Thursday, January 14, 2010
Blog Entry #2
While instrumental understanding is necessary the focus, for both students and teachers, should be relational understanding. Instrumental understanding is the way in which students work through problems. It is very similar to the term “plug-and-chug”. If you are given point A and they want you to find point B, it is through instrumental understanding that you will get there. It is quick and easy to teach this; however, if relational understanding is taught (and learned) then the basic understanding of how to get to from A to B is apparent and may even be reached through different methods. Even more importantly the operation of moving from A to B has meaning and value. Relational understanding is allowing the students to fully grasp the concepts and the meaning in the math. Skemp uses the analogy of a city, where instrumental understanding is specific directions from of place to another. This is the fastest route and can be memorized quickly. In this analogy relational understanding is becoming familiar with the city this allows the individual to find the fastest way from point A to point B, and it may take him longer to find that route; however, once he is familiar with the city he can move from place to place with a full understanding of where he is and he can not only move from A to B but also to F and G without getting lost. Instrumental understanding has value but only in the short term. If we want progress in mathematics for students then we need to focus on teaching and learning relational understanding.
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ReplyDeleteI felt that this summary of Skemp's ideas became a summary of his analogies. You summarized Skemps analogy exactly to what he meant, but it confusd me as a reader in what relational and instrumental understanding is and the connection between them. Otherwise, I liked how you explained Skemp's analogy. Although, does reltional understanding really help someone find the fastest way to point A to point B, or does it just help that person see the big picture?
ReplyDeleteWhen I read this paper for the first time, it was Skemp's analogy to traversing a cityscape that was most persuasive to me. It just so happened that I had recently moved to San Diego, and being a new resident of a large city made me appreciate the value of relational understanding. So I can understand why you value this analogy.
ReplyDeleteI agree with Holly, though, that the paragraph might have been strengthened by talking not only about the analogy, but about learning mathematics in particular. For example, instrumental understanding is first described as a way of working out problems. While this may make sense in relation to the analogy of moving across a city, I always think of instrumental understanding as knowledge of procedures and rules, rather than a particular way of doing mathematics. Naturally, if all you understand are rules and procedures, then you have very limited ways of doing math. Nonetheless, I still like to think about understanding in terms of knowing rather than doing.
The city analogy was one of my favorites too. Even though it takes way longer to learn an entire city versus just one path, it is way more useful in the future.
ReplyDeleteI guess I didn't really feel like your understanding of the assignment was the same as mine. This reminded me more of an analysis of the paper with sort of a summary weaved throughout it.
Having lived in the same town for most of my life, I love the analogy used by Skemp. It's a great way to explain the different types of learning. I'm still not sure if your summary compared the two understandings completely but it was still interesting to read.
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