Thursday, January 14, 2010
Writing Assignment #2
Two types of understanding, as discussed in Richard Skemp's article, include relational understanding and instrumental understanding. Skemp pointed out the importance of recognizing the different meanings of understanding as educators. Relational understanding refers to the "what" and "why" of a concept whereas the instrumental includes memorizing rules and applying them without knowing exactly why or how they can actually be applied. Relational understanding is difficult to teach in the amount of time educators are given, but is definitely the prefered understanding for students to obtain. Intrstrumental understanding is quickly applied by students because they dont need deep explainations. Students often feel more successful with this type of understanding because they get the right answer quickly, without spending time on the "why". The problem, however, comes when the memorized problem comes in a question posed differently from what they memorized. Now instead of just plugging numbers in, they actually need to think about what is going on in the problem, which they never learned. By the definitions, instrumental is actually included in relational understanding, relational just goes deeper into the concept rather than just memorization of rules. Both are important in the learning of mathematics, but the deeper understanding (relational) will prove to be more useful all around application.
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I think you have done a nice job of distinguishing between the two types of understanding. You also captured the main pros and cons of the two types of understanding.
ReplyDeleteI'm not sure which of the first two sentences in the paragraph is your topic sentence. The first paragraph seems to identify the two types of understanding as the topic of the paragraph, but the second sentence suggests a different purpose for the paragraph. Perhaps it would be better to choose just one of these to include in the paragraph.
Also, I felt that the initial definitions of the two types of understanding seemed to set them up as mutually exclusive. I think it might have been clearer if a reference to rules and procedures had also been included in the definition of relational understanding, and not just in the definition of instrumental understanding.
I really liked how you gave an example of how on a test the problem can vary in a way in which one must have relational understanding so that they can reason and think critically in order to find the correct answer. I felt that this example expressed how a slight change in a problem can completely throw off a student who only has an instrumental understanding of the concept. While, on the other hand, a student with a relational understanding can adapt to the slight change and make sense of the problem and therefore can solve it. Also, I appreciated how you mentioned that students feel a sense of success and can gain confidence quickly through instrumental understanding as one of its advantages. I believe that this is the greatest advantage of instrumental understanding and one of the main reasons why mathematics still emphasizes it.
ReplyDeleteMy only criticism is that I would have to agree with Dr. Siebert about how your two definitions at first seemed to set up the two types of understandings to be two unrelated items. However, later on you address this and explain that relational understanding consists instrumental understanding as well.
I think you brought up a great point when you talked about how problems occur for students when questions are posed differently from what they memorized instrumentally.
ReplyDeleteI feel like the definitions could have been a little more detailed, but other than that it was great.
By reading your summary I see your complete understanding of Skemp's ideas on understanding and think you did a great job highlighting some of the most important parts of his article. I felt like the article could have been a little more organized but you were still able to get the point across so good job.
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