Monday, January 4, 2010
Writing Assignment 2
Knowing about rational understanding and instrumental understanding is vital if you want to become the best math teacher you can. Rational understanding is knowing the why behind math. If you have a rational understanding of math then you know where your formulas come from and how to apply them to problems and life. Having an instrumental understanding of math means you know how to plug numbers into formulas in order to get right answers. Instrumental understanding is within rational understanding. You can't truly have a rational understanding of math without knowing the instrumental part of it. Teaching a student an instrumental understanding of math does have its benefits though. Students get more immediate feedback, therefore there is less frustration. Instrumental understanding is also just simply easier to grasp at first. But, without a rational understanding all math is is numbers. Change the situation in a problem and suddenly students with an instrumental understanding can't get right answers any more, whereas those with rational understanding can apply their knowledge to multiple situations. Rational understanding also helps you keep math over time. When a student does finally gain a rational understanding then they have greater satisfaction than when they simply were able to find right answers. Instrumental understanding is important, but it can become useless without gainging a rational understanding.
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I really like how your own thoughts and opinions were present throughout your entire summary. It made it feel less like the same old dull math jargon. Though I couldn't help but feel a little lead on without any results here and there. Let me explain. Especially on your very first sentence when you said "knowing about... understanding is vital if you want to become the best math teacher." I wanted to know why you thought so. So while the summary was great, your own thoughts seemed to be only half brought out and I was hoping to see your view of it too.
ReplyDeleteYou did a great job describing the importance of relational understanding. I thought that you explained all the sides of relational understanding really well. You also had a really good summary describing both the advantages and disadvantages of instrumental understanding. I didn't really understand if there were any disadvantages to relational understanding. I felt that Skemp pointed out a few of them in the article, although they are minor. You point out the advantages of instrumental knowledge which the disadvantages of relational, but I wonder if it would be better to explicitly state the disadvantages of relational so the reader can see that both instrumental and relational have advantages as well as disadvantages. I thought this was a really good summary of what Skemp was trying to explain. Great job!
ReplyDeleteHey I found your blog! It was great - not elementary at all. :)
ReplyDeleteAnyway, I really liked you opening sentence that it is crucial for one to understand the difference between relational and instrumental understanding in order to become a great math teacher. I thing that is very important as well.
I am not sure I feel as wonderful about the last sentence, however. Although knowing only instrumental understanding is not as useful as knowing relational, I would not consider knowing only instrumental understanding as being useless. It still has advantages like getting good grades on assignments and tests because the student remembered the formula, etc.
You did a really nice job summarizing the two types of understanding. You also did a great job applying it to math teachers so the article has meaning for us.
ReplyDeleteWhy does relational understanding help you keep math over time?