I did my “I am a scientist” discussion a couple of weeks ago and I think it went not completely awfully. We started with a “What do mathematicians look like?” activity, and then talked about how mathematicians take real problems and turn them into “abstract nonsense”. In particular, we talked about the seven bridges of Königsberg and I gave the students time to try and come up with a path of their own.

After about five minutes of trying, most of them decided it was impossible. When asked why, the most common response was along the lines of the fact that the graph has an odd number of edges. So I asked if such a path was possible for a triangle and it seemed that they were satisfied with the counterexample (which is fairly interesting in itself since they are demonstrating an understanding that for quantifiers the negation of a universal is an existential of the negation). There was one student who seemed to have the idea of a proof for the impossibility of a path, but lacked the eloquence necessary to explain her ideas to someone who did not already know a solution.

I noticed that the students with discipline issues tended to be more interactive, and ask questions which showed a deeper understanding of the material.

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