Wednesday, January 13, 2010
Assignment #2
Relational and instrumental understanding are are two different definitions which are used for the word understanding in the field of mathematics. These two types of understanding each have advantages and disadvantages as well as areas where they overlap one another. Richard Skemp described relational understanding as knowing how to solve a problem and why the problem can be solved that way, while instrumental understanding is described by Skemp as only knowing how to solve a problem without understanding why it works. The benefits for relational understanding include being able to adapt what you have learned in one area and apply it to another, the ability to better remember what it is you have learned, becoming an effective goal, and producing a solid base from which to go and gain more mathematical knowledge while exploring the mathematical world. The main disadvantage of relational understanding is that it takes longer to learn the material. There are advantages and disadvantages for instrumental understanding as well. Instrumental understanding is generally easier to learn, faster to learn, and the only way to understand some mathematics because relational understanding would have to include science as well. Instrumental understanding is ill equipped to help a student apply material from one area in mathematics to another, remember what it is they have learned, and be able to solve mathematical problems in more than the one prescribed way. These two types of understanding do overlap one another. Included within relational understanding is instrumental understanding as both types of understanding include the ability to know how to complete the problem, but only relational understanding includes knowing why that works. Relational and Instrumental understanding can also both be successful in helping a student solve a mathematical problem successfully.
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This was a very interesting entry to read. Your opening sentence was very unique compared to what I have read and it was intriguing. You did a very good job of explaining all of the benefits and the disadvantages of relational understanding, I was left feeling a little bit like instrumental understanding had been glossed over. There are many reasons that this might have been so, I would have liked to see a little bit more detail about instrumental understanding. Other than that minor detail you did a wonderful job!
ReplyDeleteThis entry was very concise in my opinion, at least compared to what I wrote. I thought you discussed the advantages and disadvantages well and how Skemp would have like you to understand what he wrote. I liked the word "prescribed" used in your post as well. I may not have read Skemp's article carefully enough but I didn't remember Skemp saying instrumental understanding might be the only way to understand a part of mathematics because science might come involved. So that was my only concern but I'll go back and look at what he said. I remember something about science but not that instrumental was the only way at times.
ReplyDeleteI thought you did a wonderful job of organizing Skemp's points and capturing his main arguments. The paragraph was easy to read and understand. Nice job!
ReplyDeleteOne thing that I noticed that would improve the paragraph would be to make sure that the elements in every list you make share a parallel structure. For example, in your list of the advantages of relational understanding, none of the four items have the same structure. The first two items are almost alike in structure, since both are talking about ability. The match between the two could be made stronger by using either "being able to" or "the ability to" for both of them. The biggest difference comes between the second and third item, where it changes from "ability," a noun, to "becoming," a verb. Furthermore, these final two items don't seem to match very well with the first part of the sentence. In other words, if you removed the first two items in the list, the sentence no longer makes sense. It might have been better if you separated the ideas into two sentences, since the first two items go well together, while the third and fourth items seem to be very different from the first two.