Wednesday, January 13, 2010
In Skemp's paper titled 'Relational Understanding and Instrumental Understanding' Skemp addresses two types of mathematical teaching, those being relational and instrumental. Relational understanding is a way of teaching where students understand both how to do a math problem and why they did it that way; where instrumental understanding is a way of teaching just the how. Instrumental teaching would be much easier and faster, making it possible to cover more material than if teaching in a relational way. But if students are taught only in an instrumental fashion will they be able to apply what they have learned to other similar problems? Probably not. While both methods of teaching get the teaching done and both methods help the student's pass their tests; one method, relational, is better for the students in the long run.
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Erica,
ReplyDeleteOne thing I love about your post is how simple you were able to condense Skemp's thoughts. While I was reading his article, I kept have to re-read each paragraph, trying to comprehend everything he was trying to say. In this short paragraph, you were able to relay everything to me that made me remember how great, and simple, his points could be. One thing that could have helped me relate to Skemp's thoughts better would have been to maybe give a few more descriptions of the advantages and disadvantages because I feel like all of the sudden rational was said to be the best way of learning and I wasn't quite convinced by the end of your paragraph.
Thank you for your post!
I really agree with what you said about each of the types of understanding will get the student the correct answer. It is true and it is probably a reason teachers justify teaching instrumentally. Like you pointed out, instrumental teaching is so much easier and faster to achieve, however students cannot take that knowledge and apply it elsewhere. The only thing I didn't find clear in your paragraph was whether or not there was anything negative about relational understanding. Great post though, I love that you summed it up in a short and sweet paragraph.
ReplyDeleteHaley Bly
I think that you identified one of Skemp's main arguments, namely that instrumental understanding works in the short run because it enables students to produce right answers, but may not be of most help to students in the long run because it doesn't help them remember or apply their knowledge.
ReplyDeleteOne thing that I disagreed with was that relational and instrumental understanding define ways of teaching. I always think of these two terms as ways of defining how somebody might know mathematics, not particularly how somebody might teach mathematics. Particular teaching methods may not be classifiable as either instrumental or relational, because depending on what content the teacher was trying to teach, or what content the students were receptive to learning, that particular teaching method might result in either type of understanding.
I loved your style of writing about instrumental understanding. I think you described it perfectly, accurately highlighted its advantages, but correctly summarized your thoughts on it with the fact that it is not the most useful type of understanding. As I read, I understood your inference that relational understanding accomplished that which instrumental doesn't but it might make for a stronger paragraph to list the vast advantages of relational, according to Skemp.
ReplyDeleteThat was a great summary of the article! I especially liked your summary of instrumental understanding and the pros and cons. I just missed what your thoughts were on the relational understanding. Which one do you think is better?
ReplyDeleteI like how you clearly and simply summarized Skemp's thoughts. I thought you did a good job of listing why instrumental understanding was not as good as relational, but I would have liked to hear more of your thoughts about relational understanding and why it is so much better.
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