Thursday, January 14, 2010
Blog Post #2
Thinking back on my years at school, I remember learning math different ways. Somethings I learned without knowing why it worked and others gave me real life application. These different teaching methods are discussed in Richard R. Skemp's article called, "Relational Understanding and Instrumental Understanding". As he goes through the article, he explains what Relational and Instrumental mean, what their advantages are, and how they correlate to each other. Relational Understanding is being able to understand and identify the real life application. This could be as simple as understanding why we use a specific formula to find the circumference of a circle and where we got that formula from. The advantages of this are that is is easier to remember, it can motivate the student to want to learn more, and students can may try to understand new material relationally. The disadvantages are that is takes to long to understand, the teacher has to cut out material, and somethings don't need to be understood. In contrast, Instrumental Understanding can be described as rules without reason. We do something, even though we aren't sure why we do it. For example, we multiply width and height to get the area of a rectangle. Some students don't understand why they are doing it, other than the reason that their teacher told them to. The advantages of this understanding are that it is easier to teach and understand, the rewards are immediate, and the students can get the right answers quickly. The disadvantages are they can be over-loaded with information, the teacher cannot tell the understanding of the concepts, and the students only remember the information for the next test and then lose it. Although Instrumental and Relational are different, they are also very similar. While learning Relational Understanding, you also learn about the Instrumental part of it, whether or not you actually understand it. But is not entirely the other way around. A teacher can almost easily teach Instrumental without teaching any Relational. I think that the best way to teach, is to include both ways of teaching. A good mix of both can help the students and not give them an over-load of material or keep them wondering how it really applies.
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I really like the way you transitioned between talking about the advantages/disadvantages of instrumental/relational into talking about how the two are related. I also thought it was interesting how you included more of a personal/opinion based writing at the beginning and end of your paragraph.
ReplyDeleteWhen you start talking about how the two understandings are related, I am not sure we can say that a teacher can almost easily teach instrumental without teaching relational, because in class we drew a venn diagram where instrumental understanding was imbedded in a relational understanding. So I would think that any part of an instrumental understanding that is taught, is also relational at the same time. Other, than this, your writing was very clear to me.
You did a great job with organizing your paragraph! It was really easy to follow and understandable, especially with your examples of what instrumental and relational understanding are. I almost didnt' read it though becuase it was a really long paragraph. I don't necessarily agree with your last statement about a good mix between both understanding is the best way to teach. This makes it seem like you think they are two sepearte understanding when really, if relational is taught, then instrumental is taught as well. Here is something to think about though, how would you teach relational with the disadvantages given?
ReplyDeleteI really enjoyed reading this, thank you Joanna! Your organization of the paragraph was very easy going and concise. I know that I had a difficult time condensing the information down, so it was nice to see how you were able to do so. I did feel like there was a lot of your feelings on the subject at the beginning and end, which is fine except that if I hadn't read the article myself I would have no idea how Skemp felt about the two types of understanding. All in all, a great summary.
ReplyDeleteOkay, the thing that I liked about this post is also that which I didn't quite appreciate. I thought you did a good job at restating the main ideas between relational and instrumental understanding. I also appreciated the fact that you addressed the advantages and disadvantages of both relational and instrumental understanding. However, I felt as if it was a bit of a laundry listing of Skemp's ideas. In the future I would try to think of different ways to relay the necessary information without just stating them all one after the other. I hope that makes sense. You did a really good job though. :)
ReplyDeleteI liked the way that you transitioned between different ideas in the paragraph. I thought that you captured many of Skemp's ideas about the pros and cons of each type of understanding.
ReplyDeleteAlthough I appreciated hearing about your own thinking in regards to the two types of understanding, I would suggest that you leave this part out of summary paragraphs. In mathematics education writing, we are very careful to distinguish between our own thinking and the person we are trying to summarize.
I also felt that your definition of relational understanding did not quite match what Skemp had in mind. I think the example immediately following the definition was much closer to how Skemp thought about relational understanding than the definition in the preceding sentence. I think of relational understanding as knowing the rules and procedures, as well as why they work and when to use them. Often this is connected to real life applications, but doesn't necessarily have to be so.