Friday, January 15, 2010
Relational and Instrumental Understanding in Math Education
In Richard R. Skemp’s article, “Relational Understanding and Instrumental Understanding” we find an excellent exposé about the advantages of relational understanding, one of two different types of teaching and learning in math education. Skemp defines relational understanding as learning both the “what” and “why” of mathematics and instrumental understanding as merely learning the rules without learning the reason behind those rules. They are similar in that they both teach the student the rules of math and many times how to apply those rules. Skemp leads his reader to believe that relational understanding includes in itself most or all of instrumental understanding. Both of these teaching types have been used over the years and each has its advantages and disadvantages. Skemp’s opinion is that relational understanding will give to a student a huge advantage in his or her math education by giving them solid bases on which he or she can develop new ideas. On the other hand, Skemp explains that in instrumental understanding, the student does not receive sufficient “why” to continue holding their interest and to help them actually learn and retain usable math, needful throughout their lives. The article explains in great detail this issue which is of most importance to math educators.
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I really like how you talk about relational and instrumental learning. I really liked this article and it got me thinking a lot about how i want to teach my students.
ReplyDeleteI think i would have tried to use some of my personal understanding in my paragraph.
Your definitions for relational and instrumental understanding were very clear. They followed with the author's descriptions, and the vocabulary coincides with the author's. As a result, I was not confused by the definitions, so I was impressed because I tried to put the definitions into too much of my own words and in the process I think I lost some of the author's meaning.
ReplyDeleteI wonder if there is more reasoning behind Skemp's choosing of relational understanding. It is clear throughout the article that Skemp is an avid fan and thinks highly of relational understanding. I feel this choice can be highlighted through some of the relational understanding's advantages such as how it is more flexibility, it can be applied to new problems, and it requires less memory.
I agree that your definition is very clear. I also think that you do a nice job of capturing some of the most important differences between the two types of understanding, as well as some of the advantages of relational understanding.
ReplyDeleteI noticed that you didn't include any advantages for instrumental understanding. Is this because Skemp didn't include any? Or is it because you didn't think these advantages were very important?
I thought your definitions of each type of understanding were spot on, and I loved how you connected the fact that instrumental is a type of relational. I also thought you did a great job highlighting the advantages of each, maybe I would have mentioned a few disadvantages too? But overall, I feel your summary very accurately portrayed the main points of Skemp's article.
ReplyDeleteI found what you had to say very clear. It was easy to understand what each type of understanding meant. I also thought you described the advantage of relational understanding and disadvantage of instrumental. But are there disadvantages to relational and advantages to instrumental? Yes I believe these can be self-explanatory, but it may be good to describe a bit more. But very nice on being clear!
ReplyDeleteCan you please include advantages of instrumental understanding and more advantages on relational understanding.
ReplyDelete