### Studying original sources in mathematics education

I have been terrible at posting in this blog, but I'll try to improve. I am currently at a mini-workshop at the Mathematisches Forschungsinstitut in Oberwolfach on the topic of "Studying original sources in mathematics education". The place is wonderful - the place is so green and beautiful, and there are all neccessary amenities to have a great, productive time.

On this first day of the mini-workshop, I have heard two great talks. The first one was by Abraham Arcavi. He told us about a teacher workshop he conducted with Masami Isoda, where teacher students were confronted with problems from the Rhind Papyrus, on multiplication and on solving an equation (as we will see it). The starting point of the work was that whether you are learning history or you are learning to teach, you have to learn to interpret. And maybe it is easier to learn to interpret by working on historical sources than by working on student answers, as it is harder to dismiss a historical source as being "wrong".

Arcavi gave some details on this particular workshop, not least on how "scaffolding" was necessary to ensure that the teacher students managed to work through the text in a meaningful way. The point noted in the end of the talk, however, seems to be one of the most important - how can you "upscale" such an experiment? This particular workshop was conducted by two prominent researchers in the field of "history and pedagogy of mathematics" (HPM) - how can we make "ordinary" teachers do the same (or similar things)?

One small exercise: Ron is given the following exercise: "3/5 of a number is 12, what is the number?" Ron writes: "12*2 = 24 24:6 = 4 24-4 = 20" Is Ron correct? How would you as a teacher react to his answer?

(This should show the need of a teacher to listen attentively, not just "evaluative".

The other talk was by David Pengelley, who showed us how he works with Pascal's "Treatise on the Arithmetical Triangle" with his students. I did not know this text before (although I have referred to it many times), and it was interesting to look at it a bit closer. As mentioned in an earlier posting, I tend to use exercises on Pascal's triangle in my teaching, but surely I learned something new today - even though some of the more advanced stuff, such as Pascal's use of inductive proofs, is probably not suitable for our first course at my institution...

Obviously, people are speaking to the converts at such a workshop. As mentioned already, the important thing is to (to use Pengelley's words) "convince teachers that they want to do it". Developing materials seem to be the way to do that, and I'm sad to say that materials in Norwegian are few and far between. I should do something to remedy that at some point.

On this first day of the mini-workshop, I have heard two great talks. The first one was by Abraham Arcavi. He told us about a teacher workshop he conducted with Masami Isoda, where teacher students were confronted with problems from the Rhind Papyrus, on multiplication and on solving an equation (as we will see it). The starting point of the work was that whether you are learning history or you are learning to teach, you have to learn to interpret. And maybe it is easier to learn to interpret by working on historical sources than by working on student answers, as it is harder to dismiss a historical source as being "wrong".

Arcavi gave some details on this particular workshop, not least on how "scaffolding" was necessary to ensure that the teacher students managed to work through the text in a meaningful way. The point noted in the end of the talk, however, seems to be one of the most important - how can you "upscale" such an experiment? This particular workshop was conducted by two prominent researchers in the field of "history and pedagogy of mathematics" (HPM) - how can we make "ordinary" teachers do the same (or similar things)?

One small exercise: Ron is given the following exercise: "3/5 of a number is 12, what is the number?" Ron writes: "12*2 = 24 24:6 = 4 24-4 = 20" Is Ron correct? How would you as a teacher react to his answer?

(This should show the need of a teacher to listen attentively, not just "evaluative".

The other talk was by David Pengelley, who showed us how he works with Pascal's "Treatise on the Arithmetical Triangle" with his students. I did not know this text before (although I have referred to it many times), and it was interesting to look at it a bit closer. As mentioned in an earlier posting, I tend to use exercises on Pascal's triangle in my teaching, but surely I learned something new today - even though some of the more advanced stuff, such as Pascal's use of inductive proofs, is probably not suitable for our first course at my institution...

Obviously, people are speaking to the converts at such a workshop. As mentioned already, the important thing is to (to use Pengelley's words) "convince teachers that they want to do it". Developing materials seem to be the way to do that, and I'm sad to say that materials in Norwegian are few and far between. I should do something to remedy that at some point.

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