Wednesday, January 13, 2010
Blog Entry #2
Skemp revolutionized math educators' studies of mathematics with his discovery of rational understanding versus instrumental understanding, which has led the mathematics educational world to analyze and apply his findings. He found that many students and teachers clash with their views on what mathematics understanding means. Instrumental understanding is learning the how without the why. In mathematics, this is most commonly demonstrated though formulas with no meaning to the students. Rational understanding means that the students are learning how and why to every part of mathematics. According to Skemp, these two distinct types of understanding in mathematics are actually connected. Rational understanding is instrumental learning plus so much more. If students understand rationally, then they understand everything that instrumental understanders know plus the why to mathematics as well as applicable skills used in more advanced mathematics problems. Even though they are connected, both have advantages and disadvantages explored by Skemp. Instrumental understanding happens faster and simpler, while making it harder for students to remember mathematics longer and for them to apply their knowledge to different types of problems they did not see in class. On the other hand, rational understanding, although it is harder to grasp each concept at first, should carry a student on for a longer period of time, as well as teach them the skills they can apply to more advanced problems without learning more rules like instrumental understanding would require. Overall, Skemp deeply defined and explained both types of learning and left the reader able to make their own judgments and decisions about mathematical understanding.
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I agree with your ideas and understandings. Your definitions of instrumental and relational learning are consistent with Skemp's article. However, I think that Skemp merely brought what math educators' needed to the surface rather than revolutionize math educator's studies. By this I mean that I believe that it has been an ongoing process, and many math educators have been using it subconsciously. But Skemp realized it and brought it out to everyone. I really like his definitions and completely agree with them. I also agree with what you have written in your blog, not saying that youre wrong at all. Thanks so much for you thoughts!
ReplyDeleteI also think you gave very good definitions! Oh except I think he uses the word “relational” instead of “rational”, but I knew what you meant. :) I would also maybe think about some of the drawbacks of relational learning. For me at least, sometimes relational can be overwhelming or distracting. But like you said, Skemp just gives us the opportunity to chose which type is preferable. Great job!
ReplyDeleteI agree with the advantages and disadvantages of the understandings that you wrote. I was curious, I think he referred to it as relational understanding and not rational. :)
ReplyDeleteYour paragraph was really good! I think you hit on all of the points we were asked too! You did a really good job of keeping your paragraph unbiased.
ReplyDeleteHowever, one area I disagree on is Skemp being unbiased in his article. His article appeared quite biased towards relational understanding.
Good job!
This is a very well written paragraph, along with great organization, you touched on every point we needed to.
ReplyDeleteI agree with Jenepher in the fact that Skemp was definitely biased. When he talked about the pros of instrumental learning he titled the section "Devil's Advocate" .. and then I noticed how weak those arguments were. Very good job overall though :)
You did a really nice job covering the material and distinguishing between relational and instrumental understanding.
ReplyDeleteAre there any more benefits of relational understanding Skemp brought to light in his article?