Sept 18 - Skemp Article Reflection

While reading Skemp's article "Relational Understanding and Instrumental Understanding" a few things caught my attention. Firstly, the story about Mr. Peter Burney and his students not truly understanding how to find area. I have seen this issue on many occasions and it is something I struggled with how to approach. I have tutored students who mastered problems due to the repetitive nature of the work, but when given a problem slightly different or one that required a little more investigative work, they completely froze and could not move forward because they memorized a mathematical technique (instrumental learning) rather than truly understanding why it worked. This was frustrating and difficult to get around for some students as they had grown accustomed to learning this way in school and were then uncomfortable branching out of their routine. Secondly, I really valued the idea presented about how relational learning developed ideas for understanding a topic which could then be extended to many other topics. I feel this is the way I learned a lot of mathematics in school. I never opted to memorize formulas and instead attempted to understand how they were derived in hopes that once I mastered that concept remembering the formula would no longer be an exercise in memorization, but one of understanding which I could apply to many other situations. I often made connections between formulas or concepts, which helped me better understand and remember them. I guess I never realized I was actively choosing to practice relational understanding. Lastly, Skemp's metaphor relating to the difference between relational and instrumental understanding really grabbed my attention. I think this was very valuable to me mostly because I use metaphors often. They actually help me to remember concepts better when I can associate them with something concrete. This metaphor helped me understand what the two types of understanding were, it was a very clear and helpful association. Getting from A to B is very efficient, but inflexible in some senses. While, learning the whole neighbourhood gives room for exploration and mistakes. Once someone knows the neighbourhood there are an infinite number of paths they can take to get from A to B. This also introduced another teaching strategy to me, using metaphors to help students grasp a concept may be helpful.
After reading Skemp's article I realized that it is impossible for one to live in a world with purely relational understanding or purely instrumental understanding. So I do not feel either is superior. In order to achieve an efficient and complete understanding students must use a combination of both. My stance is based on my own experiences as a learner. I remember as a high school student I often learned the instrumental understanding methods first, then I would fill in the blanks with relational understanding afterwards. I also appreciated instrumental understanding methods because they provided something similar to a mnemonic, which could help me recall simple formulas or actions quickly. However, it was not enough to memorize these methods when attempting more involved problems that combined concepts, so I sought to understand why instead. I think both methods are valuable in their own way and can be used in different scenarios, but in order to achieve mastery, I feel you must use a combination of both relational and instrumental understanding.