She started out by talking about ethnomathematics and presenting the history of Iceland. Due to a lack of metal, exchange of goods were the norm instead of buying with money. A hundred was equivalent to a cow or 240 fishes. In 1880: Danish krone adopted. Kristin gave an example of quite involved textbook problems using these exchange "rates".
The Misseri calendar was adopted in 930, and this was adjusted to the Julian calendar in the 1200s. The calendar was needed to establish the meeting times of the parliament. The practical problems with errors in the calendar (which meant that soon the parliament had to meet in the busiest parts of the farming year) was a powerful motivation for figuring out how to improve on the calendar. Later, other errors were found in similar ways. But in adjusted versions, the Misseri calendar has survived almost to our day.
Secondly, there was Gert Schubring's plenary "New approaches and results in the history of teaching and learning mathematics". He stressed that he avoided the word "education" In the title to avoid confusion with "mathematics education" (matematikdidaktik). He started by outlining the history of research on history of mathematics in school. New trends now: more specialized studies of specific countries, attempts at an international history and new methodological approaches, going beyond the administrative documents and using insights for instance from sociology. These efforts were mostly individual, but have recently also become institutional, thanks to the topic study groups of ICME from 2004 and launching the journal IJHME in 2006. In 2014 was published Handbook on the History of Mathematics Education.
If history of school mathematics is reduced to the history of curricula, the social reality is missed. Also, mathematics never occures in an isolated way, but must be seen in connection with other disciplines. Mathematics education became needed by state administrations in the same way that numeral systems and calculation with these were neccessiated by state administrations. Shubring went into some details on the origin of mathematics education in for instance China, which I cannot possibly summarize here.
Another question is how and why mathematics turned from something you should learn for state administration and into something everybody should learn. It turns out that France was the first country where this happened, after the revolution of 1789. Latin and mathematics were the two essential disciplines. Again, the amount of detail from different countries cannot be done justice here.
The second panel of the conferences had the title "The question of evaluation and assessment of experiences with introducing history of mathematics in the classroom". The panelists were Leo Rogers, Janet Heine Barnett, Ysette Weiss-Pidstrygach, David Guillemette and Frederic Metin.
Leo Rogers spent some time outlining the vast canvas we are moving about on: different target groups, different goals, different ways of including history of mathematics... These different contexts we are in, give different answers to questions such as why to assess, what to assess, how to assess, what data to collect and how to analyse and how to respond to the analyses. He also walked us through a lot of the common problems with testing/assessment, which are often of different forms when it comes to history of mathematics than in mathematics. (Of course, research on assessment in mathematics and history could have much input to us here.)
Janet talked on her work on the projects she has been involved it (with resources available online). The primary source projects have student tasks, which may be relevant for assessment. The primary goal Here is for students to learn core material in contemporary mathematics courses. But there are also hopes that these original sources support a development of a deeper level of understanding. The examination is mathematical. They also have homework where they get feedback and can rework it.
Frédéric talked about the French system, where there is a competative examination after the first year of teacher training (fourth year of university studies). Therefore, history of mathematics must also be suited to help students pass the exam. Major aims are then: - Enightening students knowledge in mathematics - Putting distance between students and mathematical knowledge - Link mathematical knowledge to other school disciplines - Training through (useful and job connected) research
Then: why assess, how assess, and is there any point in assessing the HM components, if the goal is not to learn HM? He gave examples of tasks he gives students and where it is quite simple to give similar tasks for the purpose of assessment - but still without being certain that it makes sense.
Ysette talked about maths camps where they got very few applicants, because of using the words "for gifted students". Asking students, they connected "gifted students" to the grades. These were attitudes that are problematic in teachers. History of mathematics must combat this, not strengthen it.
Concretely, comparing different textbooks' presentation of historical facts was an example on how to work on history of mathematics, which can be done in many different ways depending on students' background. They assess using lesson planning based on an historical excerpt.
Finally, David talked on experiences with preservice secondary school students, where the goal was to obtain deorientation (see his oral presentation). Assessment is problematic. Reading of original sources is a hermeneutic extreme sport without helmet. Students suffer the original sources, it includes shock and violence. Otherness is linked to empathy, keeping the subjectivity of the other alive. How to have the students suffer and maintain the empathy, how to assess the students?
Often, the evaluation is done by giving another text of one of the same authors they have worked on, trying to see if they understand the new text. Then the adventure ends. How to avoid that the relationship to the history ends?
Ewa Lakoma gave some input from her experiences in Poland, where examinations were given asking about historical facts, and group examinations where social skills were taken into account.
Evelyne reacted to the question of whether history of mathematics is a Humanities subject. HM is not in the tradition of mathematics, and helps us to speak mathematics and talk about mathematics with others. Mathematics is otherwise often taught by writing mathematics on the blackboard and by correcting papers with small signs on papers that have been handed in.
Janet pointed out that when we read mathematics, we have some techniques (for instance, finding an example) which students do not have. Therefore, many have turned to "guided reading" through tasks. (Actually, an interesting research project would be to study how different authors design the "guided reading" tasks and how they describe their reasoning between these tasks in their papers in HPM. Interviews would of course also be a possibility. It could also be compared to how this is done in other fields, such as Norwegian (L1) education.)
Tinne pointed out that the learning goals could both be on the big scale and on the small scale (the single session), and the assessments will vary according to these.
After lunch (and a much needed Starbucks ice coffee from the local minimarket), I chose the workshop of Caroline Kuhn and Snezana Lawrence on "Personalised Learning Environment and the History of Mathematics in the Learning of Mathematics". Personal is in the sense that the learner does design his own learning environment, choose tools etc.
After an introduction round, we had a round about our expectations. By this time, half an hour had passed. Then Caroline discussed different definitions of PLE. Ownership and agency are interesting in this context. Building a PLE is a good learning activity.
Four examples of websites on mathematics (which are not PLEs): Mathisgoodforyou.com NRICH MacTutor - StAndrews Mathigon.org
PLE outside mathematics: graasp Plenk 2010: connect.downes.ca/how.htm (Not PLE but a MOOC, which is simething different altogether.) Some other PLE: - works, but it is not so easy for students. (Valtonen Teemu)
After the break, in which a few of us was honestly still at a loss to understand exactly what a PLE was, we were put in groups and asked to craft an example of a teaching strategy for the tangent line problem, and then given a few sources (Apollonius and Fermat) and asked how knowledge of the sources could enhance the teaching. We all agreed that it couldn't really enhance the particular teaching ideas that we had thought of at first. This is, of course, often a problem for teachers: even though there are millions of sources online, the sources you find may not be interesting for your immediate purpose.
After the workshop, my thoughts are that my iPad (as well as my PC) can be regarded as my personal learning environment, with selected websites (bookmarks) and programs/apps, as well as resources I have made on my own. However, to be more useful in education, such a PLE needs an easy way for the teacher to suggest resources for the students, and - more importantly - it needs an ecosystem into which students may put their products and where other students may find these. A PLE with unlimited and uncurated access to "everything" will be fine for the expert, but certainly not for the student.
In the workshop, BBC's A Brief History of Mathematics was mentioned. I will have to check that out.
Thus ended Day 4. I skipped the oral presentations that started at 5:30, and waited for the Happy Hour instead...
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