Reflection on “instrumental understanding & relational understanding”

 When I read the part about students aiming for instrumental understanding while teachers are eager to teach relationally, it made me think about how I was taught mathematics in middle school. At that time, math felt like a subject where I had to memorize a lot of formulas and apply them to different questions. It was “useful” for solving problems and getting the correct answers, and it also helped me build confidence, just as Skemp mentions. However, when I think back, I realize I didn’t really understand why I was using those formulas. Compared to instrumental understanding, teaching should focus on delivering content in a way that helps students develop relational understanding within a bigger context, ultimately improving their problem-solving skills. Getting the correct answer can bring quick success, but it shouldn’t be the final goal.

Reading further, I found Skemp’s point that the advantages of relational mathematics make it easier to remember. Based on my own experience, this is true. For example, when learning a new language, reciting well-organized sentences and vocabulary provides a strong starting point. It is much faster to understand the meaning first before memorizing mechanically. At this point, I stopped and realized that Skemp is not simply arguing that instrumental understanding is “wrong” or that relational understanding is always “better.” In my opinion, finding a balance between these two types of understanding is crucial for teachers. Instrumental methods can provide students with quick wins and confidence, while relational approaches ensure that their knowledge is meaningful and lasting.