Richard Skemp Reflection

 As I was reading this article, I found the football analogy very thought provoking. I feel as if it explains a huge problem in mathematical education. When I was in junior high and high school, I never understood why my friends were struggling with math, it just made sense to me. However, thinking back on things, I think my friends just possessed mostly instrumental learning. They could do a problem that was shown to them with the exact steps the teacher did, but the moment you changed one aspect of the problem they threw up their hands. It was “impossible” because they hadn’t learned it before. I think this way of learning is more about regurgitation than actual problem solving and applying concepts. I also thought that the map analogy was very insightful. I think it describes perfectly why a relational mathematical understanding is typically better suited for solving a wide range of problems. As I mentioned previously, students often get lost when a part of the question is unfamiliar. But if students are given the tools and techniques to attack all different kinds of problems this probably wouldn’t happen as often. I think it’s important for students to understand this as well. I feel like a lot of kids just want to get the right answer with minimal thought but don’t consider how this method of attacking problems fails when difficulty increases. It is essential students understand that although there are “shortcuts” or “tricks” to get the right answer faster, it is still important to understand the underlying concepts to genuinely understand the material. Having a mental map of ways to approach and simply questions is in my opinion a much stronger method of solving problems. 

I do generally agree with Skemp. I think relation mathematics should be the goal when teaching students, it gives them the most comprehensive understanding of material and helps with problem solving skills instead of just testing memorization. However, there is the concern of time and resources. As Skemp mentioned, sometimes explaining the concepts of a topic is far beyond the level you are teaching, and students need an easy way to approach problems for tests. I think this issue stems from those who decide the curriculum, and what their goals are for students. There is also the concern of reaching every student. For some students, things will click immediately, but others may need longer to wrap their heads around things, but how do you balance this? You still need to get through an entire curriculum so sometimes simplifying problems is the only thing you can do. I think it’s a tricky issue, in theory it would be ideal if all math was taught as relation math, but in practice this isn’t always feasible.