Thursday, January 14, 2010
Blog Entry #2
Richard Skemp's article, "Relational Understanding and Instrumental understanding," discusses the two types of understanding that are widely used throughout mathematics. Relational understanding is knowing the reasons behind the arithmetic. When one is given a problem and understands it relationally, then they know both what to do and why they are applying that specific process. One cannot have relational understanding unless they understand the problem instrumentally as well. Instrumental understanding is knowing the rules, arithmetic and equations used for specific math problems. Although students can get answers right by simply knowing the rules and understanding the problem instrumentally, they will not know the reasons in which those rules are applied. Learning instrumentally can be a much faster way to learn how to solve a problem, but in the long run it is much more difficult to maintain because all it is is memorizing rules. In contrast, relational understanding may take longer for students to grasp and extend the time spent on certain subjects. However, if relational understanding is exercised, students will carry that knowledge with them for much longer because they will have a conceptual foundation that they can build off of.
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I really like how you defined relational understanding. I am excited to try and teach students in a relational way. I think it will be very rewarding in the long run.
ReplyDeleteI personally think that instrumental is definitely faster but i think it depends on the students learning type if memorizing formulas is better or not. for me personally it is better for me to memorize formulas and then just apply the formulas.
Your definition of relational understanding was well done. Not only did you take the time to define the type of understanding, but then you went one step further and showed how that applied to problem solving.
ReplyDeleteI feel that Skemp was very pro-relational understanding. As a result, I wonder how important was his discussion about relational understanding and how it allowed for flexibility and adaptation to new problems? I wonder if students truly are more motivated to explore and search new areas when they understand relationally.
I feel like this blog was just a really good summary. It was easy to follow and anyone would now know what rational understanding was versus instrumental understanding.
ReplyDeleteI am trying to find something to critique but I guess maybe you could have gone into more depth of the pros and cons of each kind of understanding.
I appreciated the amount of space you dedicated to making the distinction between instrumental and relational understanding. I also liked your description of the short- and longterm benefits of the different types of understanding.
ReplyDeleteI thought that rjack's comment about flexibility was an important distinction between the two that could have been included. I think it's important to note that relational understanding can be very powerful in extending and applying knowledge. Also, I always think of relational understanding as including knowledge about why the rules and procedures work, not just how or when to use them.
I felt your definitions were very well done. I understood very clearly what you were saying and what you meant when describing both relational and instrumental. I also thought your advantages and disadvantages were very well done. Though, like others said, I think it is important to make sure you're not sounding biased on one understanding. Though I completely agree with how you described them, the author: Skemp, described both with very good, as well as bad things.
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ReplyDeleteYou did very well in explaining the definitions of relational and instrumental understanding. I honestly feel that it was fine that you seemed biased towards relational understanding in this summary because it was a summary of Skemp's article and he was definitely biased in his article.
ReplyDeleteI would have included more of the benefits of both types of understanding, but especially a few benefits that Skemp mentioned from instrumental understanding.