Relational Understanding and Instrumental Understanding

 Hello Everyone!

To begin, while reading, I found Skemp’s music analogy interesting. It mentions that some students simply memorize the notes EGBDF, while others associate the written notes with the actual sounds and relationships between them. This connected with me because when I took piano growing up, I knew where the notes were on the piano, but reading music was the difficult part. Once I knew the notes, I would often memorize the finger movements needed to play the song seamlessly rather than fully understanding the music I was reading. This reminded me of the difference between memorizing a mathematical procedure and actually understanding why it works. I also found it interesting how Skemp acknowledges that even people who understand mathematics relationally will sometimes use instrumental thinking. This made me realize that relational and instrumental approaches are not necessarily completely separate. Instrumental thinking can be useful within relational understanding, however, instrumental understanding alone can be limiting. I also connected with Skemp’s discussion of over-burdened syllabi and how quickly mathematics can be taught. I experienced this in my own undergraduate mathematics courses, when professors sometimes moved through complex concepts very quickly or assumed certain ideas were common knowledge. As someone who was less experienced with the material than the professor, this sometimes made it difficult to build the deeper connections necessary for relational understanding.

Overall, I agree with Skemp’s argument that relational understanding should be emphasized in mathematics education. I believe there are some situations where instrumental understanding is useful, especially when students need to quickly apply a familiar procedure. However, students should not be limited to memorizing rules without understanding the reasoning behind them. As a future mathematics teacher, I hope to prioritize helping students understand both what they are doing and why they are doing it, while still recognizing that instrumental thinking has a place in mathematical learning.