I believe one of the main ideas of the article is that a teaching form which enforces purely instrumental understanding can permanently damage a students' attitude towards mathematics. The article suggests that because Benny wasn't given understanding of why the rules for fractions and decimal conversions worked, he developed his own meaning that made sense to him.
This is extremely applicable to us as math education majors because when we are teachers we'll need to make sure that our students know the reasons behind what we are teaching. If we don't, they may dislike math and believe that we are just making it up. They will work only towards "cracking the key" to our tests, and then fail to retain a deep understanding that will be lasting throughout the rest of their education.
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I like the topic sentence for Paragraph 1. I also think that you have identified one of the main points of the paper. However, I think that the paragraph could be strengthened a lot by being much more specific about the arguments that Erlwanger provided to make this point. For example, it is unclear what prevented Benny from being given an understanding of why the rules for fractions and decimal conversions work. What were the specific aspects of the context that were problematic? How did these encourage Benny to develop his own meanings? Why were these meanings problematic?
ReplyDeleteI totally agree with you! Teachers need to make sure students get a relational understanding in mathematics to get the best education! Ithink that you could expand a little more though. I remember reading in Kemp's article a while back though that there were problems with teaching so students receive a relational understanding. How will you work around those problems?
ReplyDeleteI also agree with the main point you brought up. I think it is important that teachers teach students the why's and how's to rules of fractions, etc. Though I do think it could have been expanded on a little bit more. Yet, I do think what you said is important. Especially where you talked about the students thinking the teacher's just made up the rules.
ReplyDeleteI really liked how you mentioned the fact that many students dislike mathematics because they don't fully understand it. I think this is important to express because as future teachers we need to recognize why students dislike math and how to remedy that. From your statement it's clear that the way to do this is to help our students develop a true and deep understanding of mathematics. By doing this they will automatically draw an interest in the subject and be much more likely to succeed down the road.
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