Friday, January 15, 2010
Assignment #2
In the article Relational Understanding and Instrumental Understanding by Richard R. Skemp, two different types of understanding in mathematics were described. Both of these are important and overlap in their description, yet they both have different characteristics that give them advantages and disadvantages. The first style of understanding is instrumental understanding. This is a type where people learn the basic laws of math and possibly the concept of accomplishing a task. They learn the basic steps and memorize things in order to accomplish what is necessary. The other type of understanding in math is called relational understanding. This style overlaps instrumental by people learning laws, concepts and steps on accomplishing a task. Yet, this style is different in the effect that people also learn how to accomplish it, what to do, and why they are using these ideas or this new understanding. Both of these different understandings are very important and have their pros and cons. A disadvantage of instrumental is that people are just learning the basics. They aren't learning why they are using the procedure described, or how someone came up with it in the beginning. This becomes an advantage to someone who learns by relational understanding. As stated earlier, this person can know how and why it is necessary to use a certain procedure for the learned concept. Yet, a disadvantage to relational understanding is that, for many people, it takes time. Learning why and how to apply the idea learned can take quite a while for someone to understand: time they could be using in practicing the task. The advantage to instrumental then takes place of this disadvantage by learning quickly and not taking the time to understand the application. Both of these understandings, though having advantages as well as disadvantages, are important for people and their understanding, yet are just different ways of learning.
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ReplyDeleteYou did a great job describing the disadvantages of relational understanding. Sometimes it is harder to understand the disadvantages of something that seems to make so much sense. You did a great job of pointing out that relational understanding takes time that could be spent practicing the particular procedure. You did a great job comparing the two types of understanding, but I had a hard time understanding the flow of the paragraph. I got confused sometimes as to which type of understanding was being talked about at a particular time. Great Job!
ReplyDeleteI think that you did a nice job of accomplishing the goals of the task, namely to define the two types of understanding and talk about their advantages and disadvantages. I also liked how you pointed out that the two types of understanding might lead to different ways of doing mathematics.
ReplyDeleteLike Haley, I also got a little lost in the as I read through the paragraph. This structure might have been improved by using phrases that clarified the structure of the paragraph, or by using parallel structures in the paragraph. Also, sometimes the terms confused me, such as the phrase "the concept of the task." I'm not really sure what is meant by that.
You did a very good job of explaining relational understanding and how it is the why and how of math. You also organized you’re comments well, with great flow from one idea to the next. I was a little confused on the part about the laws of math and the concepts of accomplishing a task. I think I have a different understanding of what those phases mean. I could have used a little more detail about what you meant by those phrases.
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