt "invisible" in school, there was very little interest in the countries students came from. Students also found it difficult to get Icelandic friends. (I must say that some of the findings are unsurprisingly equal to research findings about LGBT students - it is easy to be "included", but to be invisible at the same time.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Participating in Parental Support Programs to Enhance Integration in Norway" (<span style="font-weight: bold;">Therese Halvorsen</span>). Parental support is actually manditory for parents coming to Norway as refugees. There are 8 commonly used programmes, and it is proven to be able to strengthen the relationship between parent and child (but this was not in a refugee context, if I understood correctly). This study was large-scale, with (so far) 100 families (360 families needed in the end), but of course not with any final results yet.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"“I am Sámi, but I am not a Sámi”: Young Sámi pupils articulations of ethnicity and identity. Preliminary Findings from Interviews with Families" (<span style="font-weight: bold;">Anna-Maria Stenseth</span>), sadly, was cancelled as she was not able to attend the conference. (I must admit that it was her presentation that made me choose to attend this symposium.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Finally, there was the obvious highlight of the conference - my presentation... :-) It seemed that many hundred participants had not noticed this, as a minority of delegates had found their way to TS-201, where my talk was held. (Again, I'm writing this before the presentation, to show my amazing predictive capabilities.) I talked (in Network 14, on Multi Cultural Educational Research) on representation of diversity in Norwegian mathematics exams from the 1962 until today, based on a project by Aina Fossum and myself. There were also three more presentation in that session:</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Fiction's contribution to multicultural teacher education" (Camilla Häbler and Kari Spernes) was based on using four novels (for instance Tante Ulrikkes vei) in a course on multicultural education in Halden. Each student read one of the novels, discussed it in light of the academic content of the course and presented the books to each other. The novels give another way of meeting people and understanding and becoming aware. (It is interesting that in a survey of all textbooks in a selection of subjects in Norway, LGBT issues were most prominent in Norwegian (L1) and English (L2) textbooks - Smestad (2019?)) Students became aware that their ways of expressing diversity may contribute to othering.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Education for the Other in examination essays in teacher education." (Guðrún Jónsdóttir and Eva M. Dyrnes), using norm-critical approaches and narrative approaches. 110 reflection notes (each 2000-3000 words) is the material. Students take into account many different pupils in their notes. However, upon further analysis, diversity seems to be used to display competence. It does seem to become a vehicle for the students in the exam, and diversity is still a "problem" with the pupils, and the solution is within the student, not a critical perspective on the system.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Middle school students’ learning in programming" (Susanne Kjällander, Anna Åkerfeldt, Linda Mannila and Fredrik Heintz). It was a bit of a change to hear a talk on programming after all the diversity. They do multiple-lesson observations, following schools for three years, to study how teachers teach programming and - as the title suggests - how students learn programming. This presentation, though, were based on a limited part of the data. She showed examples from grades 4, 5 and 6, both when teachers themselves taught, and when teachers had gotten som volunteer (working as a programmer) to come in and teach. They looked for both affordances and signs of learning. (I won't summarize this here...)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Sorry if the notes from day 2 are too brief. It is hard to take in so many presentations in one day, and to try to find the core of each (as I understand it) before the next speaker follows. But if the notes are not useful to you, at least they may be useful for me when trying to remember a particular talk at the conference...</p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-6732136205614207952022-06-01T23:44:00.000-07:002022-06-01T23:44:46.455-07:00NERA 2022 Day 1<p> <span style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">After getting through the queues of the registration (why don't people start arriving at 8:30 for the registration, so that the queues are gone by the time I drop by at 9:45 :-) ) I was ready for the opening ceremony of NERA 2022.</span></p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">861 people have registered for the conference this year, which is a new record, apparently. I hope there will be a similar number in Oslo next year. Although the scenery around Oslo is not as impressive as the scenery around Reykjavik, we do have some major new additions to the must-sees, such as the new Munch museum and the new National Museum of Arts (opening some weeks from now).</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">As mentioned in my Day 0 blog entry, NERA is not one of my favorite conferences, both because of the themes (not very much on mathematics education, for instance) and because of its format (around 700 talks divided into lots of "networks") which seems to encourage jumping from room to room, with less chance of building groups with ongoing discussions. But still, the individual presentations may still be of great interest and make me aware of researchers and perspectives that I will wish to keep in touch with.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The opening ceremony included the usual mix of greetings and cultural performances, avoiding both the ridiculous and the longwinded, boring stuff that any conference-participant must surely have endured at times. (Bill Clinton's welcome speech at ICME in Tokyo (!) in 2000 is one example I remember, but there are so many more...) Here, reasonably short speeches were combined with jazz, which is always welcome...</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">As always, my notes from conferences tries to catch key points of the talks I hear. Of course, there will be misunderstandings and confusions on my part, as well as lots of omissions. If any of what I write is of interest, the obvious next step is to check the original writings of the presenter in question.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The first keynote address at the conference w<span style="color: #191919;">as "Education, togetherness and robust community in precarious times", given by sociologist </span><span style="color: #191919; font-weight: bold;">Unn-Doris K. Bæck</span><span style="color: #191919;">. ("Precarious times" is the keyword of the conference, as always a sufficiently unclear theme is needed for everyone to fit in. Although I'm not, of course, claiming that our times are not precarious - as any time.) Bæck has been especially interested in what she called "spacial" dimensions - how geographical contexts lead to inequality, as well as gender, ethnicity, socio-economic factors and so on. She started with the question how social integration can be maintained, and stressed the importance of the concept "community" (or "fellesskap", "gemenskap"), and the fact that the education system can of course contribute to community. The building of a national school system was a part of creating a strong nation state, and the multiculturalism of Northern Norway was unhelpful in that respect. The Norwegianisation process, with boarding schools, banning of languages and so on, tried to homogenize the population. Later, education was seen as "the great equalizer". Today, education in Norway is still supposed to create a "shared frame of reference" and to prepare people for taking part in the community. </span></p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;">On the other hand, schools of course also contributes to exclusion. It is well-known that there are regional differences at all levels in Norway. (In the talks, she did not mention if these analyses were using socio-economic background as a control variable.) She went on to discuss an interview study in which students discussed their reflections on educational plans and on their experiences, presented in Bæck (2019). Among other factors, many students in rural settings had to move to go to upper secondary school, having to get to know new people while being away from their previous support network. As they also commuted home, reducing the opportunities to have part-time work and to take part in social events at both their home and at the school contexts. </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;">(Of course, we do see relevant intersectionality issues here. It may be the children from lowest social-economic backgrounds that have most need of part-time jobs and who have to quit school to make ends meet. Queer people may of course benefit from new surroundings, but also risk being isolated and bullied in the new place. Bæck did not go into this in her talk.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;">Bæck noted that there are mechanisms (such as decentralizetion reforms or "neo-liberal" educational policies) that changed the contexts and thereby the outcomes/experiences of students. One interesting paradox is that decentralisation of power (ending earmarks for small schools) made local authorities make decisions to close local schools. (Personally, I find this reasonable.) She also mentioned how national tests and exams of course may interfere with teaching based on local context. She called on all researchers to speak out about the any dangers they might see in their research.</p><p lang="en-US" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"><span lang="en-US">After lunch (and a move from Hilton hotel to the campus), there were presentations in so-called "Network sessions". I chose two symposiums in Network 19 ("Teacher's work and teacher education").The first symposium was "</span><span lang="nb-NO">Examining the knowledge base of teacher education: An international comparison in relation to epistemic in/justice and teacher agency". There were three presentations: </span></p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; color: #191919; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Dominant knowledge and silenced ‘noise’ in teacher education in a Danish context?" (<span style="font-weight: bold;">Dion Rüsselbaek Hansen</span>): He argued for engaging with attitudes, knowledge and political issues in teacher education instead of "putting them to one side". He used examples from Denmark, for instance that politicians take inspiration from Michelin restaurants in how schools should work. It is easy to critizise such rhetoric, since students are not food materials and do not behave as such. Hansen also referred to Biesta in this regard. Also, international tests are still used a lot in the political discussions. </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">(I do agree with Hansen that it is important to take on difficult issues in teacher education. It is so easy to avoid the issues and to keep focus on what we know will be important for good education. For instance, my institution's teacher education programme has been critizised for not discussing assessment and tests enough - there has perhaps been a tendency to ignore this and instead work a lot on investigative mathematics teaching, for instance.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">He also stressed all the contradictions and challenges for teachers, for instance working on special education without seeing any children as "special", to provide security even though education is basically risky, and so on.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"An ‘Ethic of Innocence’: The Fragile Contours of Teacher Education in Canada" (<span style="font-weight: bold;">Anne M Phelan</span>): She took as a starting point the finding of unmarked graves of children in schools for indigenous children in Canada. Such schools (which had its parallells in a lot of countries). She problemitized teacher education's "love of knowledge". Knowledge is seen as good. How might teacher educators work against coloniality, for instance. Renzi's "the ethic of innocence" is a deliberate "not-knowing", not claiming that this is good. Using the word "innocence" instead of "ignorance" on purpose. She gave the example of "Lars and the Real Girl", in which Lars owns a doll that he treats as a real girl, and where townspeople treat the doll as a human being, helping Lars in the long run. She referred to several Canadian researchers who have worked in ways that can be related to "ethic of innocence". One example concerned "forgetting", another is to use pupils' biography to trouble the connection between background and identity.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">(To me, this is interesting but also deeply problematic. As teachers, we do have a responsibility to make informed choices of what is the best action to take. We can pretend not to know, but can we really be "innocent" in a concrete way without endangering the children? And while we can "forget" important information about our children, do we (in an ethical sense) have the option of actually forgetting (even if we could)? But perhaps I misunderstand - I can agree that it is important to acknowledge that there are many things we cannot know and that these things may be more important than what we do know. In that case, I think the term "choice not to know" is misleading.)</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">"Immunitas and Teacher Knowledge" (<span style="font-weight: bold;">Dion Rüsselbaek Hansen reading Matthew Clarke and Ruth Unsworth's paper</span>): The paper discussed governance of education, with increasing stress on standards for teacher competences. After terrorist attacks, schools have also been seen as part of counter-terrorism work, by promoting democratic values and so on, sometimes called "fundamental British values". For some reason, the researchers behind this paper chose the word "immunitas" to discuss such things. At the same time, the description of "best practice" is seen by the authors as "immunization" of the teachers against teachers' lack of knowledge. (In some cases, I feel that researchers are choosing to read things in the worst way possible. Also, there is nothing new in giving teachers ideas of what seems to be the best practice - in Norway, for instance, already curricula a hundred years ago had quite detailed guidelines on how to teach the different subjects. So the so-called "standardization" is not something new, and history suggests that it will not work - teachers do tend to read regulations as suggestions, as is probably also a good idea.) </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The discussant had some important questions, asking whether some of these suggestions present new straightjackets for teachers, or if they are really giving more freedom and openness for teachers.</p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p lang="nb-NO" style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The next symposium was arranged by Birgitte Lund Nielsen and myself, chaired by myself. I therefore had no time to make such notes during that symposium. It was wonderful, however. (This note is, I admit, written before the symposium.)</p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-59568211326388665472022-06-01T01:15:00.002-07:002022-06-01T01:15:20.405-07:00NERA 2022 Day 0<p>NERA is the Nordic Educational Research Association (NERA). They publish <em>Nordic Studies of Educational Research</em> and arrange an annual conference (also called NERA). The conference is mostly pedagogical/sociological, so it doesn't really fit my interests perfectly, but at times I am involved in projects which leads me to the conference. The present NERA conference, in Iceland, is my second NERA conference.</p><p>Of course, I combined the conference with a few days off work, so before the conference started I had experienced geysirs, public baths with thermal water, wonderful waterfalls, the historic Thingvellir, fascinating cliffs, the National Museum and so on, in addition to some more on-task work.</p><p>My contributions this year is to chair a symposium on Wednesday and contribute to that, in addition to having another talk on Thursday. I will try to do some blogging during the conference.<br /></p><p><br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-44600995809891247282021-08-03T23:09:00.002-07:002021-08-03T23:09:48.716-07:00Relationship between Birth Month and Mathematics Performance in Norway<p>I'm happy that the article that Annette Hessen Bjerke, Elisabeta Eriksen, André Rognes and myself have published, is online. In it, we investigate how students' mathematics score correlate with whether they are born early or late in the year. The effect of being the youngest in a class seems to last for a long time. <br /></p><p><a href="https://www.tandfonline.com/doi/full/10.1080/00313831.2021.1958371#.YQoulVhRPSE.blogger">Relationship between Birth Month and Mathematics Performance in Norway</a>: (2021). Relationship between Birth Month and Mathematics Performance in Norway. Scandinavian Journal of Educational Research. Ahead of Print.</p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-37063944005354376152021-07-18T02:21:00.003-07:002021-07-18T02:28:24.623-07:00ICME14 Day 7<p>Seven days - that's too much. Of course, it makes sense to make the most out of it when thousands of mathematics educators come from all over the world and assemble in one city once every four years, and then, also there's the added value of experiencing a new city. When instead sitting in an office at home, a whole week is a lot. Another conference I went to this year solved this by expanding the conference from one to two weeks - with shorter days (which automatically meant that when things did not interest you, you suddenly had a whole day for other work. </p><p>And still, I should not complain, as ICME is arranged in a way that means most items on the agenda is between 8.30 AM and 5 PM. People in other parts of the world have more difficult time problems. </p><p>There are some issues that need to be thought about after such a hybrid event:</p><p>- Video recorded talks work fine - but why are we all watching them at the same time? There is no real reason to include the plenary talks in the time table: they could be posted and seen at the viewers' own discretion. With a time slot at the end of the conference for interaction with plenary speakers, communication would still be taken care of. In CERME, most working groups have the rule that everybody should read everybody else's papers before the sessions. We could then have a more compact conference and more dialogue.</p><p>- Zoom meetings (with 10-30 participants) work fine. The dialogue is possible to arrange. Webinars are more challenging - the dialogue via questions in the chat is problematic, it never turns into a real discussion. </p><p>- The hybrid mode works better than expected, but it does not work well. There are far too many problems with the sound and so on.</p><p>For the future, I guess there will still be huge international (and local) conferences where you will meet people in person and start collaborations that would not be possible online only. But I think we will see a lot more short conferences that will be online only. If all talks are prerecorded and you can see all talks (and/or read papers) in advance, two or three days of 3-4 hours of actual dialogue, could be really valuable and time well spent. (I'm excited that the <a href="https://conference2.aau.at/event/45/page/40-programme-overview">MES conference this autumn</a> has chosen a format where the time table is 22PM-01AM, 6AM-9AM and 3PM-6PM (Norwegian time). The idea is that everybody should be able to attend to at least two of the three time slots. For Norway, it is possible to choose between the 22-01 or the 6-9 time slots (in addition to the perfectly acceptable 3-6PM time slot), but I do not advice to attend both the 22-01 and the 6-9 for days on end. Sleep is important.)</p><p>Oh, and I miss the social events and the excursions, of course. I have fond memories of the border between North and South Korea, the pyramids of Mexico, and then, partly as a result of the excursions and programmed social events; dinners with new and old friends. Of course, I cannot say I have any new friends after this ICME - although I certainly have a few more names and faces which will make it easier to get in touch either by email or in person in future.<br /></p><p>Enough of that. Today's first item was invited lectures, and I chose <b>Susanne Prediger: "Enhancing Language as a Catalyst for Developing Robust Understanding – A Topic-specific Research Approach"</b>. When I did <a href="https://www.fafo.no/zoo-publikasjoner/fafo-rapporter/item/pa-prove">an overview of the research on language and mathematics exam tasks a few years ago</a>, Prediger's name was everywhere, so I wanted a chance to connect a face and a voice to the words - and of course to hear of recent developments. </p><p>She talked about 12 years of projects in the research group MuM - Mathematics learning under conditions of language diversity" (as always my notes here can not possibly convey the content of the talk, but may inspire someone to look up the relevant articles). We see, all over the world, that schools fail to provide equitable access to mathematics for students with low academic language proficiency. This can be multilingual students, but also monomingual students, for instance with low socioeconomic background. This is mainly concerned with conceptual understanding, which has to do with rich relationships between concepts. It is also important that in school, <i>academic</i> language proficiency is needed, not just everyday language, and it is important that children get opportunities to learn this. Of course, stress on language in mathematics teaching and working on different representation is important.</p><p>She discussed design principles for topic-specific design research. She gave examples from two Grade 6 boys in work on fraction, where the boys' language hinders the explication of (and development of) meaning. Academic language demand mediating between the other registers. Thus, one important point is to have students connect language registers and representations (not just to talk and write much). She gave a series of examples on how traditional learning trajectorys for concept learning can be tweaked into developing discoursive practices. (Or rather: to combine a conceptual learning trajectory with a language learning trajectory.)</p><p>She went on to describe a large-scale (38 classes, 655 seventh graders), with language-responsive intervention, with pre-test and post-test (with control group). The language-responsive intervention group learned significantly more than the control group. The results held also (and were even higher) for students with high language proficiency. And they were largest for non-routine items. Thus, it works for all students. But there was a huge variation between classes. She pointed out that it is needed to look at teachers' enactment. (I would argue that one should also look at the norms of the classrooms.) In looking at teachers' enactment, they used the TRU Framework, slightly adapted. (See Prediger et al, in ZDM 2021.) 18 classrooms were video-recorded, and quality dimensions were rated every 5 minutes. They found high variance in Use of Contributions, Equitable Access and Discursive Demand, and these were related to the results. </p><p>It is quite amazing to see top researchers reflect on their research journeys and how their findings have spurred new questions and how these new questions build on other parts of mathematics education research and use multiple methods to get even further. She actually shared a link to her video to the participants at the end, and I think this will be really interesting to discuss with colleagues when the holiday is over.<br /></p><p><b>Final reflections</b></p><p>As often happens at week-long conferences, I run out of steam and can't keep up the blogging throughout the last day. I have already given some reflections on the form of the conference at the top of today's post. Now I will try to summarize for myself some of the key points to keep thinking of. </p><p>From TSG55, I am intrigued by the great variety in the papers. I did note Alexander Karp's repeated calls for contextualization and to get beyond doing studies of one textbook at a time in isolation, but in my opinion, sometimes the smaller pieces that will later fit in a larger puzzle, can be valuable research projects in themselves. I see this particularly in working with New Math in the Nordic countries, that there are so many detailed investigations that have to be done to better be able to compare and contrast different periods and/or different countries. Some of these detailed investigations can possibly fit into the rather insane four-page limit of ICME, but not if they are also to include enough of the context and research background and implications...</p><p>Being a novice to TSG12 (statistics), it was interesting to get a quick idea of where the research front is; what are the issues being discussed and what are seminal works that everybody refer to, and what are the key competencies that students are able to understand at different age levels. I was particularly impressed by some of the work on the youngest students in school. I now have several tools to look into and several articles to read to get a clearer understanding of this. In the same way, attending the discussion group on algorithmic thinking gave me an insight into where the problems are. They were not altogether surprising.<br /></p><p>The plenary panel on the collaboration and conflict between mathematicians and mathematics (teacher) educators was interesting, although in my context, I believe the division between mathematicians and mathematics teacher educators is rather fuzzy, and the collaboration and conflicts with other actors (pedagogues, politicians, administrators) are rather more frustrating and time consuming.</p><p>I did enjoy the HPM session, although I've taken part in quite a number of such sessions through the years. I also enjoyed getting an overview of Gert Schubring's research through his awardee lecture. In fact, there were a number of lectures like this (including Prediger's lecture today), with a prominent researcher reflecting on many years of research, which is a nice occation to see people's work as a whole instead of reading one article at a time. (However, one does wonder how many twists and turns are left out - from my own experience, as a quite non-prominent researchers - I know that I happen to take part in many research projects that does not fit neatly into an overall story. But that may be one reason why I am so non-prominent.)<br /></p><p>Perhaps I should now reflect on my own contribution to the conference. Blogging is one way for me to keep alert and to actively process what is happening. Even in physical conferences, my contribution in terms of questions and comments are not that frequent (although before I've always had one presentation, and I've also contributed to the HPM session some times, and also led a discussion group once). This time, I think I contributed with just two or three questions during the whole week. But in normal circumstances, we also discuss what we have heard during lunches and dinners, and during walks around the town and so on. I miss that. </p><p>This is the end of my ICME blogging this time. I hope to be back for ICME in 2024 (and of course for many other conferences before that). (Oh, I notice that <a href="https://www.mathunion.org/icmi/international-congress-mathematical-education-icme-15-2024">next ICME</a> will be in Sydney, Australia, from July 7th to July 14th, 2024. As I was originally planning to skip this ICME because I want to cut down on flying, it seems unlikely that I will be going to the ICME in Sydney. So perhaps I'll rather go to the 2028 one.)<br /></p><p><br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-20788115639639142082021-07-17T07:54:00.000-07:002021-07-17T07:54:28.412-07:00ICME14 Day 6<p>The sixth day started with the final session of TSG12 (on statistics education). The first talk of the day was <b>Saleha Naghmi Habibullah</b>, with the title <b>"Implementation of a course on Tidyverse in Pakistan under the ASA Educational Ambassarod Program"</b>. She discussed a course in the in Tidyverse - preparation, implementation and experiences. The workshop was based on the UN Sustainable Development Goals, using Tidyverse to study <a href="https://mics.unicef.org/">MICS</a> data, and was done in a competitive manner, with teams presenting their data analyses in the end.<br /></p><p><b>Michal Dvir and Dani Ben-Zvi: "Young learners' reasoning with informal statistical models and modeling"</b>. They define an Informal Statistical Model (ISM) as a "purposeful, not necessarily mathematical, representation of the process by which the observed variability was generated and includes both deterministic and stochastic components". Dvir went on to define "The Integrating Modeling Approach" (which I cannot summarize here, but had to do with switching between the real world and the probabilistic model). When student generated several samples, it spurred them to compare between multiple samples and make predictions. (Very interesting - I need to read their article(s) to get more detail than I did from a 20-minute talk. Here's one: Dvir, M., & Ben-Zvi, D. (2021). Informal statistical models and modeling. Mathematical Thinking and Learning. <a href="https://doi.org/10.1080/10986065.2021.1925842">https://doi.org/10.1080/10986065.2021.1925842</a>)<br /></p><p><b>Von Bing Yap: "The binomial model: coin tosses or clay pots?"</b> Two different models for binomial distribution: making n coin tosses (the number of heads has a binomial distribution) and removal of clay pots (which are high-grade and low-grade) from the kiln (<i>not</i> binomial, as there is lots of dependence). Many real populations are more like clay pots than coin tosses. We need to introduce simple random sampling. He gave examples of exam tasks where the binomial model is not correct, for instance when it is stated that "80 % of people..." and it is then assumed that the probability for each person is 0.8. Usually, people have different probabilities, he argued. <br /></p><p><b>Orlando González: "Variability modeling and data-driven decision-making using socially open-ended problems: a comparative study of high school students in Thailand, Brunei and Zambia"</b>. The starting point of the talk was a "Darts game" - students got the dart boards of two teams competing, and were asked who were the winners. Students had many (six) different ways of scoring the dart games, implicitly creating their own rules. Most created a scoring function based on all shots, while there were also some who considered only some of the shots. (It seems like an interesting task, but it is not clear to me which important part of statistics knowledge in particular is worked on. Rather, I imagine using it to have a discussion for more general purposes.)<br /></p><p>(Mara Magdalena Gea, Jocelyn D. Pallauta, Pedro Arteaga, Carmen Batanero: "Algebraization levels of statistical tables in secondary textbooks". Here, I was distracted by some other work for a moment, and can not reasonably give an idea of the contents.)<br /></p><p><b>Stine Gerster Johansen: "Data modelling with young learners as experiences of allgemeinbildung". </b>Johansen first discussed the concept allgemeinbildung and Lehrer&English's model for datamodelling with young learners. Modelling can contribute to bildung, but is demanding. Here, she discussed work with a Danish 3rd grade class (ages 9-10), 4 sessions, 90 minutes each. She gave examples of how children were discussing parents' quarreling, and the potential for bildung, including discussing what the use of this statistics work could be for other children.<br /></p><p><b>The next item on the agenda was invited lectures, and I went for Reidar Mosvold: "Trends, Emphases, and Potential Shifts in Research on Discussion in Mathematics Teaching"</b>. His talk was based on a review of the literature. He discussed the concept of discussion, stressing that it needs a subject ("a question of common concern") and that it concerns reaching a decision or exchange ideas (based on the OED definition and on Dillon (1994)), in contrast to idle talk. He also discussed the concept "teaching", leaning, among others, on "work of teaching" (Ball & Forzani, 2009), where core components can be described as problems (Lambert, 2001), predicaments (Cohen, 2011) and tasks (Ball, Thames, & Phelps, 2008). He discussed the problem of having systematic searches for "discussion" (which after all is a quite usual word), and the rest of the review issues. He ended up with a total of 72 studies; empirical articles on discussion and mathematics. <br /></p><p>Some of the results he mentioned in his talk was that the studies varied in focus, surprisingly few define what they mean by discussion, and a majority were small scale studies. The problems of studies for instance were about teachers' or students' actions, experiences, learning, demands. Key issues were orchestration (more than half), talk moves, norms, demands... For instance, only two or three articles had any significant discussion of norms. (This is surprising to me, as norms seem to be so central these days. I have more than three articles on norms on the reading list for a course I'm teaching, but obviously they do not all fill the criteria of Mosvold's search.) He also found that there was a surprising variety of literature refernced. Of course, Lampert (1990), Yackel/Cobb, Ball and Stein/Grover/Henningsen, were referenced by many (but only 5-10 references to each, which is surprising). Also, surprisingly few referenced studies on discussion outside of mathematics education. </p><p>One of his takeaways from the review, was that there should be more investigations on what might be involved in establishing a classroom climate for discussion. (Personally, I use Makar/Bakker/Ben-Zvi (2015) with my students. It's title is "Scaffolding norms of argumentation‑based inquiry in a primary<br />mathematics classroom" and would not be included in Mosvold's survey, as the word argumentation is used, instead of discussion. However, it is an overlap between norms of argumentation and norms of discussion, I would think.) In the discussion, he was asked about other terms such as "discourse", and he argued that it was necessary to limit the number of articles and at the same time "discussion" is an often used word. I asked my question ("I believe that the literature on argumentation, norms of argumentation and so on, would partly also be about discussions without actually using that word. Any comments on that?"), but Mosvold actually already answered that before the question was posted (one of the problems of sending questions in the chat without the possibility of withdrawing it...)</p><p>The final part of the sixth day was the final part of the TSG55 (The history of the teaching and the learning of mathematics). </p><p><b>Sian E. Zelbo: "Building an American mathematical community from the ground up: Artemas Martin and the Mathematical Visitor"</b>. This talk is on Artemas Martin (1835-1918) from the US and his journal "Mathematical Visitor", which also included contributions from leading mathematicians of the time. Zelbo stressed that the aims were different than the Journal of Mathematics, to which it has been described as simply a precursor. The aim was to reach young people, and also teachers and administrators contributed.<br /></p><p></p><p><b>Elisabete Zardo Búrigo: "The discarding of the rule of three in the 1960s: changes in elementary education in France and Brazil"</b>. The rule of three was discarded in the elementary school in the late 1960s, but was later reinstated. The rule of three was taught both for use in life and for use on entrance exams to post-elementary schools. However, as compulsory schooling was expanded, entrance exams were abolished and "New Math" targeted the rule of three as "too mechanical", rule of three was removed about 1970, in both countries. In France, a functional approach replaced the rule of three, while in Brazil, the study of proportions were delayed until later grades. The rule of three was reintroduced in France in 1985 (and was still there in many places from 1995), while in Brazil, it was mentioned in the 1997-8 plans, but from 2017 it was explicitly discouraged. <br /></p><p></p><p><b>Yana Shvartsberg: "Mathematics education for young women during progressive era: historical overview"</b>. Her period was 1890-1920 and her geographical focus was the US. High school curricula were differentiated, according to the kind of industry/position the students were planning to go to. Mathematics became an elective topic for many students. Shvartsberg's research is looking at how this influenced women. There was a belief that women did not need the same education as boys, but at the same time, and many high schools for girls did not offer the same courses as high schools for boys, and more boys than girls selected mathematics courses. However, some educators argued that the same opportunities should be available for women. <br /></p><p></p><p><b>Alexei Volkov and Viktor Freiman: "David Eugene Smith (1860-1944) and his work on mathematics education"</b>. Here's yet another talk on the US, but Smith also had international consequences, of course, being one of the founders of ICMI. This talk focused on his early didactical works. Of course, I will not try to summarize his life and works. In the talk, the connections and reactions to different European theorists (for instance Busse, Pestalozzi, Gruber, Tanck, Knilling...), were pointed out.<br /></p><p><b>Alexander Karp: "College entrance exams in mathematics in Russia before the second world war: development, role, objectives"</b>. He stressed the importance of exams, also in terms of dictating an unofficial curriculum and thereby influencing how the subject is taught in schools. He gave rich examples of how the entrance exams were regarded through contemporary sources. Critics argued that the entrance exams should just include mathematics that is actually included in the secondary curriculum and not "extremely artificial techniques". In the discussion, it was mentioned that this situation, of entrance exams taking priority over the actual curriculum of lower school levels.</p><p>That concludes the 6th day of the ICME. One day to go.</p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-10151564443358468022021-07-17T04:40:00.001-07:002021-07-17T04:40:57.549-07:00A small, free course in quantitative methods for teacher students<p>Last autumn, I was in charge of the quantitative part of a course in theory of science and research methods for teacher education students (MGVM4100) at OsloMet - Oslo Metropolitan University. Because of the COVID-19 pandemic, all lectures were turned into digital format, and I made a series of smaller videos instead of a few long ones. The videos were published on YouTube. But only today (half a year later) have I had the time to provide all the videos with subtitles. That means that the videos should make sense for people no matter what language they prefer (via YouTube's automatic translation) - although the text in the slides used are mostly in Norwegian. <br /></p><p>The students are supposed to read Peter M. Nardi's book "Doing Survey Research", 4th edition. That is a very good book, in my opinion, but the examples there are not from education (for instance science education). My videos are based on teaching the course a couple of times before, and my aim has been to give enough background in quantitative methods for the students to relate to quantitative methods in their work as teachers as well as in their work on previous research when doing their master thesis. Moreover, I hope they will have a foundation that will make it reasonable easy to study further if they want to use quantitative methods in their own research in their master thesis. As far as I have been able, I have used examples from different school subjects, and also created my own examples based on real data. By showing how things can be done in SPSS, I also hope to demystify that, so that students dare to use SPSS if they need to. Still, the course is not a SPSS course per se.<br /></p><p><br /></p><p></p><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;"><ul style="text-align: left;"><li><a href="https://youtu.be/AfeMYmihs28" target="_blank">Introduction: 0 0 Kvantitativ metode: Innledning</a></li></ul></div><p></p><h4 style="text-align: left;">Uke 1</h4><ul style="text-align: left;"><li>Introduction first week: <a href="https://youtu.be/HJvtUGMotHU" target="_blank">1 0 Kvantitativ metode: Innledning uke 42</a> </li><li>Central concepts: <a href="https://youtu.be/SonI77u7QIQ" target="_blank">1 1 Kvantitativ metode: Sentrale begreper</a></li><li>Making a survey: <a href="https://youtu.be/2MiFjXQh3tQ" target="_blank">1 2 Kvantitativ metode: Å lage spørreskjema</a></li><li>Sample and research design: <a href="https://youtu.be/6nQUJPz6XQc" target="_blank">1 3 Kvantitativ metode: Utvalg og forskningsdesign</a></li><li>Descriptive statistics: <a href="https://youtu.be/4P7yZlioDYg" target="_blank">1 4 Kvantitativ metode: Deskriptiv statistikk</a></li><li>Hypothesis testing: <a href="https://youtu.be/REDGEMM4iMs" target="_blank">1 5 Kvantitativ metode: Hypotesetesting</a></li><li>Normal distribution and Z-test: <a href="https://youtu.be/dIxU_Fqlrts" target="_blank">1 6 Kvantitativ metode: Normalfordeling og Z-test</a></li><li>Example: School Emphasis on Academic Success:<span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span><span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; 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mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span><span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span><span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span><span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span><span style="color: #595959; font-family: "Gill Sans MT"; font-size: 20.0pt; language: nb-NO; mso-ascii-font-family: "Gill Sans MT"; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-color-index: 1; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: #595959; mso-style-textfill-fill-colortransforms: "lumm=65000 lumo=35000"; mso-style-textfill-fill-themecolor: text1; mso-style-textfill-type: solid;"></span> <a href="https://youtu.be/M-JEDj9aKPc" target="_blank">1 E1 Kvantitativ metode: Eksempel: Læringstrykk</a></li><li>Example: Reliability: <a href="https://youtu.be/6MmCyUAfzBA" target="_blank">1 E2 Kvantitativ metode: Eksempel reliabilitet</a></li><li>Example: Survey: <a href="https://youtu.be/AS00L1EOPwU" target="_blank">1 E3 Kvantitativ metode: Eksempel spørreskjema</a></li><li>Example: Sample: <a href="https://youtu.be/pYOyq1ZfmdY" target="_blank">1 E4 Kvantitativ metode: Eksempel på utvalg</a> </li></ul><h4 style="text-align: left;">Uke 2</h4><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;"><ul style="text-align: left;"><li>Introduction second week: <a href="https://youtu.be/6OnzyDZS2I4" target="_blank">2 0 Kvantitativ metode: Innledning uke 43</a></li><li>Bivariate analysis: <a href="https://youtu.be/ELck_1-ByCk" target="_blank">2 1 Kvantitativ metode: Bivariate sammenhenger</a></li><li>Example 1: Chi-square: <a href="https://youtu.be/R7EsWWi3RMI" target="_blank">2 E1 Kvantitativ metode: Eksempel 1: Kjikvadrat</a></li><li>Example 2: Chi-square: <a href="https://youtu.be/WHyFWHYQJkM" target="_blank">2 E2 Kvantitativ metode: Eksempel 2: Kjikvadrat</a></li><li>Compare means: <a href="https://youtu.be/I3Sudfd3ZHs" target="_blank">2 2 Kvantitativ metode: Sammenlikne gjennomsnitt</a></li><li>ANOVA: <a href="https://youtu.be/byq2ftXYNUo" target="_blank">2 3 Kvantitativ metode: ANOVA</a></li><li>Example: ANOVA: <a href="https://youtu.be/X37TC3EEf8A" target="_blank">2 E3 Kvantitativ metode: Eksempel på ANOVA</a></li></ul><h4 class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;">Uke 3<br /></h4></div><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;"><ul style="text-align: left;"><li>Introduction third week: <a href="https://youtu.be/ILdBncKPS_E" target="_blank">3 0 Kvantitativ metode: Innledning uke 44</a></li><li>Two-way ANOVA: <a href="https://youtu.be/Qrc97TkG6r0" target="_blank">3 1 Kvantitativ metode: Toveis ANOVA</a></li><li>Multiple R: <a href="https://youtu.be/Kwq5zssH7WY" target="_blank">3 2 Kvantitativ metode: Multippel R</a></li><li>Multiple regression: <a href="https://youtu.be/Apb4Ud9J4IY" target="_blank">3 3 Kvantitativ metode: Multippel regresjon</a></li><li>The last phase of a project: <a href="https://youtu.be/00wroZbqD54" target="_blank">3 4 Kvantitativ metode: Sluttfasen av et prosjekt</a></li><li>Repetition: <a href="https://youtu.be/_W3O7X5aErw" target="_blank">3 5 Kvantitativ metode: Repetisjon</a></li><li>Example: Multiple regression: <a href="https://youtu.be/ivHm7Htugqk" target="_blank">3 E1 Kvantitativ metode: Eksempel: Multippel regresjon</a></li></ul><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;">Of course, this is just a first, short course in quantitative methods. Many would have prioritized this in another way. But I still hope the videos may be of use to some. </div><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;"> </div><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;">Of course, there will also be errors in the videos. So far, my 400 students have just found one error: that is in the video about Hypothesis testing, and there is a correction in the description of the video on YouTube as well as in the subtitles. </div><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;"><br /></div><div class="title style-scope ytd-video-primary-info-renderer" style="text-align: left;">Feel free to let me know if you have had use of the videos or if you have other input. (I am thinking of making videos about effect sizes - as my videos are as of know only occupied with significance. I am also considering more info on scales, on SEM and perhaps also on the racism involved in the beginning of the history of quantitative methods.)<br /></div><h1 class="title style-scope ytd-video-primary-info-renderer"> </h1><h1 class="title style-scope ytd-video-primary-info-renderer"> </h1><h1 class="title style-scope ytd-video-primary-info-renderer"> </h1></div><p></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-1851618201491420932021-07-16T07:56:00.001-07:002021-07-16T08:05:14.008-07:00ICME14 Day 5<p>It is day 5 of ICME14. The weather here in Oslo is incredible, with temperatures close to 30C in the afternoons, so it feels almost like being in Shanghai. On the other hand, sitting alone in my office at home has a different feel to it than attending a conference in person...</p><p>The day started off with invited lectures. This is perhaps the most difficult part of attending an ICME - outstanding scholars from around the world are holding talks simultaneously, and all you have to go by are the titles (and perhaps abstracts), and your prior knowledge of their work. But even people who write wonderfully can at times have terrible presentations (I have experienced people who spend most of their talk discussing with themselves that they have prepared far too much and that there is so much of interest that they will have to skip. Good idea: focus on claiming that what you are discussing (and have time for) is interesting...) So this year I went for an outstanding scholar which I also know give good presentations: <b>Tinne Hoff Kjeldsen</b>. Her title was <b>"What Can History Do for the Teaching of Mathematical Modelling in Scientific<br />Contexts: Why and How?"</b></p><p>Kjeldsen has previously worked with how history can be used to reveal metadiscursive rules andd make them explicit objects of reflection and to provoke commognitive conflicts, and to provide a window into mathematics in the making. In this talk, she focused on how history can help in teaching modelling. Mathematical modelling has much to offer to other disciplines, on the other hand, different disciplines have different ideas of what models should be. She gave three examples: John von Neumann's model in economics, Vito Volterra's predatory-prey model and Nicolas Rashevsky's model on cell division. (I am not able to summarize what she said about these...) In the example of von Neumann, we see that the mathematician's purpose can be different from an economist's purpose, which may be to solve concrete problems in practice. In the example of Volterra, D'Ancona claimed that the model could lead to new insights even when the model could not be confirmed by data. In the example of Rashevsky, biologists questioned Rashevsky's assumptions. He investigated possible explanations, while biologists wanted the explanations based in empirical data. (The three cases are analysed further in Jessen & Kjeldsen, forthcoming.) <br /></p><p>Kjeldsen referred to Axel Gelfert (2018) on explorative modelling - providing "potential explanations of general patterns". He mentions three functions of explorative models: aiming at a starting point, proofs of principles and potential explanations. Kjeldsen shows how these functions fit with the examples she has given. Kjeldsen pointed out that there are many elements in modelling that are not explicitly captured in "modelling cycle" models for modelling (ex. Blomhøj and Jensen, 2006), such as the purpose of the modelling, the function of the model and so on. She showed that Bouman (2005)'s account of modelling could be a good supplement, although there are still issues not explicitly captured. </p><p>At the end, she discussed an example of use of the example of Raschevky with students, and how looking at the contemporary discussion of his model, improved students' own modelling competence. Moreover, history of mathematics can provide a window into mathematical modelling "in the making", and let them reflect on how scientists get ideas, which strategies they use, which choices they make and how they argue and learn, and discussions about what counts as valid arguments and what mathematical modelling can provide in scientific contexts. She also discussed the concept of "historical awareness" and how the Raschevsky project helped students develop this. <br /></p><p>I really like Kjeldsen's approach, giving in-depth discussions on how history of mathematics can provide specific awareness and knowledge, which is valuable contributions to the literature on history of mathematics in mathematics education.<br /></p><p>(One thought after listening to Kjeldsen, is that teaching of modelling is necessarily limited by the teachers' knowledge of pertinent subjects where mathematical modelling is used. This also reminds me of Trude Sundtjønn's work, where attempts to make mathematics relevant for students in vocational education, met hurdles connected to the teachers' (lack of) knowledge of the vocations in question. Too often, examples of modelling in textbooks are simplistic, perhaps because authors try not to presuppose knowledge that teachers and students do not have. A good thing with history is that both the mathematics and the science involved may be simpler than using real-world examples from today.)</p><p>The next item on the agenda was a plenary lecture: <b>Mercy Kazima: "Mathematical Work of Teaching in Multilingual Context"</b>. Kazima based the lecture on what we know about teaching and learning in a language different from the home language, and on the work on "mathematical work of teaching" (Ball, Thames & Phelps, 2008). She pointed out that although Ball et al is framing their theory in a general way, it is important to investigate in different contexts - for instance they may not fully cover the issues in multilingual classrooms. (As a matter of fact, it is rather usual that Western researchers formulate general theories based on local empirical data.) She also referred to Sorto et al (2018), including the knowledge of obstacles encountered by ELLs, knowledge of resources that ELLs draw upon in learning mathematics, and knowledge of instructional strategies that help ELLs in mathematics. (ELL means "English Language Learners", thus is based in a context where students have one home language while school is conducted in English. Hopefully, these are also relevant to learners that have no interest in learning English in their context...)<br /></p><p>She gave some context: teaching in grades 1-4 are in Chichewa or other local languages (with textbooks in Chichewa), while in grades 5-7, teaching is in English. Teachers generally know at least the two languages Chichewa and English. This differentiates Malawi from countries in which teachers only know the language of instruction and not the students' home languages.<br /></p><p>She gave some lessons from Malawian studies: <br /></p><ul style="text-align: left;"><li>She pointed out that students' meanings for mathematical terms are oftten different from the mathematical meanings, and that these are influenced by home languages.</li><li>Code switching can be used effectively to make mathematics accessible to students.</li><li>Bilingual approach where use of home language is planned and proactive can be effective in making mathematics accessible to learners.</li><li>Teacher education does not prepare teachers for the teaching in multilingual contexts.</li></ul><p>The first of these means that the teachers should know the corresponding words in home language, different meanings of these words and how home language can be used to improve understanding of the mathematical terms. Based on similar discussions of the other three lessons, she discussed four types of mathematical work of teaching related to
teaching in a multilingual context: 1)
identifying resources in home language; 2) identifying obstacles in home
language; 3) identifying obstacles in English; and 4) identifying
strategies. She then gave examples from Malawi, which I do not try to summarize here. Just one example, though: the equal sign is translated as zikhala, which literally means "will become", which is of course an unfortunate understanding of the equal sign. Teachers can choose to instead explain using the word chimodzimodzi, meaning "the same as". Such vocabulary work is part of the mathematical work of teaching.</p><p>After lunch, there was the second (of three) plenary panels: "Mathematics Education Reform Post 2020: Conversations towards Building Back Better". As it does not make sense to sit looking at a computer for days on end, I decided to skip this one. </p><p>The final item on the day's agenda was Topic Study Groups. I returned to TSG12 (on statistics):</p><p><b>Gail Burrill: "Margin or error: connecting chance to plausible".</b> Burrill talked about ways of teaching margins of errors and confidence intervals. (My notes below will probably mostly be useful for myself as a way to remember some of her points... ) Both teachers and researchers have problems interpreting margin of errors and confidence intervals. To see the mean as a balance point helps students look at deviation from the mean. Using simulations helps students discuss what is the probablilty of getting particular outcomes when drawing a sample of a certain sizes. They learn the difference between sample size and numbers of samples. But what happens when we are supposed to say something about the population using our sample? </p><p>Task: draw a sample of 30 M&Ms, to estimate the true proportion of blue M&Ms in the bag. Handing out M&M bags with different, but known, proportions of blue M&Ms. After a while, students go on to simulating. Then we can ask them: who have bags where 8 blue M&M would be plausible? A range of numbers are given, and this gives a starting point for what a margin of sampling error might be. Back to M&Ms: all bags now have 40 % blue M&Ms, they set a margin of error, and it turns out that (often) at least one of the groups do not have 40 % within their margin of error. So students learn that the margin of error is not giving an absolute bound.</p><p>I didn't get manage to note all the rich ideas, but I noted the use of StatKey as useful software to sample distributions. In addition she used TI Inspire (from Texas Instruments) and applets from <a href="https://education.ti.com/en/building-concepts/activities/statistics">Building Concepts Statistics and Probability</a>. (I did get a little lost in thought, as I tried to think how I can use some of this in teaching quantitative methods to my 400-500 students this fall.)<br /></p><p><b>Cindy Alejandra Martínez-Castro, Lucía Zapata-Cardona & Gloria Lynn Jones: "Critical citizenship in statistics teacher education".</b> Zapata-Cardona discussed the concepts of "critical citizenship" and "statistical investigations". She argued that investigations of crises in society would contribute to critical citizenship. (It is interesting to see the difference of the first two presentations today - the first one very detailed both on how the teaching was done and on the resulting mathematical understandings of students, the other one being less detailed on the statistical content, and more occupied with the general critical citizenship potentially promoted by such work.) In the discussion, a resource for working on critical citizenship was shared: <a href="http://iase-web.org/islp/pcs/">http://iase-web.org/islp/pcs/</a>. <br /></p><p><b>Adam Molnar and Shiteng Yang: "Mathematics ability and other factors associated with success in introductory statistics". </b>This talk was about a diagnostic test to study factors associated with success in a course in university. A methodological point of interest is that the students who answered the test, tended to do better than those who did not (that is; people who don't like mathematics, tend not to like to do a test either). The main finding was that "College GPA" (which seems to be the grade point average from college in the US) is highly corellated to the results in the introductory statistics course, and that adding the diagnostic test results, didn't really improve the model by a lot.</p><p>(By the way, a feature of online conferences, is that the discussions about one talk continues in the chat after the time for live discussion is up and during the following talks. I'm not sure if this should really be seen as a feature or as a bug - it does of course tend to take the attention away from the following paper, while adding flexibility.)<br /></p><p><b>Karoline Smucker and Azita Manouchehri: "Elementary students' responses to quantitative data". </b>Her research was on five third grade students (8-9 years of age), and she wanted to look at students prior to explicit instruction. The activity was collecting "wingspans" from fellow students. During graph creation, they were focused on creating the "right" graph and to follow rules. They had trouble graphing the quantitative data, but eventually, they decided to create groups, which meant that they made something close to histograms. There were several interesting findings connected to these "histograms", one of which was that some students were careful to include all the original data in the diagram. In their "analysis", the shapes of the diagrams, the center and the variability (what other third grade classes would look like) were included. Thus, we see that third grade students can get quite far in working on quantitative data without explicit instruction. </p><p>In the discussion it was pointed out that these third grade students did better than teacher students do in research: <a href="http://dx.doi.org/10.1080/00207390902759584">http://dx.doi.org/10.1080/00207390902759584</a>. It is highly interesting why this is. Maybe, it was pointed out, there was one student who had a good idea that the class ran with. On the other hand, as Dani Ben-Zvi argued, teacher students have gone through years of schooling where they learn that bar charts is the way to present data. Also, it was discussed what would have happened if the students had access to TinkerPlots instead of paper and pencils. <br /></p><p><br /></p><p><br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-24924517511653950922021-07-15T02:52:00.002-07:002021-07-15T02:52:46.610-07:00ICME14 Day 4<p>On the fourth day of the conference, apart from Thematic Afternoon in the morning (Norwegian time), and China Art and Culture Performance in the afternoon (which I will not blog about), the only ingredient was a plenary lecture by <b>Robyn Jorgensen</b> titled <b>"Equity in Mathematics: What Does It mean? What Might It Look like?"</b> (As I am currently doing some work myself on diversity in mathematics education, including race, gender, sexuality, class, functionality, culture, geography and ethnicity, I'm especially interested in this topic.)</p><p>She started the talk with addressing the myth of ability. We know that people's lack of success is often not connected to innate qualities. There is a difference between equality and equity - we do not want to treat everybody equally; people need to be treated differently. During the thirty years she has been working on equity (and even before that), there has been many concepts that have been in play: ability, giftedness, talent, ability grouping, access, sucsess, achievement and participation, recognition of difference, ethnomathematics (D'Ambrosio, Gerdes...), socially critical theories, habitus, Bernstein, power, hegemony, ideology, groups (race, gender, class, language...), "post" theories, identity, race theory, linguistic diversity, culturally responsive pedagogy... She stressed the importance of the organization and conferences "Mathematics Education and Society" (which I will attend for the first time this year - it will be interesting).<br /></p><p>She claimed that the field has done a lot of work, but has not made a lot of impact in the 50 years. Therefore she wanted to point to problematic practices. For instance, the programme Direct Instruction in Remote Indigenous contexts has had questionable impact, and seems not to be culturally responsive. We need to approach a strength-based pedagogy, instead of identifying gaps and trying to fill them with scripted instruction. Different people have different world-views, and these need to be taken into account. </p><p>She then went on to talk about a project called "<a href="https://serc.edu.au/remote-numeracy/">Remote Numeracy Project</a>", a project researching successful learning (instead of "what do teachers/leaders... do wrong?"). Approximately 40 schools were included, all over Australia. (This seems like a very good approach, different to most research, as seen in Smestad/Gillespie 2019...) Some schools that were doing well in mathematics, "protested" that they did not focus on mathematics at all - they focussed on well-being, safety, getting the students to come to school and to have healthy food... The schools seemed to have ways of enabling their teachers, who were often novice teachers. The researchers therefore looked at the envisioned practices, the enabled practices and the enacted practices. (Which is an interesting variant on Goodlad.) She discussed each of these in some detail, which I'll not try to summarize here. She stressed the importance of "embedding mathematics" - both in the contexts and cultures and in the brain. Also, mathematics is as much about language as it is about mathematical concepts, and for instance using the home language in mathematics was important. Also, being explicit about what was expected and how lessons were structured and so on. </p><p>Although Jorgensen gave a complex picture that I have in no way been able to convey here, much of it was what is today generally considered good mathematics teaching, but with some extra elements concerning the vision and leadership of the school and the extra focus on the home language and culture. But there is surely more detail to be found in the articles, reports and case studies produced in the project.<br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-23720858306071972112021-07-14T07:58:00.000-07:002021-07-14T07:58:31.385-07:00ICME14 Day 3<p>Day 3: The first item on the agenda is the lectures of awardees. The somewhat strange idea is that highly competent people have awarded five people/organizations for their lifelong, important contributions to the field, and they are then giving one-hour lectures <i>in parallell</i>. Needless to say, it is difficult to choose: should you go to learn more about someone you are not that familiar with, or should you go for the awardee that is closest to your own field (and who you therefore know). </p><p>I decided to go for <b>Gert Schubring</b>. I have heard him a number of times before (always impressive in the depth of his knowledge) and read many of his writings, of course. (As usual, I will only note down here some short points that caught my attention, and as always with the caveat that I may misunderstand. Always take what I write only as a pointer to be able to go to the source.) Schubring has of course been important to the field of history of mathematics education, both in his own research, in heading conferences, editing the journal on history of mathematics education and so on.</p><p>As Schubring received the Hans Freudenthal, it was fitting that he talked about his relation with Freudenthal throughout the years. Schubring himself started studying mathematics, and did not hear anything about the history of mathematics or its teaching. He defended his PhD in 1977, on the genetic principle ("Das genetische Prinsip in der Mathematik-Didaktik"). He praised the context at Bielefeld university, with interdisciplinary research and with theorists such as Niklas Luhmann. (It is interesting how such elements are (seen as) important to the path into history of mathematics education.) Thus, he was introduced to history of science, as a complex system, a sort of social history of science.</p><p>He discussed several of his early research projects, including the problems of obtaining and reading sources in those times. (Of course, the problems are still much the same, even though you may be lucky to find some sources online these days.) In 1979, he was invited to the first congress on social history of mathematics, meeting Henk Bos, Herbert Mehrtens and Ivo Schneider (among others). Gradually he developed two research strands: analysis of the development of mathematicsal concepts (the development of negative numbers as a major focus) and The history of the teaching and learning of mathematics. The second one is quite complex, as it has to do with for instance the education system, the labour market, the sciences, and so on. He did work on teacher education of mathematics teachers, on history of teaching mathematics and also the sciences in general. </p><p>He stressed the importance of comparative research. Much research on history of mathematics education (and history of education in general) is considering one nation state at a time, where one may easily take the national characteristics for granted instead of researching them. (I am paraphrasing quite heavily here.) Schubring worked on both Germany and Italy, and in his talk, he detailed some of the important differences in mathematical histories which influenced mathematics education heavily - and the functions of mathematics teaching. He also argued against the traditional practice of history of mathematics teaching as a history of the curriculum, syllabus, textbooks etc. Schubring stresses the analysis of texts combined with contextual analyses. An example is the analysis of changes within various editions of one textbook, finding corresponding changes in other textbooks, and connecting these changes to changes in the context (syllabus, debates, ...)</p><p>In the last part of his part, he talked about the development of the field into a broad international area of research. Elements to this development was the Topic Study Group (from 2004) with proceedings in Paedagogica Historica, the International Journal for the History of Mathematics Education (2006-16), a bi-annual series of conferences (proposed by Kristin Bjarnadottir - the next one in Mainz in 2022) and The Handbook on the History of Mathematics Education (2014) and two Springer series. <br /></p><p>In the end, he discussed colonial/decolonial perspectives, which I find interesting.</p><p>After this, I went to the part of the ICME where affiliated organizations are presented. As usual, I went for <b>HPM</b> (International Study Group on the Relations between the History and Pedagogy of Mathematics) - a group I've been a part of for about 20 years now. This was a two-hour session with short presentations by leading researchers in the field, followed by a discussion session. </p><p>After a short welcome by Snezana Lawrence, Ysette Weiss gave a presentation of history of HPM, its relation to ICMI and some of its most recent activities. It was interesting to note that at the meeting in 1976, history's relation to the New Math reform was a topic of discussion. </p><p>Secondly, David Guillemette provided some theoretical perspectives of HPM. His starting point was two papers: Barbin, Guillemette, Tzanakis (2019) and Clark, Kjeldsen, Schorcht, Tzanakis and Wang (2016). Both call for more empirical research to study effectiveness, but also deeper understanding of theoretical issues. The field is in search of theoretical and conceptual frameworks. Fried et al (2016) points out that the nature of mathematics itself must be problematized, as must our view of history and the nature of matematics education.</p><p>Guillemette then went on to discuss five perspectives: the genetic perspective, the humanist perspective, the hermeneutic perspective, the discursive and pragmatic perspective; and the dialogical and ethical perspective. The humanist perspective he connected to Fried (2001, 2007), with mathematics contributing to students growing into "whole human beings". The hermeneutic perspective is connected to Jahnke (1994, 2014), the discursive and pragmatic to Sfard (2008) and Kjeldsen. Finally, the dialogical and ethical perspective he collected to Radford (2012, 2013, 2018). He also included his own work on "otherness", "empathy", "nonviolence" (Guillemette, 2018). He stressed the importance to situate ourself, both epistemologically and methodolically. </p><p>After a (rare) coffee break, Alexander Karp talked about the history of mathematics education. Obvioiusly, this overlapped somewhat with his introduction to the TSG55 and with Gert Schubring's talk this morning (see above). He mentioned two important surveys: Karp/Schubring: "Handbook on the History of Mathematics Education" and Karp/Furinghetti: "History of Mathematics Teaching and Learning". (The second one being freely available.) He stressed that history of mathematics education is a part of general social history, and that everything can be a source (not just textbooks...) He mentioned three examples of important questions in history of mathematics education: Why was commercial arithmetic so popular in 15-16 century? Why was not discrete mathematics represented in Soviet curriculum? Why was mathematics curriculum in Western Europe reorganized so strongly since 1960? (As examples of questions showing that history of mathematics education is part of social history.)<br /></p><p>Lastly, Desiree van den Bogaart-Agterberg talked about history of mathematics in the classroom. She started by referring to Jankvist's division between history of mathematics as a tool or as a goal. She also referred to the seminal 2000 ICME Study, discussing different ways of including history of mathematics in classrooms. More practically, she referred to a forthcoming article by herself, where she identifies four formats: specks, stamps, snippets and stories - focusing on the size (but also the function) of the HM inclusion. (It is interesting with these different ways of analysing how HM is included in mathematics textbooks. However, it would be interesting as well to study how these different ways are actually used in the literature - which are the most fertile ones?) Bogaart-Agterberg then went on to discuss the use of original sources, which is also an important way of including HM. (Here, it is also tempting to mention my own article on different ways of including HM, which for instance also includes plays, which seem to be missing in some other "lists".) In the end, she mentioned the TRIUMPHS project, which has important resources, and also the importance of HM in mathematics education.<br /></p><p>Thereafter, there was a discussion. Granted, the webinar format (in Zoom) is not very interactive. (As a participant, I don't even have an idea of the number of participants.) But there were some questions from the auditorium in Shanghai, which were discussed by the participants. Also, I added a question: "Could I challenge Desiree and David on the connections between their two talks: Are there perspectives discussed by David that are particularly useful in practical classroom implementation? Are there elements of what Desiree discussed that have particularly interesting theoretical connections?" David argued that we have to be careful in how we introduce history, because we can introduce history in a way that shows how mathematics is evolving, and that mathematicians in the past were also struggling and arguing. Desiree argued, in the chat, that the genetic principle and the humanistic principles are good places to start when thinking of including history of mathematics into teaching. (Sorry for suddenly using first names - it is a bad habit that happens sometimes when I mention people I know.) </p><p>(Personally, I'm not too happy with using the genetic principle, as it can be viewed quite narrowly. In this talk, I have to point out, Guillemette was quite explicit in defining it broadly. Still, it is connected to the simplistic idea that pupils' learning recapitulates humankinds' evolution of mathematics, and this idea is, to me, fundamentally problematic. Pupils are so different and there is no <i>one</i> "humankinds' evolution of mathematics" - the evolution of mathematics have been different in different cultures and different localities. A very broad concept of genetic principle - something like "there are often some resemblance between a particular students' learning of mathematics and the development of mathematical concept in some culture - becomes so general that I'm not sure it is helpful. I therefore prefer concepts such as "epistemological obstacle" (which Guillemette also mentioned).)<br /></p><p>After lunch, there was the the second session of TSG55. </p><p><b>Antonio M. Oller-Marcén: "The beginning of modern mathematics in Spanish primary education: a look through textbooks and curriculum."</b> Although Spain did not attend in Royaumont, New Math was fully implemented in the 1970 LGE (General Law of Education), after being introduced in the offical syllabus for ages 10-14 in 1967. But already in 1965, there were elements of modern mathematics in primary school. There has not been done much research on New Math in Spain, and Oller-Marcén's objective is to analyze the 1963 and 1965 sullaby and analyze two editions of textbooks. In 1965 syllabus, the idea of set is included in grade 1, the communitative and associative properties of addition and multiplication are explicitly included in grades 2 and 3. In the textbooks, one-to-one-correspondence was included, and numbers are defined in terms of sets. Moreover, sets and symbols from set theory are far more frequent than the syllabus would suggest. The set theories ideas were absent from the other parts of the textbooks, which is different from textbooks in the 1970s. <br /></p><p>Dirk De Bock asked whether there was an explanation for why New Math arrived so early in textbooks in Spain - it is a bit strange given that the Spanish were not prominent in later meetings. We do not have an explanation for this currently. (This talk is actually a very good example that such careful analysis of textbooks is important, also in giving rise to further questions that can be analysed further.)<br /></p><p>Johan Prytz asked whether textbooks had to be approved by the government, and Oller-Marcén clarified that they did. So these textbooks were approved.<br /></p><p><b>María Santágueda-Villanueva and Bernardo Gómez-Alfonso: "Missing arithmetic methods: On the rules for the mixing of analogous things". </b>The kind of problem looked at is "In what ratio must a grocer mix two varieties of tea costing Rs. 15 and Rs. 20 per kg respectively, so as to get a mixture worth Rs. 16.50 per kg?" They looked at different methods given for solving such problems in different textbooks.<br /></p><p><b>Pilar Olivares-Carrillo and Dolores Carrillo-Gallego: "The calculation in the first commercialized Decroly's games". </b>The games in question were made for special education students, but later published for both "anormal" and "normal" children. They included sensory games, calculation games and reading games. There were three purposes: motivate, learn, and to assess the learning. Olivares-Carrillo described the numerical games (impossible to summarize here). <br /></p><p></p><p><b>Yoshihisa Tanaka, Eiji Sato and Nobuaki Tanaka: "Mathematical activities focusing on Japanese elementary arithmetic and secondary mathematics textbooks in the early 1940s". </b>The activities were analysed using a method by Simada (1997); "A model of mathematical activity" (which seems like a model for modelling). He showed a number of problems and how they can be solved. The highlighted processes were to see similar cases and to generalize solutions.<br /></p><p><b>Zhang Hong: "Development history and course setting of mathematics department in early universities in Sichuan province in modern times (1896-1937)". </b>This was actually the first of the presentations done from the auditorium in Shanghai. After some initial feedback problems, the sound was clear, and Hong presented the history of the Sichuan University (and others) - which again is very difficult to summarize here. However, one main point was how mathematics education went from being inspired by Japanese ME to being inspired by European and US ME. <br /><br /><b>Li Wei Jun: "A probe into compiling mathematics textbooks by Christian missionaries in Late Qing Dynasty". </b>The missionaries introduced Western ideas by compiling and translating textbooks. One example of such a missionary was Calvin Wilson Mateer, born 1836, who established schools in China and wrote several textbooks. Another example was John Fryer, who translated a lot of mathematics works with Chinese colleagues. A third example was Alexander Wylie. The translated textbooks introduced new methods, symbols and mathematical concepts to China.</p><p>Alexander Karp at the end stressed the importance of clarifying what is the original contribution, by describing what was already known and what the research has added. (While I of course agree to that in a general sense, I believe that in the format of ICME, with four-page papers and seven-minute talks, there is a lot that have to be left out, both in terms of theoretical assumptions, previous research, methodological considerations and implications for later research. These short talks can at best be an inspiration to look at the researchers' work in more detail when it is eventually published (or by getting in touch with the researcher).<br /></p><p>The final part of Day 3 was discussion groups and workshops. I chose the <b>Discussion Group 1: "Computational and Algorithmic Thinking, Programming and Coding in the School Mathematics Curriculum: Sharing Ideas and Implications for Practice".</b> Again, I got tired of sitting at the keyboard, and changed format:<br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1DxVQhyk0kmQFQSY_js6jRMgju_bebVXXwAOprJwkQKzILoJ9M1WZRj-q-DheuxiKgaFgfUqcuvf-57BHdNTeeht2I2OECaTRdq5VursTlTXjQu1x_ucUQSVMG8qf6yujhmLaWmQIu8ym/s1872/Jobb+-+page+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1872" data-original-width="1404" height="475" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1DxVQhyk0kmQFQSY_js6jRMgju_bebVXXwAOprJwkQKzILoJ9M1WZRj-q-DheuxiKgaFgfUqcuvf-57BHdNTeeht2I2OECaTRdq5VursTlTXjQu1x_ucUQSVMG8qf6yujhmLaWmQIu8ym/w318-h475/Jobb+-+page+2.png" width="318" /></a></div><br /><p></p><p> Some resources:</p><ul style="text-align: left;"><li><a href="https://protect-au.mimecast.com/s/ROPNCE8knvs3QQzMYsNEImT?domain=mi.sanu.ac.rs" target="_blank">DG1 website</a> <br /></li><li><a href="https://onlinelibrary.wiley.com/toc/14679639/2021/43/S1">https://onlinelibrary.wiley.com/toc/14679639/2021/43/S1</a> </li><li><a href="https://iase-web.org/islp/pcs/">https://iase-web.org/islp/pcs/</a></li><li><a href="https://hal.archives-ouvertes.fr/hal-02423497/document">https://hal.archives-ouvertes.fr/hal-02423497/document</a><br /> </li></ul><p>Bonus photo: me at ICME14: </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMVHw63ea9p7kIB1o06bHaEp6N0RcRNb4VcdL4wqLOjZx6cAkWyDdiGYbSxXrHvPS5LlX-PevNPEObPDjNqZ4r8rkgPjC3aMK0eaRyMHbDMXke_4FLTOGLEu6nezPUzppCEjdb3pdL1DmH/s2048/IMG_5840.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMVHw63ea9p7kIB1o06bHaEp6N0RcRNb4VcdL4wqLOjZx6cAkWyDdiGYbSxXrHvPS5LlX-PevNPEObPDjNqZ4r8rkgPjC3aMK0eaRyMHbDMXke_4FLTOGLEu6nezPUzppCEjdb3pdL1DmH/s320/IMG_5840.jpg" width="320" /></a></div><br /><p><br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-18819348132353129592021-07-13T07:58:00.006-07:002021-07-13T07:59:51.156-07:00ICME14 Day 2 Part 2<p>After lunch on the 2nd day, I attended TSG12, the topic study group on teaching and learning statistics. This is not because I am doing research on it (I'm not), but rather because it would be nice to learn more about this, and some of the talks seemed interesting. </p><p>The first talk was by <b>Lonneke Boels</b>, presenting "<b>Designing embodied tasks in statistics education for grade 10-12</b>". Her research question was "How can literature—on misinterpreting histograms and on embodiment—in combination with results from an eye-tracking study inform embodied task design in statistics education?" Many students confuse bar graphs and histograms, and many think one of the axes should be time. Boels discussed an experiment with eye tracking, asking students to find the means from different diagrams. Eye tracking made it very obvious that the students were interpreting the histograms as if they were bar charts, and also that the students carefully read the text and the labels on the axes). The results were depressing. Thereafter, they did some experiments where students had to make boxplots themselves by dragging each data point to its correct position. They also had tasks where students had to find the balancing point (which is the mean) of the boxplots. (In a way, it doesn't make sense to summarize in this way, because the devil is of course in the details in such tasks. For instance, the software gave feedback when the balancing point was set correctly. Such details will influence the learning in some way. However, the point of my blog is obviously not to replace the article but to give a small taste which may lead you to look at the article...) Working with students merging and splitting classes seems to be a useful strategy.</p><p>(Being a novice in this area, I notice words such as CODAP, iNZigt, Tinkerplots and VUStat, only some of which I understand. I should investigate...)</p><p>In the discussion, it was asked what an "embodied task" is - is that dependent on the task or on your perspective when looking at the task? That is a good question, and I would perhaps answer that no mathematics task can be "non-embodied", but of course the way and degree to which a task is embodied, is an important consideration in task design. (This reminds me of a recent fad: to call everything "semiotic". I have read about "semiotic representations", but never of "non-semiotic representations". But of course, I am not saying that looking at embodied learning is an unimportant "fad".)<br /></p><p>The next talk was <b>Hanan Innabi, "Teaching statistics and sustainable learning".</b> Her starting point was variation theory. The idea is that (based on Marton) students work on variations lead to sustainable learning. She shortly presented a research project with Marton, and mentioned the special thing that variation is an inherent thing in statistics, because uncertainty is an important part of statistics. (So in a sense, it is hard to teach statistics without much variation - although textbooks of course have statistics tasks where the data are given and variation is lost.) At the end she mentioned a couple of examples of how to work on this using variation.<br /></p><p>The third talk of the TSG session, was <b>Daniel Frischemeier's "Reading and interpreting distributions of numerical data in primary school"</b>. After giving a background of previous research, he presented his project of supporting primary school students to read the data and read between the data (not including the third level, reading beyond the data), with 19 primary school students (age 10-11), with use of real data, TinkerPlots and collaboration. The teaching was based on the PPDAC cycle (another FLA that I didn't know before). The conclusion was that ... and here the time was up, sadly. I suppose an article will be available at some point in the future. (In the discussion afterwards - in the chat - the distinction between stacked dotplots (such as in TinkerPlots) and messy dotplots (such as in Minitools) was stressed. Children find stacked dotplots more difficult to understand than messy dotplots.)<br /></p><p>Then followed <b>Carlos Monteiro and Karen Francois' "Statistical literacy as central competence to critically understand big data"</b>. Monteiro pointed out that students need to understand that they are also producers of big data, understand the power issues and to be able to analyse them critically. This is not an issue of how to handle the data technically, but to understand the origin of the data. </p><p>(At this point, a small misunderstanding regarding time was sorted out, and Frischemeier got five more minutes to finish his presentation. The posttests were, not surprisingly, better than the pretests.)<br /></p><p>The final presentation of the first session of TSG12 was <b>Florian Berens, Kelly Findley and Sebastian Hobert's "Students beliefs about statistics and their influence on the students' attitudes towards statistics in introductory courses"</b>. In their experience, students have negative attitudes towards statistics when entering university, even though they have not had statistics before. They measured attitudes by the six-dimensional SATS-36 instrument, and created their own instrument for measuring the beliefs about statistics (descriptive perspective, investigative perspective, confirmation perspective and a rules-based perspective). They did find some correlations between attitudes and beliefs of statistics. In particular rules-based beliefs are connected to negative attitudes, while investigative beliefs are connected to positive attitudes. This raises interesting questions for teaching of statistics - probably also on lower levels than university.<br /></p><p>Then the day ended with the Plenary panel on <b>"Actors for Math Teacher Education: Joint Actions versus Conflicts"</b>. To be honest, I have attended very few good panel discussions in my life, mostly because they often end up not being panel discussions but instead turn into a series of barely related short lectures. Thus, I decided to take some time off from my blog-writing duties to just follow the plenary panel away from my keyboard. Instead, I watched it with pencil in hand, making some notes as it went along. Here it is:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ7qC8rZkwiZHOQVZS2gfdfIP_jwxCGX7jXb9T2j2crvrLaWPA8hqBGhRZ27Hdp3fCsEShqCASxGGwRRwg8vW03qxsg5YDsE3Grqk7OZBCLbFQIujjtsOfELsZj6vJdA52zxjm3vCLOZXY/s907/Jobb+-+page+1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="907" data-original-width="680" height="526" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ7qC8rZkwiZHOQVZS2gfdfIP_jwxCGX7jXb9T2j2crvrLaWPA8hqBGhRZ27Hdp3fCsEShqCASxGGwRRwg8vW03qxsg5YDsE3Grqk7OZBCLbFQIujjtsOfELsZj6vJdA52zxjm3vCLOZXY/w394-h526/Jobb+-+page+1.png" width="394" /></a></div><br /><p></p><p>That was the second day - and the first full day - of the ICME14. Five more days to go.<br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-11703816081001506192021-07-13T03:13:00.003-07:002021-07-13T03:13:42.914-07:00ICME14 Day 2 Part 1<p>The first item on the agenda was the first session of the Topic Study Groups. While usually going to the "The role of history of mathematics in mathematics education" TSG, but this year I joined TSG55, which is in the history of mathematics education. (The names seem alike, but the difference should be obvious...)<br /></p><p>Alexander Karp welcomed us and mentioned that the field of history of mathematics education is getting recognition, for instance there are two series on history of mathematics education on Springer now, and Gert Schubring of course received a prestigious prize yesterday. The format of this TSG is talks of at most 10 minutes, followed by five minutes of discussion. <br /></p><p><b>Vasily Busev and Alexander Karp: "Pafnuty Chebyshev and the mathematics education of his time". </b>Chebysev was of course a major Russian mathematician who was also interested in mathematics education. Vasily Busev will publish a complete publication of Chebyshev's educational notes, which will give an interesting view of mathematics education at Chebyshev's time. For instance, he reviewed textbooks, and he was arguing that if a mathematical result can't be proved rigorously within the capabilities of the students, then students should be told so directly, instead of giving an almost rigorous proof.</p><p><b>Dirk De Bock: "Frédérique Papy-Lenger, the mother of modern mathematics in Belgium". </b>De Bock has written an impressive book on New Math in Belgium, and this is especially interesting to me as I am doing some work on New Math in the Nordic countries currently. The talk is based on Lenger's collected writings and the reactions to these. Lenger vas part of the CIEAEM community. Already in the mid-50s, she thought that the focus on relations and structures in modern research mathematics could be a model for mathematics in school. She married the mathematician Papy in 1960, and became an important researcher in New Math in Belgium. Among her most important work was "Les Enfants et la Mathematique". She also worked with the Comprehensive School Mathematics Project in the US. Later, she worked on mathematics education for disabled children. Her work was important, but she did not get the recognition that she deserved. One possible reason was that she focused on the development, not on theory (which is an usual way to get overlooked). Also, she was overshadowed by her husband. Moreover, she was so connected to New Math that when New Math lost its position, so did many of its proponents.<br /></p><p><b>Ildar Safuanov: "The history of mathematics education of Tartar nation". </b>Safuanov discussed the history from medieval times until the 20th century. (As I know little about this in advance, it is difficult to give even a short summary of its history.)</p><p><b>Maria José Madrid, Carmen León-Mantero, Alexander Maz-Machado: "Mathematics and mathematics education in the 18th century Spanish journal "Semanario de Salamanca". </b>The study of journals is an interesting supplement to studies of textbooks and other books. The journal in question was published twice a week, including both scientific articles and news from the city. For instance, it included mathematical problems, book reviews and job offers. Thus, we see how the study of journals can give an insight into the history of mathematics (including the role of mathematics in society). </p><p><b>Maja Cindric: "Arithmetic textbooks in Croatia in the premodern period". </b>Cindric talked about the history of Croatia and how it relates to neighbouring countries. In the period in question (in the 18th century), schools were run by Jesuits, not compulsory. There was no compulsory secular education until 1774. She looked at two arithmetics textbooks, from 1758 (by Mihajl Šilobold) and 1766 (by Mate Zoričić). Cindric gave details on differences between these books (which I am unable to detail here). As far as I understood, Šilobold's book was more focused on what we would call "problem solving". Cindric stressed how misconceptions in school can often be collected to terminology, and that the etymology of terminology can be traced by studying textbooks.</p><p><b>Karolina Karpińska: "Gnomonics in mathematics secondary school education on the territories of Poland in the 17th-20th century".</b> Gnomonics is the theory behind the constriction of sundials. (I cannot think of sundials without thinking of my wonderful colleague Peter Ransom, who has often talked on sundials in lectures and outside of lectures.) She discussed the basic theory behind sundials, combining astronomy and mathematics. She discussed how gnomonics was taught in Poland - including different kinds of sundials and of course also whether they were treated generally (regardless of geometrical position). From 1812, gnomonics was introduced as an obligatory part of mathematics in 5th grade (in physics and chemistry). Later, it was part of geography lessons.</p><p><b>Shinnosuke Narita, Naomichi Makinae, Kei Kataoka: "Approach of an early 1940s Japanese secondary mathematics textbook to teaching the fundamental theorem of calculus". </b>Calculus was introduced into textbooks in the 1940s, in 10th grade (4th grade in junior high). Narita detailed how the textbook introduced calculus, showing that students were expected to develop their knowledge through solving problems, before giving definitions later in the textbook. (Which seems reasonable - but it must be stressed that the role of the teacher is difficult to establish, so how free students actually were to develop their calculus.)<br /><b></b></p><p>This was a demanding start of a day - two hours of presentations and discussions without breaks, on a wide variety of topics. In addition, Zoom is for some reason more demanding than physical meetings to me, particularly for my neck - it has something to do with having to sit in front of the camera in a particular way. Nonetheless, these first two hours of TSG55 showed clearly the variety and the tensions in history on mathematics education - sometimes very focused on the mathematics, sometimes on the institutions or on the discussions on mathematics in society and so on. Some researchers are very detailed on one little piece of a large puzzle, without including the context very much, while others give a lot of attention to context and less to detail. Of course this is also a matter of the limits imposed: four-page papers and 7 or 10-minute presentations. This is not conductive to including both detail and context sufficiently. But even disregarding these limits, I believe still researchers have different leanings, and that is fine. For instance: detailed accounts of a series of textbooks can be very valuable to another researcher, who can build upon them further. <br /><b></b></p><p>The second item of the day was the plenary lecture by <b>Lingyuan Gu: "45 Years: An Experiment on Mathmeatics Teaching Reform." </b>This detailed mathematics reforms near Shanghai from 1977 to 2022. Giving just the highlights will seem like a string of buzzwords: from 1977 to 1992, the stress was on "affection, progression, attempt and feedback", from 1992 to 2007, the stress was on "comprehension" and "experiencing variation", while from 2007 to 2022, the focus was on "inquiry and creativity". This may seem silly, as everyone in mathematics education - from 1977 till today - will surely agree that affection, progression, attempt, feedback, comprehension, variation, inquiry and creativity are important factors. So the point is obviously not to jump from one to another of these (or to pretend - as Norwegian directorate of education tends to do - that every new curriculum includes some new focus that has never been thought about before). Instead, the point is to do a careful analysis of the current situation and try to establish what part of this mix of "buzzwords" (which are, after all, important concepts) need to be prioritized for a period of time going forward. Such an approach, with careful research, testing and so on, has been followed in Shanghai. They combined macro studies with quantitative means, with micro studies with observations of low-scoring students and their interactions with their teachers.</p><p>I did enjoy his example of introducing parallell lines. Some teachers will just give a definition and many students will be able to resite it when asked. Other teachers give students an example ("are like two tracks of train"), thereafter opening up to a discussion about what else is or is not parallell lines ("Are they still parallel lines if the train makes a turn?". In this process, both what is and what is not (but are "nearly") will be included in that process. That's a nice close-up of some of the principles at work in a classroom.</p><p>It was interesting to see that even though inquiry had been an underlying principle for most of the time, results were not good by 2007. Therefore, inquiry was one of the main foci after 2007. That is perhaps not very surprising, I think - it is hard to break the habits of minds in classrooms, where everyone expects that no matter what the teacher says, the teacher still has the a script of what is supposed to be thought in a classroom. (Yes, I mean "thought", not just "taught"...) Results now are promising. </p><p>One of the interesting points of going to international conferences is seeing that the problems people struggle with on one continent is often the same as on other continents, even though contexts are very different. Gu's talk was impressive while the main concepts were familiar. Lastly, he stressed the importance of video in educating teachers, to make available the analysis of classroom occurences in detail - with the teachers or teacher students. (Of course, then we start getting into the Lesson Study field, which I remember hearing a lot about at the 2000 ICME and which has been worked on a lot also in Norway, but has still not - as far as I know - become a normal part of education for all teacher students.) I also liked that Gu stressed that the point of this line of research is not to write "the perfect paper" but to improve teaching, which means that there will always be mistakes and wrong turns, but still, in the long run, improvement.<br /></p><p>Already, this blog post is getting rather long, so I think I will end it here, and have the rest of the day in a brand new blog post...<br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-2067094054009199072021-07-12T08:22:00.001-07:002021-07-12T22:29:39.817-07:00ICME14 Day 1<p>The first day of ICME14 was a short one - lasting from 1:30PM to 5PM (local time in Norway). It consisted of the opening ceremony and a plenary lecture by Cédric Villani.</p><p>Needless to say, attending an opening ceremony is a bit different when you have travelled to another continent, are adjusting to a new time zone, and can congratulate yourself that you have been able to find your way around the conference area. At least you have found the room that is easiest to find: the place for the plenaries. As these often have a capacity of thousands of people, you may get the feeling of attending something important. At my first ICME, there was even an address from the US President at the time, Bill Clinton - quite surprisingly, as the conference was in Japan and had little to do with the US. (The address was on video, of course.) The sense of fulfillment in finding my office-at-home and managing to log in to the conference platform is not comparable.<br /></p><p>The <b>opening ceremony</b> followed the usual format, including the mentioning of individuals and organizations that have been important in getting the conference in place, information about the city (Shanghai) and the conference, well-chosen words on the importance of mathematics and mathematics education as well as the awarding of prizes. To me, who is neither a native English or Mandarin speaker, having the English sound overlaid with simultaneous translation into Mandarin, made it rather difficult to follow what was said Some of the addresses were subtitled, however, and I did, for instance, notice that more than 120 countries are represented in ICME this year. Towards the end of the opening ceremony, more than 15000 viewers were logged on, which is surely a new record (and also probably was a reason for some transmission interruptions).</p><p>Two of the ICME awards, the Felix Klein award and the Hans Freudenthal award, are biannual, thus this year there was both the 2017 and 2019 awards to celebrate. The Emma Castelnuovo award is just awarded every four year. For more on the awards, see <a href="https://www.mathunion.org/icmi/awards/icmi-awards">ICMI website</a>. The winners were: </p><p>2017 Felix Klein award: Deborah Ball</p><p>2017 Hans Freudenthal award: Terezinha Nunes</p><p>2019 Felix Klein award: Tommy Dreyfus</p><p>2019 Hans Freudenthal award: Gert Schubring</p><p>2020 Emma Castelnuovo award: NCTM (USA's National Council for Teachers of Mathematics)</p><p>These are all well known names for the mathematics education community. Personally, I've perhaps had most to do with the work of Gert Schubring, who has been so important in strengthening history of mathematics education as a research field. Of course, Deborah Ball are famous for the Mathematical Knowledge of Teaching oval, but has since moved on to other (and more fertile) grounds - on the moment-to-moment dilemmas teachers face in classrooms. Therezina Nunes and Tommy Dreyfus are important names that I have not personally been as occupied with. Nunes is of course co-author of "Street Mathematics", and have later worked further on mathematical thinking. Tommy Dreyfus has for instance worked on AIC, abstration in context. NCTM, of course, has had huge influence in the US, as well as internationally, through their journals, guidelines for teaching and many other publications.<br /></p><p>It is nice to hear how these important figures in mathematics education are pointing out the importance of teamwork - new findings in mathematics education are rarely the product of an individual mind.<br /></p><p>The opening ceremony finished about 30 minutes late, and then we moved almost straight on to the first plenary lecture of ICME14: <b>Cédric Villani on "Mathematics in the Society"</b> (which is a promising title, given that I will be going to the Mathematics Education and Society conference for the first time this autumn). Villani is a mathematician (Fields medalist!) and a member of the French parliament. He started by saying that he went to a television show to talk about the essence of mathematics, and he brought three objects: Euclid's Elements, a gömböc and a smartphone. In this way he brought forward how mathematics is about reasoning, but at the other hand has wonderful applications. Mathematics is both beautiful and useful. Also, mathematicians bring progress by introducing new ideas and looking at things from another viewpoint. Also, he talked about the connection between new problems and new concepts: new problems lead us to find new concepts to solve them, but new concepts give rise to new problems.<br /></p><p>In mathematics, you are not obliged to believe the teacher: you can find errors in what the teacher is saying, and if the teacher is a good one, the teacher will be convinced of the reasoning if you are right. This does not work in the same way in other sciences. He claimed that the three most important parts of mathematics work is tenacity, imagination and rigour (with rigour third).</p><p>He talked, inspiringly, about the work he has done after his Fields medal, including a book about what it is to be a mathematician, a comic book and a photo book. Towards the end of his talk, he discussed his work as a politician (in the Scientific Parliamentary Office - I wonder how many other countries have them...) and on AI. He ended by saying how important it is to remember the past and learn from the past, which is a welcome message.<br /></p><p>Of course, this was (as usual) just some of the points that I liked and managed to write down, it is not meant to be a full discussion of the lecture, which was, by the way, entertaining and lively, although it was a bit unusual, as it took the form of a autobiography more than a classical plenary lecture.<br /></p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-87995420601330204422021-07-07T07:39:00.003-07:002021-07-07T07:39:30.576-07:00ICME14 Day 0<p><span style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt;">What will be my sixth consecutive ICME conference, will start in a few days. ICMEs are the huge, crowded conferences in math education that are wonderful at giving an overview of math ed research - and at making you feel lost. I have many good memories from previous conferences, but had decided not to take part this time, as the train ride from Oslo to Shanghai and back was a bit too far. (I want to reduce my carbon footprint, thus flights were not tempting.) However, COVID-19 made it a hybrid conference, so I changed my mind.</span></p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">The conference experience depends a lot on your choice of TSG. As my research interests have moved to history of math ed lately, I will abandon my normal favorite (history of math in ed) and join the TSG55 instead. As a supplement, I will take part in the group on statistics teaching, I think.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"><br /></p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">Strangely, the Chinese hosts have made the time table very Europe-friendly, so I won't have to changed my daily rythm, but still, attending ICME from the comfort of my office-at-home will feel weird. But in a good way, I hope.</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">I have attended a few conference during COVID (NORMA and ISCHE, to name two), but haven't blogged much. I hope to go back to blogging daily during ICME. See you on Monday!</p><p style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;"> </p>Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-44770278978240685052019-06-28T10:40:00.000-07:002019-06-28T10:40:01.319-07:00IEA IRC 2019: Day 3<div style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">
The final day of the IEA IRC 2019 started with Anna Rosling Rönnlund's talk "For a fact-based worldview". Of course, I had been looking forward to this, her book "Factfulness" (with Hans Rosling and Ola Rosling) is a wonderful eye-opener. She started by telling how the three of them have spent many years trying to make numbers more understandable and easily available. Then she went on with our results on the "test" (from Factculness). Actually, 43 % of this conference got it better than chimpanzees on these questions, while in representative surveys, 10 % do better than chimps. In average, we got 4.2 points out of 12, which is 0.2 points better than an average chimp. (In representative surveys, the average is 2. Personally, I think having read Factfulness helps a lot...)</div>
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People tend to answer systematically wrong - they think the situation is worse than it is. (Moreover, if I remenber the book correctly, people tend to answer "correctly" based on the situation fifty years ago. People should not learn about the world by heart and then think that they don't have to update their worldview.) Looking out of the window, we don't see the slow global trends. In newspapers, we see diseases and catastrophes, the extraordinary events.</div>
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She spent some time on Dollar Street - where differences in living standard are illustrated by lots of photos from 350 homes around the world (so far). She illustrated how families in different countries are amazingly similar when they live on the same income level, while diversity in each country is amazing. For instance, as the income doubles from 2 to 4 dollars a day, people tend to prioritize the same regardless of continent: stove instead of fire, toilet instead of no toilet, mattress instead of sleeping on the floor and so on.</div>
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Towards the end, she gave a few of the rules of thumb of critical thinking that is also in the book. I highly recommend reading the book...</div>
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Finally, she showed some animations using TIMSS data. They were interesting, but as hung up we are on confidence intervals, it would be good to have a way of marking that to avoid making a point of differences that are not actually differences or trends that are not trends. But she stressed that the tool should be seen as a hypothesis-generating tool, to notice things that seem interesting. Of course, we need to include the statistical models to investigate the hypotheses.</div>
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After this, the penultimate session I went to was "TIMSS, PIRLS and ICILS: Utilizing in-depth analysis of large-scale assessment data to improve teaching". The first talk here was Franck Salles: "Clarifying TIMSS Advanced mathematics 2015 results: A didactical approach through levels of mathematics knowledge operation". The ministry of education in France does detailed analysis of task performance to inform inspectors and teacher educators. In TIMSS Advanced, there was a 1 SD drop in French students' performance from 1995 to 2015. There had been large maths curriculum changes in that period. Of the three cognitive domains, France does relatively badly in "applying". He showed how two different tasks concerning "applying" was very different, illustrating the need of a better math task analysis model. One part of the model he proposed is tasks assessing mathematical knowledge as an object or assessing it as a tool. As an object, there are items asking for a computation or asking to show the understanding of a concept. As a tool, there are items asking for a direct application of knowledge, there are items asking for application with adaptation, and there are items asking for applivation "with intermediary" - students have to add something not in the task already. This classification wass done by a national expert panel. He showed how the classification of a task of course has to depend on the prior knowledge of students. The classification then had to be done based on the national curriculum, making it a national classification which would have been different in other countries.</div>
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Secondly in that session, I heard Jeppe Bundsgaard talk on "Differential item functioning as a pedagogical tool". He used ICILS 2013 (where Denmark didn't quite meet the sampling criteria), and the Rasch model. Differential Item Functioning (DIF) refers, of course, to the phenomenon that an item works differently for two different groups of students. Bundsgaard wanted to see if grouping items with DIF can identify challenging areas in the study. He studied DIFs for the countries together and the DIFs of Norway, Denmark and Germany separately. The short conclusion is that Norwegian and Danish students are better at items related to computer literacy, but worse at items related to information literacy.</div>
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Thirdly, Olesya Gladushyna and Rolf Strietholt talked on "Nerds or polymaths? Performance profiles at the end of primary education". Latent profile analysis (LPA) was used to try to see whether students (of 4th grade) have qualitatively distinct profiles (even though not differing quantitatively) (I'm not sure whether what I'm writing her makes sense.) They did find different models with different profiles, for instance the three-profile model included one profile where students are better in math than in reading and science, one profile where students are worse in math than in reading and science, and one profile where students are equally good in all three. (The designation of those who are better in math as "nerds" is troublesome, as another result was that children with a home language other than the language of test tend to belong to that group, which does probably rather mean that they are not so good in reading and science, not that they are outstanding in math.)</div>
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Finally in this session, Nani Teig and others had the title "I know I can, but do I have the time? The role of teachers' self-efficacy and perceived time constraints in implementing cognitive-activation strategies". She used a framework for instructional quality with three basic dimensions: classroom management, supportive climate and cognitive activation. The focus here is cognitive activation strategies (CAS). This can be divided into general CAS ("asking challenging questions") and CAS specific to science - inquiry-based CAS; learn about how to do science. We know that teachers have a lack of confidence in enacting CAS, and that CAS can be demanding and time-consuming. This study focused on the interplay between teacher self-efficacy and teacher perceived time constraints, using Norwegian TIMSS 2015 data. They found that general and inquiry-based CAS are distinct but correlated constructs. They found significant correllation between self-efficacy and both kinds of CAS, but only significant correlation between teacher perceived time constraints and inquiry-based CAS (which makes sense, I guess), but this is significant only on grade 9 when analysed for each grade (at that point, of course, the number of students got smaller).</div>
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The final session (the closing ceremony excluded) was on "Socioeconomic background and student achievement: TIMSS and PIRLS". Here, there were three talks, the first of which was Rune Muller Kristensen: "Deconstruction of the negative social heritage? A search for variables confounding the simple relation between socioeconomic status and student achievement". They used Danish TIMSS data from 2015. ESCS (Economic, Social and Cultural Status) cancelled out other effects in that study, including school and class size. The point of this project was to understand these relationships better. However, no matter how many relevant variables were thrown into the model, not much of the variation between ESCS and performance was explained. (The discussant at the end asked whether the variations of the ESCS and the potential confounding variables are too small in Denmark, and whether different results could be found in other countries with more variance.)</div>
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<a href="https://www.blogger.com/blogger.g?blogID=2210497064207378386" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>Secondly, Andrés Strello and others had the title "Effects of early tracking on performance and inequalities in achievement: Combined evidence from PIRLS, TIMSS and PISA". They studied all available cycles of the three studies and 75 countries, sorted according to when (or if) they started tracking, looking at dispersion, social inequality and performance level. They did 45 pairs of comparisons, and then used a meta-analytical approach (Card 2011). The meta-analysis showed that tracking has a significant effect on inequality as dispersion, on social inequality and on performance level. (It seemed, however, that tracking has a negative effect on reading performance as measured in PISA.) Also, the earlier tracking takes place, the larger the effects. (In the discussion afterwards, and in the presentation itself, it was pointed out that tracking is a complex phenomenon with different implementations between and even within countries. Still, that makes it perhaps more surprising that significant findings were found.)</div>
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Finally, the last talk of the conference was Vasilik Pitsia and others: "High achievement in mathematics and science: A multilevel analysis of TIMSS 2015 data for Ireland" (using 4th grade data). They divided the students into high level achievers (TIMSS Advanced International Benchmark) and non-high achievers. As usual, confidence correlates highly with being high-achievers (probably meaning partly that high-achievers notice that they are high-achievers). Also, home resources are important. However, the chance of being high-achiever decreases when pupils think they get engaging teaching. (This was the results for mathematics, I didn't note down the results for science.) (Of course, it is tempting to find an explanation for the last result. May high-achievers be less easily engaged, because level of mathematics in the teaching is too low?)</div>
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Then, there was only the closing ceremony left. We were invited to join the IEA IRC in United Arab Emirates in 2021. For me, there are many reasons to avoid a conference in UAE. Of course it is difficult to get to the UAE from Northern Europe in a climate-friendly way and it is unpleasant to have a conference in high temperatures. A lot more importantly, at least for me, is the human rights situation, where for instance gays are arrested and in theory get a death sentence. There are examples of gay men being raped in UAE only to be investigated for illegal gay sex. So I will leave the 2021 IRC for more thick-skinned people than myself, and instead aim for the 2023 IRC.</div>
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(I have nothing personally against the UAE representative advertising for the beauty of UAE and the happiness of its people, but it would have been fair to mention that certain subgroups of the population are not happy at all.)</div>
Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-69123368052358592252019-06-28T10:21:00.000-07:002019-06-28T10:21:07.486-07:00IEA IRC 2019: Day 2<div style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">
The morning plenary at day 2 of the IEA IRC was Aaron Benavot's talk "How can IEA make a difference in measuring and monitoring learning in the 2030 agenda for sustainable development?" He is a former director of UNESCO's Global Education Monitoring (GEM) Report. GEM Reports, published yearly, previously monitored progress on the 6 Education for All Goals, now they monitor educational targets in the 2030 Agenda for Sustainable Development. </div>
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He discussed the history behind the merging of several processes into the Sustainable Development Framework with 17 goals, 169 targets, 230 indicators. He stressed how this is the most aspirational and comprehensive international education agenda ever. This comprehensive agenda reinvigorate earlier debates on how to measure and monitor learning. The countires are supposed to have voluntary national reviews, and there will be an elaborate indicator framework with different indicators and measures - at least one global indicator per target, a number of thematic indicators (globally comparable indicators), regional indicators and national indicators. For instance, the target 4.1 talkes about relevant and effective learning outcomes, while the global indicator narrows this down to reading and mathematics. However, the measuring on the global indicators is to be done in close cooperation with each state.</div>
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He stressed how different ways of measuring gives very different results. For instance, the traditional way of measuring literacy is by census data, where often the leader of the household is asked who in the household is literate. Now, a few countries are moving towards testing - for instance asking people to read a sentence for the census taker. This reduces the literacy estimates. He gave examples of how IEA might help in developing ways of measuring.</div>
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He also discussed how the international assessments are increasingly supplemented by regional and national assessments; more than 150 countries have performed national assessments since 2000.</div>
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There was a discussion after the talk about the country-led nature of the reviews and measuring. A researcher from South Africa stressed the importance of each country being able to determine what are the education priorities in their context. If South Africa cannot itself decide but has to adopt measures from western "North" countries, that would not be suited to the local context.</div>
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Again, I decided to skip the panel (which was on PIRLS and not part of my research interest presently).</div>
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After lunch, there was a Norwegian symposium on the TIMSS. There were three presentations from the University of Oslo research team (CEMO: Centre for Educational Measurement). The first was Rolf Vegar Olsen and Sigrid Blömeke: "Predicting change in mathematics achievement in Norway over time". He started out by pointing out the dramatic fall in Norwegian TIMSS results from 1995 to 2003 (comparable to twice the difference between 8th and 9th grade in 2015), followed by an increase from 2015.</div>
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The method used for this paper was the Oaxaca-Blinder Decomposition, a method for studying the mean differences between two groups - basically looking at both the constant and the slope of the regression lines for the two groups. (Actually, they used a threefold OBD, with "endowments", "coefficients" and "interaction" terms.) They wanted to include predictors which had changed in the period used. However, fairly little of the change in score could be explained by the included predictors. (A lot of possible predictors had to be excluded because the questions were different in 2003 and 2015.)</div>
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The second talk was Trude Nilsen, Julius Björnsson and Rolf Vegar Olsen: "Has equity changed in Norway over the last decades?" First, they discussed the definition of equity: it could be defined as lack of achievement differences between schools, a small SES effect on achievement or as a low proportion of pupils getting low scores. They looked at all cycles of TIMSS and PISA. While many measures had changed over time, "Number of books at home" had kept stable in both TIMSS and PISA. The findings was that the total variance had decreased over time (which may, however, be because the proportion of high performing students have decreased), while on the school level there has been different developments in the different studies. The variance explained by SES has increased over time. The main problem however is the lack of stability in the SES measures. A solution could be to combine ILSA (international large-scale assessments) with register data (but that could be controversial for privacy reasons).</div>
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The third talk of this symposium was Hege Kaarstein and Trude Nilsen: "Twenty years of science motivation mirrored through TIMSS: Examples of Norway". Their goal was to look at the development of science motivation. Methodically, every TIMSS study was compared to the 1995, in addition comparisons between 4th and 8th grade and between girls and boys in all cycles, was planned. They studied intrinsic motivation, self-concept and extrinsic motivation (the third one not measured in 4th grade). It is an important point that it must be checked (within the means available) that questions are understood similarly over time, but the details of the scalar measurement invariance (MI) I am not able to repeat. The results of the study were mixed, but the motivation seem to have increased. Self-concept has the highest correlation with performance, but the self-concept did not increase significantly in 8th grade. (However, Norwegian students already reported very high self-concept from the beginning.)</div>
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Jan-Eric Gustafsson was the discussant, who picked up on the difficulties of looking at change over time, and asked how the ILSAs could be improved to make it easier to study change over time. He also pointed out that many of the independent variables used here are prone to large errors in measurement (as they are self-reported by students), which can lead to regression coeffisients being underestimated. He also pointed out that the PISA scales vary in reliability from year to year, while TIMSS scales have higher reliability. He also noted that "number of books at home" is shown to be working differently in different countries, so it may also be assumed to be working differently over time in one country. (It was actually pointed out in the plenary on Friday that the proportion of pupils with many books in the home, is decreasing in rich countries.) Also, he criticised cutting out lots of the comparisons based on the MIs, as the MI analyses has so high power that they detect substantially insignificant differences. (A very interesting point although he himself admitted that including these comparisons may make the paper impossible to publish.)</div>
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He also provided a fun example of problems of measuring: when a new grade scale was introduced in Sweden, confusion followed as teachers did not use the new scale consistently. This lead to increased variance in the grades (and less correlation with the underlying competence of pupils, I guess), leading to a decrease in the SES effect. (Of course, if grades are more randomly assigned, all correlations between grades and other variables will decrease.)</div>
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Then, there was the last session of the second day. The first talk was Samo Varsik: "Differences in students' and teachers' characteristics between high and low performing classes in Slovakia". He used PIRLS 2016 4th grade data from the Slovak republic. The methodological approach is based on similar research done in Czech Republic. He first showed how SES has a huge impact in Slovakia. But he also looked for differences in teaching methods between high- and low-performing classes, but found very few significant correllations. The only two significant differences were connected to high-performing classes being tested more often and being more often asked to summarize the main ideas. The second part of his work was regression models, showing for instance that students' confidence n reading is, not so surprisingly, correllated with performance, also when controlling for SES, gender and so on. However, he did not find significant results regarding teachers' characteristics. (Other than this, I did not manage to write down so much of his results.) At the end, he noted that an important limitation of his method is the "Modern Teaching Methods" variable, based on a few self-reported questions.</div>
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The second paper of the session was supposed to be Bieke De Fraine et al: "Reading comprehension growth from PIRLS Grade 4 to Grade 6", but this was cancelled.</div>
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The third paper was Marie Wiberg and Ewa Rolfsman: "Nordic students' achievement and school effectiveness in TIMSS 2015". (Nordic = Sweden & Norway). They looked at student variables (sex, native father (NF) and number of books) and school variables (student behaviour, urban school location, school climate (teacher, student, parents), aggregated SES, aggregated NF, general resources at school and resources in mathematics) and used linear regression. They included the concept of "effective schools" based on them having better results than expected based on background data. Students's background was important everywhere. In Norway, school location and school climate was significant, while in Sweden only school climate was significant. For future research, the possibility to connect to register data will make possible other analyses.</div>
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The final paper of the day was André Rognes' talk on "Birth month and mathematics performance relationships in Norway", written with Annette Hessen Bjerke, Elisabeta Eriksen and myself. Of course, I knew the paper quite well in advance: the main point is that the Relative Age Effect (RAE) is statistically significant in all content and cognitive domains of mathematics in 4th, 5th and 8th grade. There were no statistically significant RAE in 9th grade. We also tested whether there was a significant difference in RAE between 4th and 5th grade and between 8th and 9th grade - there was not.</div>
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We did get a question about whether we had looked at SES in our research. We had not. It is unlikely that birth month can be predicted by SES (and a colleague actually pointed out that he had checked it. Whether the RAE is larger in some SES groups than others, is another question that it would be interesting to investigate. (Although I fear the Norwegian data alone would not provide enough power to find out. Even with more than 4000 students in each cohort, the number of students per month gets quite small if dividing into different SES groups.)</div>
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That was the end of the second day. For me, this day was more aligned with my research interests than the first, so I was happy about it.</div>
Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-58367931616493395332019-06-28T04:50:00.000-07:002019-06-28T10:21:23.817-07:00IEA IRC 2019: Day 1<div style="-webkit-text-size-adjust: auto; font-family: Calibri; font-size: 11pt; margin: 0in;">
My first IEA IRC (the 8th IEA International Research Conference) took place in Aarhus University in June 2019. As this was my second conference in this venue, I was not surprised to find that the conference was actually in Copenhagen... However, unlike the ESU five years ago, this conference started with a song (allsang): "Svantes lykkelige dag" and "I Danmark er jeg født".</div>
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The first keynote was Christian Christrup Kjeldsen: "Global attitudes and perceptions of social justice among youth: When no (in)differences make the difference". He reminded us of the concept of fuzzy set, where elements can be a member of a set to different degrees. Becoming a subject is part of life, and (I suppose) people cannot always be put 100% into the fixed boxes. (He argued based on his reading of Bourdieu, but of course I'm not able to summarize that.) Part of his talk was on what is significant: the differences between (the continuum of) statistical significance, (the continuum of) substantial issues in a moral philosophical approach and (the continuum of) effect sizes. He argued for the concept of "substantian significance": differences in capabilities supporting a life that the individual has reason to value. When talking about effect size, he connected this to Hattie, who he claimed could serve as an inspiration. At the end, he talked about a case in which he merged results from different studies in a fuzzy way while trying to keep enough noise to not understate the variance. Again, hard to summarize.</div>
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I think there was food for thought there. Take gender as an example. Of course, we are well aware that gender is more complex than the oldfashioned binary "man"/"woman" concept. However, there are important differences between "men" and "women" in most fields of research, when treated as a binary concept. So which underlying concepts can be found that can explain the differences, without having to keep using a binary concept that we know is too simplistic?</div>
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As happens at conferences, I had to spend the next slot doing some last-week edits to our presentation with my colleague. For the after-lunch slot I chose to take part in the "Open source publishing with IEA" panel. Of course, if we are to do more analyses of international studies, we need to know as much as possible about the publishing possibilities.</div>
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The journal "Large-scale Assessments in Education" has had its fifth anniersary, and is now a Springer open source journal, giving it more visibility. Also, there is the IEA Research for Education Book Series, often 80-150 pages long. Calls for proposals are published biannually. (The authors actually get 25 000 euro for each book.) Unsolicited applications are also considered. Only IEA studies can be used for the book series, while the journal is more forgiving. The full process from accepted proposal to finished printed book is usually about two years.</div>
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Finally, Seamus Hegarty talked about the review process for the Book Series: There is a pre-review, then review of each chapter (based on an annotated ToC, which is mandatory for proposals). The review is not double-blind - only the reviewers are anonymous.</div>
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He gave some examples of some usual editorial suggestions:</div>
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<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Do provide an argument about the significance of your work</span></li>
<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Contextualise your work</span></li>
<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Detail your methodology</span></li>
<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Be rigorous and coherent (especially difficult to obtain coherence when different teams of authors write different parts of the book</span></li>
<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Write clearly</span></li>
<li style="margin-bottom: 0px; margin-top: 0px; vertical-align: middle;"><span style="font-family: "calibri"; font-size: 11pt;">Organise your own review! It is useful to use colleagues to do a "review" before the real review.</span></li>
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Then, for the final session of the day I decided to attend the session on "TIMSS and ICCS: Students' attitudes and achievement in TIMSS, TIMSS Advanced mathematics, and ICCS". The first paper was by Laura Palmerio and Elisa Caponera: "Relationship between students' attitudes and beliefs, and achievement in advanced mathematics". The TIMSS Advanced questionnaires and tests were supplemented by a national questionnaire given to the same students, on self-efficacy and anxiety. They found that self-efficacy is highly correlated with mathematics performance, not surprisingly. This could be a sign that we should work on students' self-efficacy.</div>
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A side note: they showed that "self-efficacy was the best predictor of mathematics performance" (according to the abstract). I think this is a good example of how the language of "predictor" can be problematic, as the relationship between self-efficacy and performance is of course going in two directions - performance leads to better self-efficacy and self-efficacy leads to better performance. (In the presentation it was very clear that self-efficacy and performance are part of a circular relationship which also includes behaviour and anxiety.)</div>
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The next talk was Michaelides and others: "Meaningful clusters of eight grade students in 2015 TIMSS mathematics using motivation variables". They focused on confidence, enjoyment and value (all three scales administered in 8th grade, the two first also in 4th grade), to look at what the interactions between them are. For instance, some students report that they value math but do not enjoy it. They did this across 12 jurisdictions, in TIMSS cycles 1995-2007. The analysis was based on a two-step clustering approach. These clusters were developed per country, and then the clusters' participants' achievement and gender composition was explored. In inconsistent clusters, value did not play much of a role for achievement - self-confidence and enjoyment was more important.</div>
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The third talk in this session was Dupont et al: "The role of parents' literacy attitudes on children's reading achievement (PIRLS 2016)". They had different hypotheses on the connection between parents' reading attitudes and the outcomes (students' reading motivation and students' reading achievement). Regression analyses were done, controlling for home resources for learning. They found high correlation between parents' attitudes and students' reading achievement. (Some of the diagrams here could be useful in my teaching on quantitative methods in our master courses.) The study underline the importance of parents' literacy practices on students' reading achievement and attitudes.</div>
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The final talk of the day was Kwong and Macaskill: "The relationship between student engagement and achievement across countries within regions using latent class analysis". They looked at Asia, Europe and Latin America as three regions. First used Exploratory Factor Analysis to explore relations among the attitude indices. Thereafter LPA was used - a two level LPA model used for the Asia region. (Obviously, I can not summarize all the tables showing the results of these analyses.) Through lots of diagrams, we were shown how the three regions had different profiles, although for instance Taiwan seemed to stand out a bit from the other Asian regions included. (Sadly, complex diagrams with lots of small type do not work very well when sun is flooding the room, so it was hard to get the details.)</div>
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That ended the first day of the conference. It is a different experience than many other conferences, as I usually go to conferences where I can choose talks on topics I am very interested in. Here, I more often find myself listening to talks where the topic in itself is not that relevant to my interests, but where the methodological ideas can very well be useful for me to explore other topics. So it is a different focus.</div>
Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-54975850393643292882017-02-04T23:33:00.001-08:002017-02-10T03:41:37.268-08:00CERME 10 Day 4The first TWG session on Saturday consisted of four ten-minute presentations, followed by discussions. As I had one of the presentations, it's a bit hard to give details on them (one does get a bit too occupied with one's own presentation in such circumstances). They were:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Rodolfo Fallas-Soto: "Variational strategies on the study of the existence and uniqueness theorem for ordinary differential equations"<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Me: "Design research with history in mathematics education"<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Antonio Oller-Marcén: "Analyzing some algebraic mistakes from a XVI century Spanish text and observing their persistence among present 10th grade students"<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Katalin Gosztonyi: "Understanding didactical conceptions through their history: a comparison of Brousseau's and Varga's experimentations"<br />
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In the discussion, some of the points were:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Tradition and contextualisation are important - the traditions researchers come from are important (in the case of my design research project). It is important to be clear about the context of them (but on the other hand, it is also important for design research projects to consider and describe which context they may be relevant for).<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• There was a chicken-and-egg-discussion on what comes first in historical research - the question and/or method or the data. (Arguably, all the world is data - or; you can say that they only become data when they can be helpful in answering a question someone poses.)<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• In what way do theoretical frameworks "work"?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• What to do once epistemological obstacles are identified? Should we face or avoid them (until students are "hungry" - why feed them if they're not?).<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Design research - can it be called a "theoretical framework" (as the chairs did in their framing of question for the group discussion). (My answer would be no. A participant also said that it could rather be seen as a framework of aspects to be thought of in such projects.)<br />
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The next part of the programme was a plenary panel. The panellists were Marianna Bosch (Spain), Tommy Dreyfus (Israel), Caterina Primi (Italy) and Gerry Shiel (Ireland). The topic of the panel was "Solid findings in mathematics education: what are they and what are they good for?" Marianne Bosch was the chair. The background for the panel was EMS' series of articles on "Solid findings in mathematical education". "Solid findings" are defined as important contributions, which are trustworthy and that can be applied. The panel wanted to examine the notion of "solid finding" and consider possible utilities and weaknesses.<br />
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Tommy Dreyfus pointed out that there are not many review articles in the field of mathematics education. The European Mathematical Society (EMS) decided to help remedy this. (The articles are in the Newsletter of the EMS issues 81-94.)<br />
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One example: we know that many students "prove" a universal statement by providing examples, across many age levels and countries, including teachers. We call this "empirical proof schemes". But to be called "solid", an explanation is also needed, and here the explanations are varied. But the main criteria for being "solid" holds. Another example: concept image. Students tend to think with their personal image rather than the definition. This occurs at all levels, in many countries, for almost 40 years and across many topics of mathematics. These are often formed by prototypes. Instruction plays a (limited) role. These findings can be considered "solid".<br />
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Solidity cannot be "proved", expert opinion is crucial, and experts from several fields should be consulted.<br />
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Caterina Primi talked about how psychometrics could contribute to solid findings in mathematics education. We often measure something else than the trait we are interested in - for instance signs of anxiety, even though it is the unobservable trait anxiety we are interested in. Of course, we can create instruments to try to measure the trait based on them, and these can also be used to find differences between groups. (And so on. It is hard to see how this rather elementary discussion of psychometrics contributes much to the general discussion of solid results - unless her talk is an implicit argument that psychometrics are more important than other research approaches to get solid results - as many would of course say about their own pet approach.)<br />
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Gerry Shiel's perspective was whether outcomes of international assessments (PISA) can contribute to evidence-based decision-making. Are PISA findings solid? On the one hand, it is huge (more than 500 000 students have contributed to it). He gave an introduction to PISA and how it tries to be an evidence-based series of studies including testings. He gave an example of how Ireland's performance in TIMSS changed over time, with a significant dip in 2009. This dip has not been explained. Ireland rebounded, while other countries had a dip in 2015 when digital testing was done. Also, Ireland has an increase in the gender difference between boys and girls, which is hard to explain. PISA results are used to inform policy - and PISA surprisingly tries to impact teaching directly by publishing their speculations on what can be inferred by the data.<br />
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In the discussion (which did not work very well, because of a somewhat confusing combination of "questions" from the floor and "questions" sent electronically), it was asked "solid for whom" - implying that what is solid for researchers may not be solid for teachers (and vice versa). This is an interesting point. Gabrielle Keiser mentioned that we need some methodology for writing review papers - it is a very difficult task, and for instance quantitative analyses are not always helpful.<br />
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(But in hindsight, it is easy to see that this topic invites people to promote their own research or conception of research...)<br />
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The last part of Saturday (before the gala dinner) was the last session of the TWG. First, there was a part where participants talked about planned or ongoing projects with calls for cooperation. Then we talked about future conferences, where I presented the plans for ESU8 in July, 2018. Plans for the HPM satelite conference to the ICME conference in Shanghai 2020 were presented - it will be somewhere in Asia. Then the process of the proceedings were discussed, and finally there was discussion on the report of the conference, the result of which will of course be seen in the proceedings of the conference.<br />
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Due to travel arrangements, for me the conference ended with the gala dinner on Saturday evening (which had much Irish music and rather less talk). Thus, this is the place for summarizing the experience. This was my first CERME conference, and I realized that CERME is not really one conference, it is rather ~25 mini-conferences under one roof and with shared amenities and a few common talks. This means that it in one sense is an intimate conference in the same way as smaller conferences are. However, getting the intimate feel demands some consicous choices - not to switch groups no matter how interesting the talks going on elsewhere are, and to try to socialize with people in the group and not be tempted to only socialize with the people you already know. Then, the CERME experience is quite different than for instance ICME, which is a smorgasbord of interesting talks where you risk never running into the same people twice (even though even ICME has some working groups, of course, so I am exaggerating a bit).<br />
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Dublin was great, the LGBT guided tour was great and the atmosphere throughout was also great. I did learn some new things during the conference, of course, but most importantly, I think, it solidified my determination to try to focus more in the future. I want to spend my research time to get deeper knowledge in some areas rather than having many parallell projects with different foci. I'll see how this works out...Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-51411746380741096882017-02-04T07:37:00.001-08:002017-02-04T07:37:49.432-08:00CERME 10 Day 3Day 3 consisted solely of TWGs and an excursion. The first TWG session was devoted to discussion on the draft chapter on this group for an ERME book. It was introduced by Uffe Jankvist, who has written the chapter with Jan van Maanen. I did not note down anything from that discussion - but I was perplexed to be put in an "old-timers" group despite this being my first CERME. :-) (My feeling of being "young" was destroyed due to my participation in similar conferences since 2000...)<br />
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The rest of the morning session was spent on participants sharing informaion on important publications that the others should know of. I have notes of this somewhere, but we were also promised an email later summarizing this.<br />
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The second session started off with Renaud Chorlay's paper, about using parts of Nine Chapters in teacher training. He has three goals for working with this problem (which may be a problem, as students often focus on at most one). Liu Hui gave two justifications for multiplication of fractions, the second of which could probably be used in teaching, in my opinion. The use of a semantic embedding (word problem) is a resource, but also a worry as it can decrease the generality. Renaud argued convincingly that this example can be useful for discussion with teacher students, even though (according to him) perhaps not useful for direct work with children. I am a big fan of Renaud's work and am happy that he is now working in teacher education, as it means that his work - which is as always historically solid - now includes sharp analyses of what might be the use of the historical examples in teacher education.<br />
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Next, Regina Moeller and Peter Collignon talked on their paper which concerns the work on infinity with children. The concept has a long history, while teacher education students tend to have only the epsilon-delta based concept. (Of course, this is context-dependent - most Norwegian teacher education students would look at you wide-eyed if you mention epsilon or delta.) In their opinion, teachers need to know other conceptions that may be closer to the steps children go through. They look especially at Hilbert and Cantor - including the hotel of Hilbert, of course. The work can make students more aware that there exists different conceptions that they have not learned and to be more open-minded.<br />
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Then, Rui Candeias presented "Mathematics in the initial pre-service education of primary school teachers in Portugal: analysis of Gabriel Gonçalves' proposal for the concept of unit and its application in solving problems with decimals". This is part of a larger research project comparing different textbooks for teacher training. He presented in detail the steps adviced by Gonçalves. (Which makes me think that it could be a good idea to study historical teacher guides in Norway to point out to students the evolution of the field of mathematics education when it comes to concrete advice given to students.)<br />
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Maria Sanz gave the last presentation of the day; "Classification and Resolution of the Descriptive Historical Fraction Problems". She proposes a classification of the problems based on which methods can be used to solve them. It is unclear to me what this classification brings to the table - other aspects (known/unknown context, size of numbers, distractors included and so on) could be as important for practical use in classrooms. In the discussion, she was asked about connection to the mathematics education research on the same issues. It was also mentioned that in some countries they are "banned" from textbooks, while in others they are obviously not banned.<br />
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Some comments that turned up:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• What can these examples bring to teacher training? The common denominator seems to be that they are in a preliminary phase - but they can work to show students that problems are not something to be solved but rather something to be analysed to decide whether and how to use in their teaching.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Could students solve and classify problems in the way of Maria themselves? Would that be more useful than being presented with a classification?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• History can be a good tool to connect algebra without the symbolism with algebra with symbols.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• A book by Brian Clegg on infinity was recommended.<br />
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I do think that a closer collaboration between maths ed people and history of mathematics people is called for. In some cases, we see discussions on how historical sources can be used in teaching of subjects where there exist a huge amount of literature in the field of mathematics education, but where this work is disregarded. This is every bit as bad as the huge number of papers in mathematics education that completely disregards the history of the subjects that they want to discuss.<br />
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This was the end of the third day. Well, not quite. I was lucky enough to take part on the "lavender walking tour", which was a walking tour of Dublin LGBT History. We saw the Oscar Wilde monument, the Parliament, Dublin Castle, the national library and many other places of importance. We got detailed and enthusiastic information on the liberation fight, including the disgraceful attitudes of the government when activists tried to save lives by distributing condoms (which were illegal at the time). Today, Ireland has moved in a liberal direction and is one of the few countries where gay marriage has been decided in a referendum - although relgious fundamentalists still have a role. The tour ended at a gay pub where we got to continue the discussion over some Irish refreshments.<br />
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CERME is the second big international mathematics education conference in less than a year with something concerning LGBT issues on or near the programme. I do hope that this is an emerging trend.<br />
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Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-58480313643844784862017-02-04T07:08:00.003-08:002017-02-04T07:08:50.940-08:00CERME 10 Day 2The second day of CERME 10 started where the first one ended - with a TWG (topic working group session). Please excuse my extremely short descriptions of the papers - the authors were just given ten minutes to remind participants of their papers as a basis for discussion, and I do not have the time to go back to the papers to give more detailed accounts. First, Kathy Clark talked on the very interesting TRIUMPHS project, a big design research project based on original sources. At this time, the project reports on a pilot study in the first year. I notice an inteesting focus on meta-discursive rules and on views of mathematics. They use Törner's aspects and his instrument - but the number of students included in the analysis at this point was small. It will be interesting to follow the project in years to come!<br />
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Rainer Kaenders talked about "Historical Methods for Drawing Anaglyphs". In this project, students draw 3d drawings using historical methods. The point was not to learn the methods, but to understand the mathematical principles in order to be able to do the drawings. Again, this was an interesting project giving ideas for working on geometry in new ways. Kaenders had used this in extracurricular activities with students, for which it seemed well suited.<br />
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Thirdly, Rita (Areti) Panaoura talked about the paper "Inquiry-based teaching approach in mathematics by using history of mathematics - a case study". In Cyprus, which has a centralized school system, history of mathematics is seen as a tool to investigate the mathematical concepts. She reiterated Siu's reasons that teachers hesitate in using HM. She gave examples of teachers' attitudes and knowledge. Teachers could not connect the HM and the inquiry-based teaching approach which was also mandated. Understanding what teachers need in order to include history of mathematics in their teaching, is very important in order to implement HM in teaching. As such, I find this paper interesting. A participant questioned whether the use of Egyptian multiplication is helpful. I think that depends on the goal. According to Rita, there are no teacher guide saying what the point is, therefore it is difficult to see if the example is well-chosen or not - and difficult for teachers to use it in a meaningful way. Thus, this paper shows the problem of giving teachers resources without giving them the reasoning behond them.<br />
<br />
The fourth presentation was of the paper "Teaching kinematics using mathematics history" (Alfredo Martinez). This is a paper concerning a reconstruction of a method of measuring time which Galileo may have used. Students were able to measure time using a rhythm, thereby being able to recreate Galileo's results. It is a bit unclear to me if this really fits in the history of mathematics group or would rather fit in a history of science group (at some unspecified conference), though.<br />
<br />
Then there was a group discussion and sharing. Some points:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• It is a shame that the scaffolding was not there for the teachers or students in the Egyptian multiplication example to see the connection to our algorithms.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• What "scaffolding" is needed? Notes to teachers and workshops are parts of the project Kathy talked about. Also, use of history of mathematics should also be included in teacher training.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• A historical document is not necessary, historical problems (without giving the actual source) worked on with students are also useful. But what difference does the source make? (Of course, many authors have written extensively on this.)<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Can all topics be taught using history? Are there too big obstacles in some cases?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Can we do good history and good mathematics at the same time? (My answer would be that we are never "perfect" in the classroom, teaching is always full of compromises. So there is a question of what is good enough.)<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• The geographical and cultural distance is important. Is Greek mathematics more motivating for pupils in Greece?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• How much of the original context must a teacher understand?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Choice of examples: should they be "exemplary" or could we have "fringe" examples? Papers that are most interesting from a historical point of view, may not be the best ones from an educational point of view.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• How do teachers come to have materials that they can use? And how do they (learn to) orchestrate the classroom experience?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span><br />
Then, there was time for another plenary: Lieven Verschaffel on "Young children's early mathematical competencies: analysis and stimulation". Researchers today believe that children have a "starter kit", object tracking system and approximate number system (ANS). Gradually, there is a development towards a symbolic representation. There are significant correlations between numberical magnitude understanding and early mathematical achievement.<br />
<br />
The ordinality aspect of number is neglected in the cognitive neuroscientific work. But research suggest stronger correlation/predictability between ordinal aspect and mathematical skill. For instance Hyman Bass argues for developing number based on measurement. Basing the number concept on cardinality means that later developments, such as fractions, will be more difficult.<br />
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There is also more interest in children's understanding of basic arithmetic concepts and relations. There is little research on the consequences of this for later mathematics learning. Nunes et al (2015) is an exception.<br />
<br />
Other researchers have looked at pattern and structures. Mulligan et al (2015) is the most comprehensive, looking at children's awareness of mathematical patten and structure (AMPS). A related intervention study shows no improvement in general mathematics achievement.<br />
<br />
The research studies mentioned so far look at children's abilities, not their dispositions. (I.e. Asking children to look for a pattern, not measuring whether they see the pattern without a prompt.)<br />
<br />
SFOR (spontaneous focusing on quantitative relations) - individual differences, and has a direct effect on mathematical results at end of elementary school. Several other such FLAs (four letter acronyms) were also mentioned- we do not know much about their development and interrelationship.<br />
<br />
Then he went on to talk on domain-general (not domain-specific) abilities, such as attention, flexibility, inhibition, working memory etc. There is evidence of these abilities' importance - to a greater degree than domain-specific abilities.<br />
<br />
Other aspects mentioned in the talk was the role of parents and early caregivers, preschool to elementary school transition, and the professional development of caregivers and teachers. He concluded by listing a whole range of important aspects which need to be further developed in years to come.<br />
<br />
For the third session of the TWG, the first person was Luciane de Fatima Bertin, presenting the paper "Arithmetical problems in primary school: ideas that circulated in São Paulo/Brazil in the end of the 19th century". She highlighted the notion of appropriation and the notion of purpose. The word "problem" is undefined, but seems to be synonymous with "exercise", so it has no connection to the modern understanding connected to "problem solving". There was no discussion in the journals analysed on the use of problems in teaching.<br />
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Asger Senbergs<span class="Apple-tab-span" style="white-space: pre;"> </span>talked on his article "Mathematics at the Royal Danish Military Academy of 1830". His article is based on his Master thesis. The research was based on his curiosity about why mathematics became the main topic when Denmark created a military academy. The value of mathematics as a goal in itself was prominent - not just as a tool for action on the field.<br />
<br />
Ildar Safuanov's paper "The role of genetic approach and history of mathematics in works of Russian mathematics educators (1850-1950)" was up next. The paper details early Russians ideas on the genetic approach. The genetic approach was connected to the idea that pupils should not just witness but also create mathematics, and was included in the guidelines for mathematics teaching after the 1917 revolution.<br />
<br />
Tanja Hamman talked about ""Sickened by set theory?" - About New Math in German primary schools". The title is from Der Spiegel from March 1974 ("Macht Mengenlehre krank?"). She has looked at textbooks and teacher guides from West Germany to see whether the main ideas were present in the textbooks. Traditional education did influence the implementation, it is not possible to create a clean slate when dealing with teaching.<br />
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Then, it was time for group discussions. Here are some points from the discussion:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Do we see history of mathematics education mainly as part of general history, part of mathematics education or as part of history of mathematics?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• It is interesting to look at historical cases to investigate conditions for ("successful") implementation of educational reforms. (Which is part of the value of history of mathematics education for teacher education?)<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• How does it matter that a subject has a history? Does it provide a knowledge base to look at your subject?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• Who decides what are popular and unpopular subjects? What are the forces behind which topics are in vogue at a given time?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• When you know more about the past, you have more tools to deal with the present.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• New Math - was it never, anywhere, implemented as intended, with the intended outcomes?<br />
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Thus ended the second day of CERME. Although most participants probably continued their discussions into the early hours of the next day, I returned to my hotel room to prepare for the university board meeting next week. It is necessary to mention this, as some colleagues have developed an unhealthy interest in my nightlife while in Dublin... :-)<br />
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Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-16579869059899785262017-02-04T06:41:00.002-08:002017-02-04T06:41:44.714-08:00CERME 10 Day 1CERME 10 was my first CERME, taking place at Croke Park in Dublin. With a capacity of more than 80000, the stadium had plenty of space for the 800 participants. The opening ceremony included short adresses from various dignitaries (of course, including the leaders of the groups actually doing the work of preparing the conference). For instance, we learned how Hamilton got a key insight (concerning quaternions) by the Royal Canal (which passes just outside the stadium). In addition, there was some beautiful Irish music, of course.<br />
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The first plenary lecturer was Elena Nordi. Her title was "From Advanced Mathematical Thinking to University Mathematics Education: A story of emancipation and enrichment". She opened with an image from the Coen film "A serious man" - pointing out the popular conception of what university mathematics teaching look like: a professor filling a blackboard. University mathematics teaching today is much more varied than that - the demands on the teachers are quite varied. In her talk, she wanted to give an overview of the CERME work on university mathematics since the first CERME, in a way she called "impressionistic" and personal.<br />
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She pointed out that the field is quite young, for instance important papers such as Yackel & Cobb ("Sociomathematical Norms, Argumentation, and Autonomy in Mathematics") arrived in 1996. She pointed out that research on university mathematics education has in this period been moving away from being a "hobby" done by mathematics professors without a connection to the general mathematics education research. However, she also mentioned how her field differs from other fields in that there is a less clear distinction between teacher and researcher - the university lecturers are also often researchers. However, she did not fully go into the implications of this.<br />
<br />
Her (rapid) talk discussed a huge number of papers from different CERME conferences, pointing out developments. For me, who is not doing research on or teach advanced mathematics, the talk was so full of unfamiliar names and developments that I will not attempt to summarize here. Sadly, the speed of her talk also excluded some participants - not all of which speak English on a daily basis. (In fact, 50 countries were represented in the conference.)<br />
<br />
The main feature of the CERMEs are the TWGs (Topic Working Groups), which one is supposed to stay loyal to throughout the conference and which takes up most of the conference time. The first session of the TWG took place at the end of the first day. Renaud Chorlay gave a quick introduction to the working of the group.<br />
<br />
After we had all introduced ourselves, we were ready for the first paper. That was Elizabeth de Freitas' paper called "A course in the philosophy of mathematics for future high school mathematics teachers". She talked about a course she has given for three years ar Adelphi University in New York, which was actually an alternative to a history of mathematics course. One important aspect is the philosophical paper students have to write - where they have to take a stand and defend a position on one central question from the philosophy of mathematics. Maurice O'Reilly presented his paper on "Multiple perspectives on working with original mathematical sources from the Edward Worth Library, Dublin". He stressed the scaffolding of students' work - helping and encouraging the students reading unfamiliar sources (to them) in foreign languages. These were short presentations as we had all read the papers in advance. Then we started discussing the expected and actual impact of the teaching projects. The discussion centered on whether there are ways of collecting data and convince others of the potential value of such approaches. Here are some points:<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• The researchers had some data that could have been analysed to shed light on the potential. However, as some of the assumed values concerns students' long-term approach to and image of mathematics, maybe longitudinal studies are neccessary?<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• In some cases, The visceral reactions of the students are powerful but not measurable? Some participants in the group recognized their own reaction in students' reaction.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• The role of the teacher seemed to be different here than in "usual" teaching. The projects can give ideas on how to teach to avoid the students' imitation.<br />
<span class="Apple-tab-span" style="white-space: pre;"> </span>• There is a pull to prove effectiveness, but also a danger of being drawn into the metrics. We need more research that convinces others than ourselves, but we also need development and ideas that can later be explored more. So papers such as these are valuable although they may not convince others.<br />
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That was already the end of the first day at CERME. Three more blog posts will follow.<br />
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Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0tag:blogger.com,1999:blog-2210497064207378386.post-6071560791500870932016-07-31T12:15:00.004-07:002016-07-31T12:15:46.450-07:00ICME13 Day 7 #icme13<div style="font-family: Calibri; font-size: 11.0pt; margin: 0in;">
The 7th day of the
ICME13 conference was short. First a plenary panel on "transitions in
mathematics education". Panellists were Ghislaine Gueudet<span style="text-decoration: underline;">,</span> Marianna Bosch, Andrea diSessa, Oh
Nam Kwon, and Lieven Verschaffel. The panel's theme - transitions - has many
interpretations, including transitions between themes (arithmetic to algebra),
transition to formal proof, transitions between school levels, transitions
between contexts, for instance language contexts, transitions between
curricula. In this panel, they focused on transitions as conceptual change and
on transitions of people as they move between social groups. To look at this,
they had epistemological, cognitive and socio-cultural perspectives. The result
of the work is a survey: "Transitions in </div>
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Mathematics
Education".</div>
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diSessa started by
talking about "Continuity versus Discontinuity in Learning Difficult
Concepts". Bachelard talked about epistemological obstacles, while others
talks about "pieces and processes" instead, arguing for more
continuous change. Misconceptions belong to the left side of this divide. The
answer to the discussion may be found in microgenetic perspective (J. Wagner) -
some research find incremental learning across many contexts, for instance when
trying to learn the law of large numbers. diSessa thinks the continuist side
will win, which will mean we will look at resources more than obstacles or
misconceptions. (Personally, I'm not sure I believe any side is 100 percent
right. Why can't both be right in different contexts? That is, that some
development is gradual or stepwise, while other develop is mora abrupt and
discontinuous?)</div>
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Kwon talked on
"Double discontinuity between Secondary School Mathematics and University
Mathematics". The double disconuinity concerns first moving from secondary
school mathematics to university mathematics and then back (as a teacher). She
then discussed Shulman, Ball and then Heinz et al ("School Related Content
Knowledge") and Thompson (Mathematical Meaning for Teaching Secondary
Mathematics).</div>
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While listening to
her talk, I wondered if it could it argued that the Norwegian system, in which
teachers for (lower) secondary schools are educated in teacher education
programmes in which mathematics and mathematics education courses are merged,
and where the mathematics is not "university mathematics" as such,
avoids such double discontuinities? In fact, the suggestions she ended her talk
with seemed to align almost exactly with the Norwegian model. But it must be
stressed that for upper secondary schools, the problem is present also in
Norway.</div>
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Borsch talked on
"Transitions between teaching institutions". Individual trajectories
are shaped by the institutions they enter, their activities and settings. The
transitions between primary and secondary and between secondary and tertiary
education, are much studied. There are many different levels of analysis which
are present in the literature. The main differences between primary and
secondary are pedagogy (interaction, autonomy, transmissionist) and discipline
(specialist teacher, more division between subjects). Many proposals for
smoothing the transition are found in the literature (and in the report).</div>
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The differences
between secondary and tertary education are similar to differences between
primary and secondary. In addition, teachers are researchers. There is more
research on particular topics (i.e. Algebra) and there are more proposals.
"Bridging courses" are discussed, but university mathematics content
is rarely questioned. It is not clear whether all perspectives are equally
represented in the literature.</div>
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Verschaffel talked
on "Transitions between in- and out-of-school mathematics". Much
learning and use og mathematics take place outside school. While this has
previously been "romanticized", currently, more interest is in what
happens at the boundaries. Of course, part of this is research on the
didactical contract when playing the game of word problems, in which
out-of-school experiences are often unwelcome. There are efforts to facilitate
and exploit transitions, for instance RME, "funds of knowledge",
Greer. Then the panel ended with a discussion, based on question from an
internet forum, at which point I stopped making notes.</div>
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Then, there was the
closing ceremony. Secretary general of ICMI, Abraham Arcavi, had a warm and
pleasant speech closing the conference. Then there were many speeches of thanks
to different contributors. There was a presentation of the next venue for ICME
(Shanghai ). And finally, a wonderful musical number.</div>
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What did I get out
of ICME13? (And why will I go to ICME14 in Shanghai in 2020?)</div>
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As I noted earlier,
there are many possible outcomes from such a conference, and I can summarize
some of them, in no particular order of importance:</div>
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<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Meeting new (or old) people
with which future collaborations are possible. At this conference, I can
think of at least four people I didn't know before, with whom there can
possibly be some sort of collaboration some time in future.</span></li>
<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Getting ideas for future
research projects: During the conference, I wrote a list of nine research
and development projects that I would like to do. Not all are new ideas,
but many have been expanded while I've been here. And some are directly
adapted from talks here. I only hope I can follow up on some of them when
I get back home...<span style="mso-spacerun: yes;"> </span>Hugh Burkhardt's
talk on design research was very inspiring, and I want to do something in
that direction (more systematically than I've done before).</span></li>
<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Getting ideas for my own
teaching (which can of course also turn into research projects): Marjolein
Kool's project on making students creating non-routine mathematics
problems, Megan Shaugnessy's and others' ideas on simulations of classroom
situations (some of these concerning the notion of "noticing").</span></li>
<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Getting an overview of a
field which will make it easier for me to read more about it later: For
instance, I hope it will be easier for me to face Brousseau now that I've
had a tiny introduction and some context.</span></li>
<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Listening to lectures and
realizing that I do actually know something: it would be impolite to point
out which talks contributed to this realization. But perhaps it is a good
sign that for every ICME I go to, I think "been there, done
that" a bit more frequently. This is not to critizise ICME (too
much), of course not everything can be new to everyone.</span></li>
<li style="margin-bottom: 0; margin-top: 0; vertical-align: middle;"><span style="font-family: Calibri; font-size: 11.0pt;">Socialize with new or old
colleagues: of course, the tendency to cluster based on nationalities may
be seen as a problem (and meetings like the LGBT get-together may
counteract that a little), but it is a reality that many countries have
few meeting-places, so that socializing with colleagues from the same
country does make some sense. There's been a lot of that here.</span></li>
</ul>
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The main problem
with ICME is of course its size - it's complete lack of intimacy. The trick is
of course to find a home in a TSG, but still there will be situations when
you're all alone and see hundreds of strangers walk past - which is a challenge
for smalltalk-challenged people like me. But still, there is every chance that
I'll go to ICME again in four years' time. </div>
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But before that,
we'll arrange our own conference (ESU8) in Oslo in 2018. That will be fun - and
intimate. And I hope I'll go to CERME in February, 2017. </div>
Bjørnhttp://www.blogger.com/profile/16158361595130866728noreply@blogger.com0