Response to Skemp (1976) article

Faux Amis reminded me that the word “gift” in German actually means “poison”, as I learned in my German reading class! From reading this article, though (more on topic), my entire high school math education experience was based on instrumental understanding. I did very well in math classes in high school, but it was moreso because I knew what formulas to use, what “type” of question was being asked and the methods to answer it, and the style of questions and what was expected of me. It wasn’t until I started working students with poor fundamental understanding of math (or, at least, I thought so – it was more the operational understanding of math) that I realized how difficult it was to explain the simplest concepts; sometimes, I still do. Most of the math websites I visit offer an operational explanation and method to solve problems, as opposed to relational. I’ve searched for some time for an explanation of the origins of the sine, tangent, and cosine ratio that stems beyond the ratios of a right triangle, but have not yet come up with a book that explains how they are derived.

Reading the section where the author describes transcription of music and instrumental learning…. No wonder so many students dislike math. It’s not to say that there aren’t more issues underfoot, like a weak basis for math and a lack of confidence in using the tools that they do have, but if all the math is for them is “a bunch of formulas” and “all those word problems”, then of course we have students who dislike it and vow never to take it again, cheering at the end of grade 11 because “they don’t have to take math anymore”. Relational mathematics, it seems, is difficult to teach, but it sounds more rewarding. I didn’t see the author mention it, but I feel as though relational mathematics stays in a person’s memory longer. This is nice, because I’ve heard the argument that “we don’t need to learn math” because “we can look it up online”. I find this disturbing.

When it comes to dislike of the topic, though, I’ve discussed this with many teachers. Some insist that, in fact, it comes from having teachers that have no formal training in math. I don’t exactly disagree, but I feel as though anyone may have a more instinctive understanding of math, not just a math teacher. Now, I do believe, that guardians/parents/family and culture can influence a dislike of math. I grew up in a family where my mum encouraged me to do math and tried to insist that math is a game. I think this helped! However, among parents of the students I tutor, I often have them say, “Oh, I could never do this, I’m so glad that you are here to help with it” or, “I was never good at math, I didn’t like it in school”. I don’t expect everyone to be mathematical geniuses. However, the attitude that they “can’t do something” and therefore “didn’t like it” or were afraid of it is likely to influence students to feel the same way. Saying that something is fun is more likely to encourage someone to do something than saying that it is difficult.