Thursday, January 14, 2010
Understanding, more than just a word
When does a child truly understand mathematical concepts? Does it have to do with gettign correct answers on homework assignments and tests, or is it more than that? Richard R. Skemp thinks that -- to say a student understands is ambiguous, because "to understand" can have two meanings. According to him, there is relational understanding, which most people are familar with, and there is instumental understanding. Relational understanding means that a person comprehends how to do something and why. Instumental understanding is knowing what to do, but not knowing why you do it. Thus, relational understanding encompasses instrumental understanding. That might be why instrumental understanding is found most common. It is the most easily taught considering the students need only to know how to solve a problem and not why. This means they only need to memorize formulas or rules without understanding why they work. Relational understanding on the other hand, may enable the students to understand why and how, but unfortunately it takes longer to teach. The overall advantage to teaching relational understanding over instrumental is that it enables students to adapt methods to various problems.
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I agree with almost everything that was said here. The reason for this is that you did a good job of summarizing the material, as that was the goal of the paragraph. Your paragraph summarizes the material well and I goes over just about all of the material that we were supposed to cover. I thought you did a good job of simplifying the relational and instrumental understanding. I think it might have been good to go into a little more depth with would be your last sentence. In order to help others (who haven't read the article) better understand relational understand, I think you could expand on the "why" in your definition.
ReplyDeleteI think you did a great job summarizing the material in the article in your own words. You made the connection between relational and instrumental understanding very clear and concise. However, I was confused by the "why" in your paragraph. What exactly was meant by why? I would understand it more clearly if you explained the what the why refers to.
ReplyDeleteI really enjoyed the way you first of all, set up your summary, and then on top of that, how you showed that it was Skemp's ideas. That was the assignment after all, and you mentioned him fairly and explained that it was from his article that you were getting these ideas.
ReplyDeleteIf I were to change anything about this, it would only be that I would add more. I feel like you talked about everything that was necessary, but I would have loved to read more about the details of each, the pros and cons. Not just the basics on them, but specifically examples of how each can be a great way to learn, and how they could possibly be detrimental. Really though, I enjoyed reading your summary. Good job.
You did a good job of organizing and condensing the information to just produce a summary. You also did well in being clear and defining the points. I would have liked to have "students" replaced by the they for a more professional style as well as saying "the why" could have been put better.
ReplyDeleteI like how you followed the instruction to write a blog summarizing Skemp’s article, and I think you did a good job of doing that. I came away seeing what Skemp said from a different perspective and I think your summery was great. You had all the right ideas in your paragraph though I can see that a different structure might be beneficial to the reader. I find that when a blog has a good title sentence, it is a lot easier to see the fulfillment of the author’s purpose throughout the whole blog.
ReplyDeleteI really liked your title and you did a nice job discussing the points.
ReplyDeleteWhile a major benefit to relational understanding is adaptability, I think Skemp also mentioned a few other benefits in his paper.