Skemp on two approaches to teaching and learning mathematics

 I definitely agree with what Skemp is arguing about the importance of relational understanding. I think having a relational understanding is especially important when learning more complex topics because it allows students to understand how ideas connect and apply their knowledge to further topics. This also made me think about my experience learning in IB, where making connections between concepts and applying knowledge in different contexts is emphasized, so I think relational understanding is especially important in an IB classroom. However, I also think instrumental understanding can be a useful starting point and has its own advantages, as Skemp discusses. 

When I was tutoring math, I would often adjust how I explained a topic depending on the student and how much time they had. For example, if a student came in the day before a test on a topic they had not covered much, I might explain it more instrumentally by making sure they knew the formula and could apply it correctly, rather than spending time explaining the reasoning and context behind it. If a student was being introduced to a new topic and brought in their schoolwork, I would usually take more time to explain the reasoning behind the concepts and things they might not have learned in class. Both approaches definitely have a place depending on the situation.