Skemp Article Response

In large part, I also share Skemp's preference for relational mathematics over the instrumental approach. As someone who enjoys the beauty of deep understanding and making connections in mathematics, I have always preferred this approach. Moreover, I have plenty of personal experience observing different students approaching mathematics with either relational or instrumental understanding as a subconscious goal, and the differences I've witnessed in both their enjoyment and performance favour those students who seek relational understanding. I have always aimed to teach math in such a way that would promote conceptual understanding in my students, and I have only taught in an instrumental way when there was a much greater immediate utility. It was interesting to stop and reflect about this a bit more consciously though by reading this article.

The analogy that Skemp used, of finding one's way through a town, resonated with me in a particularly powerful way as I was able to instantly relate this to my own experiences both in physical navigation and mental navigation of mathematical concepts. Similarly, his analogy from music also spoke to me greatly as I learned music in a relational way from a young age. By the time I finished the article, I realized just how much I think in relational terms in the majority of my endeavours. I think that most of us who have studied math at the post-secondary level likely think this way, and we might often take it for granted. I suggest that we need to be aware that thinking this way may not be as intuitive for others as it is for us, and this realization should encourage us to be intentional and patient in our teaching. 

I also found Skemp's points regarding assessment particularly interesting: specifically, "the backwash effect of examinations" (as he calls it) and how it can be difficult to ascertain the way that a student is reasoning from a generic assessment. I think that these points highlight a need for mathematics teachers to very carefully examine how they create assessments for their classes and how those assessments not only measure learning, but influence it.

Lastly, I also personally related to the point about relational knowledge being effective as a goal in itself, and being organic in nature. I completely agree with this from my experience, as the rewards of struggling and eventually reaching deep understanding has motivated me consistently to learn more (not just within mathematics). 

As an aspiring teacher, I hope to be able to find ways to make teaching mathematics in a relational sense more practical, so that, wherever possible, it is the primary approach that I share with my students, and that I only divert to an instrumental approach for intentional, logical reasons (not out of necessity).