I found this reading assignment to be rather interesting. It brought up ideas I never have thought about before, yet ideas that actually have been quite applicable in my experience of schooling. While reading through the article, I was able to draw some distinctions between the the topics of discussion: instrumental and relational understanding.
Instrumental understanding is the type where students have been taught the rules and shortcuts to doing mathematics. Although they have these basic tools necessary to solve problems, they do not always know where they are applicable -- that is where relational understanding comes into play.
Relational understanding is more or less the concepts behind mathematical operations. It is the understanding of why, when, and how. It is possible one may get through a mathematical homework assignment with just the instrumental understanding, but they most likely will not know why they are doing the particular steps, or how to apply it to related problems. If one understands the instrumental AND relational, however, they more likely will be able to apply what they know to related problems. Also, they will be able to retain the knowledge for a longer period of time.
In my own experience, teachers who have taught instrumental understanding are the ones who, for example, would teach for you to just memorize the formula a^2+b^2=c^2 for whenever you see a right triangle. Those that have taught relational understanding are the ones who teach us the formula, but then also teach how the formula came about, what a, b, and c represent, why the formula works, and when to use it. When this is done, I have found that even when I have forgotten what the formula was, the relational understanding enables me to contrive it once again.
Subscribe to:
Post Comments (Atom)
Your first paragraph was good to get your readers attention. You said that what you read in the Skemp's paper was "quite applicable", so of course I want to know what you meant by that. I also enjoyed the rest of your comments. Good job!
ReplyDeleteYou talked about needing to understand relation and instrumental understanding, and then maybe students will be able to apply what they know better, and remember it. I was just wondering if you mentioned understanding both because you view them to be two separate levels of understanding? Or do you think that one encompasses the other? I'm confused. If you do think that relational understanding is instrumental understanding and more, then would it not be sufficient to say a student only would need to understand relationally?
I like how you introduced what you were going to be discussing. We learned in class that we needed to come out and say it, and you did. I liked that it tied into how you think/feel about the article. It drew me in at first and then you got right to the point and you told the reader what this summary was focused on, relational and instrumental understanding.
ReplyDeleteI really liked how you tied the whole paper back to your own experiences, but I feel like I would have learned more if you talked more about what Skemp had said, and how he said it. I think this would have helped me understand the article better. However, the way you wrote it really did help me to understand what you thought of it better. Overall, great job.
You did a very nice job defining the two understandings. I also really enjoyed your personal story applying it.
ReplyDeleteI feel more time could have been spent summarizing Skemp's advantages and disadvantages to each understanding. If relational understanding is so superior, why do some people only want to gain an instrumental understanding?