September 14th Reading (Skemp and instrumental versus relational learning) Response:

    The first thing that made me stop was at the beginning of the article when Skemp described the difference between relational and instrumental understanding/mathematics, as this was a concept I implicitly knew, but had never heard put to paper before. It was gratifying to have those definitions spelled out as I believe it helped me organise my own thoughts on the subject. The second thing was when he talks about how building relational understanding is difficult when students are already used to largely instrumental ways of learning, and so the value of implementing relational ways at an early age. It makes me wonder what sort of values versus obstacles there would be to enacting this at a secondary level if the students are coming from years worth of instrumental learning backgrounds – or if they even are, as things might have changed since this article was published. And finally, I was also really struck by Skemp’s mental map analogy at the end, as this really helped make things concrete in my brain on the difference between relational versus instrumental, especially since I am not very music minded and the previous music analogy was thus not as influential. I also feel that this analogy would even be appropriate to share with our kids if we feel that there is value in describing these ways of doing mathematics in order to help guide them towards attempting more relational learning than instrumental. Definitely something I’ll keep in mind.

    I think there is real value in what Skemp argues for relational mathematics, as it has incredible implications not only for student’s enjoyment and success within their math careers, but its transferable skills to other subjects and daily life. I do want to acknowledge, however, that while the ideal of teaching exclusively relational mathematics is a noble one, the feasibility of that in schools today could be in question. Especially since Skemp made it clear that relearning the way to learn (i.e. from instrumental to relational) can be incredibly hard and demoralising for students (if they even attempt to at all), and particularly coming into the secondary program, where students have had years of mathematics behind them - most likely instrumental - it might be near impossible to effectively shift all their mindsets to relational within the school year. So, in theory I am in support of his argument, but I also want to leave room for acknowledging the faults it could have in complete implementation at the high-school level, and I am eager to get first hand experience on what type of instruction is currently going on during our practicum (especially since this was written so long ago).