Friday, January 15, 2010
Relational and Instrumental Understanding
In his article, Skemp addresses two types of understanding and expounds on them. He details relational and instrumental understanding in respect to mathematics learning. Instrumental understanding is when students are taught how to apply mathematical principles to situations. They are not taught why something works but rather told that it does work. Learning instrumentally can help students understand better when to use a procedure; it teaches them a blueprint to follow when solving certain types of problems. Students may be better equipped to do their homework, but when a problem is slightly changed on the test, they do not know how to solve the problem because they were never taught the why. However, when students learn relational understanding, they are taught both why something works AND how to apply it. Relational understanding encompasses instrumental understanding. Learning relationally can be more challenging because students must comprehend the theory behind the application, but it is more beneficial in the long run. Students will understand why they use y = mx + b for the equation of a line instead of simply using a formula or equation that was given to them during class.
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I appreciated your topic sentence at the beginning of the paragraph. It clearly introduced the content and purpose of the paragraph. I also thought that your contrast between relational and instrumental understanding captured many of the important differences between the two types of understanding.
ReplyDeleteI was a little surprised by a few of the terms in this paragraph. I wondered if "mathematical principles" was the appropriate term in the second sentence. I think I might have chosen to write "procedure" instead, because that is largely what I associate with instrumental understanding. I also probably would have used the term "concepts underlying" instead of "theory behind" in the eighth sentence. When I think theory can often be understood instrumentally, such as memorizing a theorem or a proof. While someone could probably also do the same thing with a concept, we typically don't. In that same sentence, I think I would have used the term "procedure" instead of "application," mostly because I wasn't sure what exactly was being applied.
Good job at organizing your post. I really enjoyed how you covered all your bases in a very brief paragraph and it was well organized. I am a little confused with your definition of Instrumental Learning. It seems like you put in a little pit of the Relational Understanding with it, although that just may be the way I read it. I would have put in a little bit more information about the comparison of the two. Altogether I think you did a really good job :)
ReplyDeleteI really liked how you covered all the bases of the assignment, but still made your paragraph have the feel that relational understanding is superior to relational, the point I feel Skemp was trying to make in his article. I didn't exactly understand your word choice for describing instrumental understanding, i would have made it simpliar and just said the equations without the why, but i think your way of saying it is more creative.
ReplyDeleteI enjoyed the way that you presented Skemp's ideas on relational and instrumental understanding in a very concise, but adequate paragraph. It was well organized, and put together well. I think it might have been better to compare and contrast the two types of understanding more, so that we could get a better feel of the two types of understanding. I thought you did a good job.
ReplyDeleteI felt your definitions were very easy to follow and I liked the format of your paragraph. I found it easier to follow as you put the disadvantages and advantages after each definition of relational and instrumental understanding. Though, if I had written my paragraph as such, I may not have added the examples given in this paragraph, such as y=mx+b. I found those a bit distracting while describing each definition of understanding. Overall though, I really liked how your wrote your paragraph.
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