Thursday, January 14, 2010
#2
According to Richard G. Skemp, there are two methods of learning and teaching mathematics. The first way is for instrumental understanding which is an understanding of how to find a solution but not necessarily why it works. Instrumental mathematics, he says, is easier to understand and provides an answer quickly which is why it is appealing to some students and teachers. However, this method is harder to remember since it is based mostly on memorization and students will have a harder time seeing how things relate because they will not have an understanding of how they got the right answer. The second method involves relational understanding. Teachers who teach relational mathematics teach the how and why (how to get to the answer and why the steps taken give the solution). Relational mathematics includes everything in instrumental mathematics and then some. He says that relational mathematics is easier to remember and more adaptable. I know, from my own experience as a student that having teachers go into depth about why a process gives us the answer we are looking for can leave me feeling very overwhelmed, lost, and not interested. However, understanding why the process taken provides the answer helps when learning future concepts. Either way a teacher decides to teach, there must be moderation. Like most things in life, focusing too much on one thing is never good. Both methods will give the process to reach the correct answer so neither way is wrong. Teachers should determine how to teach most effectively considering the students and material that is being taught.
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I liked the way you organized your paragraph and brought in both the teacher and the student perspective. I thought the way you expressed the ideas in this paragraph was very clear and easy to follow. I also liked how you said relational includes everything instrumental and then some. This made it very clear to me how the two types of understandings were related.
ReplyDeleteThe only thing I would maybe suggest is when you talk about the disadvantages of relational, use more evidence from what Skemp said instead of just your own experience. Also I think it could be beneficial to point out some more advantages/disadvantages for both types of understanding that Skemp mentions in his article. But really, I thought it was a good paragraph, so great job.
I really liked the organization of this post. It was very smooth and really got to the point without becoming choppy. You also have a good understanding of relational and instrumental understanding. I do however feel that relational understanding is better if it can be achieved. You were right that in some situations instrumental understanding is really the only feasible way of teaching a subject, but I feel that Skemp highly favored relational understanding for most situations.
ReplyDeleteI like that you brought in your own personal experience. It's important to always think of how things apply to us as we read.
ReplyDeleteI didn't understand Skemp's definition of instrumental learning as being easier to understand. It is sometimes easier to compute because you're following an example and just doing exactly what was done before.
Both understandings often yield the right answers. Is being able to get the right answers the ultimate goal in a mathematics classroom?
I liked how you brought your own thoughts into the assignments instead of just Skemps. I think that you are correct when you said that teachers need to get a feel for how their students will best understand and then adapt their teaching to that. One thing that could be made more clear is the fact that instrumental is included in relational; from your article they seemed to be defined as seperate rather than integrated.
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