I agree wholeheartedly with Skemp's view on the importance of relational math and relational understanding. I believe that relational learning build intrinsic motivation in students, and also helps students view math as a part of an ecosystem of interrelated subjects, rather than a stand-alone, abstract topic. Similarly, I agree that it is then essential for teachers to teach math relationally. For this reason, I found it especially interesting that Skemp mentions on page 11 that perhaps even many teachers do not have a relational understanding of math. This makes me reflect on my own high school teachers, who at times would say something like “this is just how it is” when explaining some concepts in math. I remember my classmates being confused and frustrated by statements like that, and I now realize that my teacher at that time likely only an instrumental understanding of the topic, and I saw firsthand how detrimental that can be to classroom comprehension and morale.
As I read the article, I realize I might understand math more instrumentally that I previously thought. In examples given throughout the text, such as the example of multiplying two negative numbers to get a positive number (page 8), I realize I don’t have a good explanation for this result. This is surprising to me, as I find my favorite parts of learning math are when I finally connect the instrumental procedure to a deeper relational understanding. However, I’m beginning to think maybe since I learnt about multiplying negative numbers so long ago, and since it feels so intuitive to me now, that perhaps I’ve just forgotten the relational understanding I once had of the topic. Lastly, I really appreciated Skemps analogy of getting to know a city, and mor specifically when you look at someone walking you can’t easily tell whether they are exploring or following a prescribed route. This is something I hadn’t really considered in a learning context, and the story gave a really grounded way to explore this topic for me. I think that especially while I complete the short practicum, I will be paying attention to the students and trying to decipher what kind of learning is going on for each of them.
There is a common belief that if you are good at math, then you must be able to teach math yet, we all have experiences of teachers who may be mathematically strong, who are unable to teach math. What characteristics of a "good" math teacher due you think are necessary and how will you develop these in your own practice? You also make an interesting point - are some of our mathematical understandings so ingrained that we have forgotten why it is that way? What steps can we take as teachers to assist students with not forgetting?
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