Skemp’s Approaches

My first stop is probably similar to a lot of my peers: “instrumental understanding vs. relational understanding.” I definitely feel called out when Skemp mentioned “turn it upside down and multiply” and “take it over to the other side and change the sign.” This is how I learned mathematics, and I am just starting to realize that I have no idea why we do it as long as I got checkmarks. Then, when he brought up the relational understanding of pi in terms of circumferences divided by diameter, it is really testing my own relational understanding of math… I have never made that connection! And adding onto that, when I stumbled across Skemp mentioning that relational understanding is easier to remember, I definitely disagreed at first. Again, since I am biased just like him, I thought instrumental understanding carried me through mathematics just fine. However, I was quickly reminded by him that the formula for calculating areas of shapes can quickly be found if we understood proportions. I then though about volumes, if I had to guess the volume of a square pyramid, I would’ve probably guessed along the lines of “around half or a third of a cube or rectangle,” which is actually pretty close to the actual formula. So even though I didn’t agree with that relational understanding is easier to remember, it did stop and make me think about where those connections can be used in solving math problems. And lastly, I realized that I also use relational understanding near the end of the article. When Skemp brought up the map analogy, I realized that that is what I do. I walked around the campus for the first few days to familiarize myself, so now, even when I am lost, I can reasonably guess which is the fastest way to the Nest or to the closest bubble tea store on campus. I never really thought of this in terms of understanding math, so this blew my mind quite a bit.

And now, in terms of my stance, I can safely say that I am very open to and very eager to learn about relational understanding. Since I learned math mostly through Kumon (a math tutoring service), everything is taught to me as “use this algorithm to get a checkmark.” So now, as a math teacher, I want to ensure that my students actually understand why we do all of those algorithms, which is more important then getting 100% on an exam. I thought it was interesting when Skemp labelled instrumental understanding as a short term solution, since for example, I have completely forgotten how complete the square works because I forgot the algorithm for it. If I relationally understood why complete the square worked, I probably would’ve still remembered how to do it if I just looked at a graph. This is very exciting for me since I get to be a student still, learning alongside my future students to relationally understand math that I’ve done my whole life!