As other conferences, it started with a series of welcome messages by people who are expected to say something at such an occation.

Then there was the first plenary lecture - Kristina Reiss gave a talk with the title "You can't teach an old dog new tricks? Developing mathematical competence over the life span." Her topic could also be framed as: What is lifelong learning of mathematics? I it important for non-mathematicians? And is it possible? Of course, she gave many reasons why it can be important, both personally and professionally. One example; wireless plan.

She described an experiment from Wynn (1992) - where she showed that four months' old children "understood" that 1+1=2. The experiment is also replicated on monkeys. She also described how such understanding is a predictor of later knowledge in mathematics. Thus, she gave examples of how matematics education research has developed to make us better at teaching mathematics to children (although it is still an important area of research, of course). The natural question is then what we know about how to develop mathematical knowledge with adult learners. Cohen (2003) says that adult education is under-researched, under-theorized and under-developed.

She noted that many "standards" that have developed are wonderful if you have wonderful students, great teachers and perfect equipment, but that they are less helåful if you have diverse classrooms including children with learning problems and so on. She also points out the paradox that mathematics is a unique subject in being axiomatic and based on proof, while school mathematics use quite different approaches. According to Reiss, we lose far too many students by making them believe that mathematics is too difficult. Felix Klein described a "double discontinuity", and (if I got this right) she borrowed his concept to describe the situations for prospective mathematics teachers in that they go from school mathematics to a more rigorous and formal approach and then back to school mathematics to become teachers.

She noted that adult learners tend to learn things when they are particularly motivated for it, for instance if they need it, while younger learners tend to learn because they "have to" learn it. However, I think that although we have the "power" to make younger students learn because we decide they have to, it may be an idea to get even them to learn because they are interested and see that they need it... (Not that this point necessarily is at odds with Reiss' opinion, of course.)

After this plenary, there was a social programme that I will not blog about. Thus ended the short first day of the conference. Tomorrow will be the first full day, with a scientific programme from 9 to 19...

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