In Erlwanger's paper about Benny's knowledge of fractions, his most important point was that students must have a relational understanding of math concepts. Benny did not know the rules to fraction arithmetic, such as addition, subtraction, multiplication, and division, so he made up his own rules that where not correct. He was not taught the rules, let alone why they work, so he thought that the rules (which he made up) were random and did not make sense. This was confusing for him and led him to think of arithmetic of fractions as a "wild goose chase."
This is, absolutely, still applicable for math teachers today. Students must be taught not only the rules but why they are necessary to come to the correct solution of a problem. Like we read in Skemp's article, relational understanding is easier to remember because it should make sense. If Benny would have had a teacher that taught him the correct rules and why they work, he would have been much happier mathlete!
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ReplyDeleteGreat blog! I totally agree that teachers appeal to relational understanding so that the math will make sense. I also found this to be a main point in Erlwanger's article. It is important that students are taught the information so they don't make incorrect assumptions. I wonder if it would be better if your first sentence could be a stronger topic sentence. Maybe you could state what exactly is applicable for math in the first sentence that way the reader knows what you mean right away. Great Job!!
ReplyDeleteI completely agree about the main point of the article. Erlwanger definitely emphasized the importance of relational understanding and knowing why something works instead of just knowing that it works. You also made a good point about it being applicable today. The only suggestion I have is that I could have used a little bit more of an explanation in the second paragraph. I would have maybe included more ideas directly from Erlwanger or more ideas about how it is applicable today.
ReplyDeleteI agree that perhaps Erlwanger's most important point was that students need to develop a relational understanding of mathematics. But do you think this was also his MAIN point? Your Paragraph 1 does not convince me that the point you identify as important is something that is addressed in a majority of the paper. Is it possible that the importance of relational understanding is merely an argument in support of a larger, more central point of the article? Or do you think you could provide more evidence that relational understanding was the central point of the paper?
ReplyDeleteI agree that relational understanding is the most effective and that teachers need to actually teach this to their students. The only thing I would suggest is to maybe elaborate on your points a little bit in the second paragraph so it isn't so broad. Great job.
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