Thursday, January 14, 2010
Blog Entry #2
In Skemp's article he compares two types of mathematical understanding: relational and instrumental. While these two types have the same end result, the solution to the mathematical problem, they differ in the means of reaching the solution and therefore have different advantages and disadvantages. Skemp describes instrumental understanding as a list of equations, simply plugging numbers into the correct formulas. The advantage of this style of learning is how easily a teacher can teach it and how quickly the student can arrive at the answer. The main disadvantage of instrumental teaching is that the students typically don't understand the reasons behind their solutions, they understand "how" but not "why." Skemp describes relational understanding as having both the "how" and the "why" knowledge. This type of understanding takes a lot longer for the teacher to teach and is thus the reason that it is not used in schools today. This type of teaching has the huge advantage that students understand what they are learning. In this article, Skemp portrays relational as the better of the two understandings.
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I liked the clarity on the importance of moving towards more relational understanding in schools. I thought the advantages and disadvantages that Skemp presents were summarized well in this paragraph. I thought that it might be possible to better describe how the two types of understanding are related. Cause I think that the means to reaching the answers are often the same for both types of understanding, but that the difference lies more in the reasoning behind the steps taken to reach the answer.
ReplyDeleteI really liked the way you organized what you had to say. It was clear as to what the difference was between instrumental and relational understanding. I think you discribed them accurately.
ReplyDeleteWhen you referred to bother instrumental and relational understanding "have the same end result", at first I thought you were trying to say that they were both good forms of understanding because in both the students end up understanding. Though as I read on, I could see that is not what you meant. So I would ask, how would you word that sentence so it is a little more clear as to what you mean? The other question I have is, do you really know that every teacher teaches instrumental understanding? Or did you mean that, "Thus, that is why relational understanding is so uncommon..." I only ask because of the sentence, "This type of understanding takes a lot longer for the teacher to teach and is thus the reason that it is not used in schools today."
I thought you presented your ideas in a very clear and meaningful way. I liked how you expressed Skemp's ideas. I think your post could have been even better if you discussed relational understanding a little more in depth so that the reader could better contrast the two learning styles.
ReplyDeleteI think that the conciseness of your post is one of its greatest strengths. You cover everything, and the order in which you put forward the points is sensible and easy to follow. It feels complete, yet at no point labored.
ReplyDeleteI wasn't quite sure about the sentence "Skemp describes instrumental understanding as a list of equations, simply plugging numbers into the correct formulas"
Not every Mathematical situation has an equation, and unless you wish to define in what sense you mean equation, perhaps algorithm would be a more accurate term.
I like how you have stated the advantages, disadvantages, and meanings of both instrumental and relational understanding. It was very clear what was meant by each. You also did a good job of showing what Skemp said in your own words. I did find that while I was reading there were a few sentences that could be interpreted in various different ways.
ReplyDeleteYou did a nice job organizing your paragraph in manner that was easy to follow.
ReplyDeleteDid Skemp discuss more benefits of relational understanding? If it takes longer, why does he think it is the better way to go?