Arbitrary and Necessary

Overall I did not like this article. I felt that Skemp's article on relational versus instrumental knowledge stated these ideas in a better way. When we talk about instrumental knowledge, I think it's the use of 'arbitrary' knowledge. For example, students don't know why a negative times a negative is a positive, they just use it blindly from memory. I think that Hewitt would view this as a necessary fact, that is being taught in an arbitrary way. Whereas relational knowledge is having the deep understanding of why things work. What I gathered was that Hewitt's position was that teachers should be teaching the why, and not teaching necessary things as if they were arbitrary. 

I agree with this sentiment wholeheartedly, however Skemp's breakdown spoke to me more. I did not like in Hewitts article how he asserted that math lies in properties, and that it does not lie in the practicing of conventions. I thought that this was a very narrow view of mathematics, and devalued the work that goes into communicating mathematics. I believe that communicating math is doing math, and inherent to communicating math is using these set standards and conventions properly. You can have all the understanding in the world, but if you are unable to share this understanding, what is it worth? This devaluation of language reminds me of the hierarchy of academia - where sciences are put at the top, and 'softer' subjects such as english are put towards the bottom. I think all subjects are inherently intersectional, and almost tossing aside this aspect of math, to me, seems callous. 

As of right now, I don't think that this article will have an impact on my teaching. Like I mentioned, I totally agree with Skemp's article on relational versus instrumental knowledge, and I think allowing that to influence my teaching is better, because that approach doesn't devalue math communication in the way that I feel this article did.