Sunday, 20 September 2015

Reflection on Our Instrumental vs. Relational Class Discussion

I was surprised at the evenness in how our class split on the discussion of instrumental vs. relational understanding in a math context. I much prefered relational, though I did see some of the benefits of instrumental, and I found it interesting how some of the points from the opposing side I felt completely different about. For example, when they raised the topic of technology, I thought that was a point in favour for relational understanding. Now, with computers to do most of the grunt work of calculations, I think it is more important for us to know how and why things work instead of the number-crunching, 'rules without reasons.' I also think, for certain concepts at least, learning relationally first, not instrumentally, is much more intuitive, not the other way around.
However, I do agree that, in terms of time-saving, instrumental understanding seems like the clear winner. It is much faster to teach, and when it comes to doing practice problems, it is much quicker. Understanding what multiplication and division is relationally is very important, but eventually you just need to memorize shortcuts to get things done in time! That speed and comfortableness is the "fluency" students need to move on to new topics. And though relational understanding is ideal, with the given constraints of class time, making sure every student can abstractly consider each topic isn't feasible.
I think both understandings are inherently linked to the way with must teach math. If I was teaching logarithmic rules, for example, students would understand how logs relate to exponents, and we would use that relational understanding to explain why log(xy)=log(x)+log(y). This meaning-making is important, but eventually for ease and quickness (i.e. fluency), students will memorize the rule.

1 comment:

  1. I think that most of the topics you mention can be taught for both understanding and fluency without taking up very much time. I do agree though that not every student will take on every topic with equal enthusiasm and to the same depth of understanding!

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