Skemp Article Response

While I was reading this article I instinctively agreed with Skemp that teaching relationally is superior. As the article went on, I did not change my mind about this, but I did have some thoughts about when instrumental mathematics might be useful. I don’t think that instrumental mathematics is what should be exclusively taught in schools. However, I think instead of discarding it completely it might be better to instead use it as a tool to help teach relational math. The example that comes to mind for how this could be a useful tool is something that we see more in university math than in high school. In university textbooks and lectures we often see theorems where the proof has been omitted. This is often done because the theorem is needed to understand (relationally) the topics being taught but the proof is too difficult for the level of the class. This is essentially instrumental math since we are given a theorem and told to believe it without being told why the theorem holds. However, in many cases this is done to give us a stronger relational understanding of other theorems. This is similar to how Skemp says teachers may use instrumental math because “a skill is needed for use in another subject (e.g. science) before it can be understood relationally with the schemas presently available to the pupil.” (and him saying this is likely what made me think about this). Except sometimes it is not within another subject that a skill is needed but instead within math itself. Sometimes a topic or mathematical process is mathematically useful within the context of teaching relational math. But the explanation of why that process works is still too complicated for the current level that the students are at. So, I think instrumental understanding can be a good tool if it is used for the broader goal of relational understanding.