Response to Skemp's Relational Understand and Instrumental Understanding

The first thing that stood out to me was the sport analogy that Skemp used where football and rugby players were playing against each other as a comparison to relational and instrumental understanding. I think part of the reason why it made me stop and reflect was because it drew quite an image in my mind. I also think that it may have tried to highlight some problems that I am not sure are necessarily a big deal. In particular, I am not sure if relational and instrumental mathematics deserve separate courses. 

The second thing that jumped out to me was the idea that syllabi are overburdened in schools. I couldn't help but agree with this argument wholeheartedly. Sometimes I reminisce about what I learnt in math classes and I remember my teachers being overwhelmed with the content they had to get through. Then I compare this to what I remember, and even as a math-lover there are large chunks of information that I know I will have to review before I teach it myself. At the same time, I think about how there was so much university Math content that I felt behind in as a BC student in comparison to international students. And I am not sure what the solution to this dilemma is either. 

Third, I think Skemp's argument that these two types of mathematical understandings could be separated into two subjects is quite thought provoking. I think about my own experience where I barely had any formal relational understanding in high school and then took a large amount of proofs courses in university. Similar to high school, I'm not good at remembering content even from my most recent math courses, but I have to say that learning how to do proofs and logic was a good skill for me or anyone to learn. So in that sense I think I would agree with Skemp that relational understanding is not taught enough. At the same time, I think I also agree with Skemp that the instrumental math should also be taught for more direct applications. However, I disagree that they necessarily have to be in separate courses. As a UBC math student there were many proofs courses I took that also required an instrumental understanding. Sometimes I think that the professors would include instrumental understanding in the course to encourage us or allow another skill set to be used. I wonder if this choice is influence by the fact that we are not used to relational understanding. I am really curious if teaching young children relational math would be effective. I think that it may be more applicable for some people to learn this type of math and learn some really important soft skills.