Wednesday, January 13, 2010
Blog Entry #2
According to Skemp, both relational and instrumental understanding can be beneficial or disadvantageous depending on the situation. Relational understanding is defined as knowing both the why and how behind a problem; whereas, instrumental understanding simply addresses the how and relies either on the teacher’s why/reasoning or does do even address the why. As a result, instrumental relies heavily upon memorization or learning of rules and procedures. These rules and procedures are also part of the relational understanding, but the student also learns the why or the reasoning behind using and formulating these rules and procedures. Therefore, relational understanding encompasses instrumental understanding. Consequently, Skemp favors relational understanding; however, he acknowledges there are benefits and downsides of each type of understanding. For example, since instrumental focuses on the rules and procedures it is more simplistic. However, at the same time it becomes complex quite quickly because the students need to memorize numerous rules; often this memorization results in students giving up on and disliking the subject. As a result, relational seems beneficial because less memory work is involved, so students usually have a more pleasurable experience and continue studying voluntarily. Additionally, relational understanding allows for adaptation and flexibility for the student to apply concepts to new problems. Not only may students apply concepts to new problems, but they may also search for and explore new areas. While relational understanding appears superior, there are times when relational understanding is too difficult for a topic or takes too long to achieve. As a result, the more basic instrumental understanding is preferable. Through instrumental understanding, students can more quickly get answers, which produce a greater sense of success and accomplishment. Overall, there are benefits and downsides to both relational and instrumental understanding and each type can be preferable depending on the situation.
Subscribe to:
Post Comments (Atom)
Becca,
ReplyDeleteYour paragraph is very clear. I felt like it was a perfect summary of the article. You really hit on Skemp's most important points. I particularly liked how when you reflected on the advantages and disadvantages of the two types of understanding, you weaved the sentences altogether. Instead of saying "instrumental is good because of a, b, and c, and bad because of a,b, and c" and "rational is good because of ... and bad because of ...," you allowed the comparing and contrasting to overlap each other and lead one thought from one into another. This to me made me feel like you really internalized what Skemp's thoughts were. One thing that could have helped me understand what was said better would have maybe been to explain Skemp's concepts even more in your own words, so then it wouldn't follow too closely with exactly what he said in the article.
Thank you for your post!
Thanks for your post! I thought it was very clear. I hadnt read anyone elses before I wrote my own,but yours seemed to make more sense than mine did. anyway, I liked what you said about why people tend to give up and dislike the subject when there are too many rules to remember becasue that is so true. I am always curious to hear different ways people may or may not like something, in this case, math. I honestly did not disagree with anything in your blog as i read through. I feel that you did a good job explaining briefly what Skemp was talking about. thanks again!
ReplyDeleteI liked your discussion of the advantages and disadvantages of the two different types of understanding. I agree with Annalee that the way you weaved the ideas together clearly shows that you understand the argument. I also think that you accurately captured the important ideas of the paper.
ReplyDeleteI wondered a little about your definition of relational understanding, particularly the use of the term "problem." I didn't feel like this term really captured what it is that we are understanding the why and how about. I think Skemp might choose to write "rule" or "procedure" in that particular spot. At the same time, I don't think that Skemp viewed mathematics simply as a collection of rules and procedures as well as the concepts that surround them. Instead, I think he thought of mathematics as a series of big ideas, and that procedures and rules were derived from these ideas. So I'm not sure I like replacing "problem" with "rule" or "procedure." Hmm. Do you have any ideas?
I really liked how you explained how instrumental understanding is more simplistic at first but can become very complex the more rules and procedures you have to memorize. I also really liked your overall understanding of Skemp’s article. You explained relational understanding very well. I was a little confused about the teacher’s why/reasoning part. I could have used a little more clarification about what that meant.
ReplyDeleteI really enjoyed your paragraph. I thought it portrayed Skemp's ideas very well, and yet it was in your own words. Your definition of the two different types of understanding was very well written, and your comparisons of them were very well put. However, I think that Skemp still feels that relational understanding is best, even if it takes a long time to grasp it. Instrumental understanding can be quicker to understand, but, in the long run, it ends up costing more time because you have to keep remembering and relearning rules and procedures. I thought your paragraph was really well written though, and the flow of it was great.
ReplyDelete