Entrance Slip Week of Sept. 13th: Response to Skemp

One point that Skemp makes that made me stop and think while reading this article is about the two kinds of mathematical mis-matches that can occur between teachers and students. As a math tutor I am seeking to make students understand relationally to enable them to have continuing success in their math classes so this summarization feels very true to me. I think the key to moving students from wanting to learn instrumentally to relationally is interest and engagement with topics that they want a deeper understanding of. The analogy that Skemp makes about music lessons is also very interesting as it reminds me of many classes that I took during my undergrad where ideas were presented but not expanded upon, making it very difficult to imagine applying those ideas farther afield. Another point that sticks out to me is ‘relational schemas are organic in quality’ because I think that is one of our primary goals as educators: to foster a love of learning. Pupils that are able to expand relational knowledge to new ideas, new concepts because they are able to get satisfaction from learning will be much better off in their future studies than their peers who lack that ability.

Skemp raises the issue of whether relational mathematics and instrumental mathematics are two distinct subjects or two ways of understanding the same subject.  I agree that they are so completely different ways of perceiving a topic that they could be considered different subjects, however, I think that ultimately the two are connected. I think that instrumental mathematics is like a brick wall made only of bricks and no mortar while relational mathematics is a complete brick wall with bricks and mortar. Relational mathematics contains everything that you might learn in instrumental mathematics but it goes beyond by connecting all of those pieces and holding them together.