Erlwanger's main point is the necessity for reasoning behind mathematical rules. He stresses the need to understand the concepts underlying the procedures. Benny's main problem was that he was not able to derive his rules from mathematical concepts. When Erlwanger questioned Benny's rules, many of them had shaky reasoning. Benny had no idea why his own "rules" were correct, he simply used them. Erlwanger's paper is pointing out that had Benny been taught mathematical concepts, his rules would have made sense to him, and Benny could have enjoyed mathematics.

This goes back to the difference between relational and instrumental understanding. Benny thought math had no reason. He called it magic and he said it didn't make sense, however he was doing very well on his exams and homework assignments. This is a little warning sign to teachers that good grades do not always mean the student understands. Sometimes in math classes we are pressured into working more for the grade and less for the understanding. This is a problem teachers need to try and avoid because as we were shown in Benny's case it is detrimental to actual learning.

This goes back to the difference between relational and instrumental understanding. Benny thought math had no reason. He called it magic and he said it didn't make sense, however he was doing very well on his exams and homework assignments. This is a little warning sign to teachers that good grades do not always mean the student understands. Sometimes in math classes we are pressured into working more for the grade and less for the understanding. This is a problem teachers need to try and avoid because as we were shown in Benny's case it is detrimental to actual learning.

Your second paragraph is written well in that you took a nice spin off of the major point you mentioned in your first paragraph to how it applied today. This seemed to re-strengthen the points you mentioned in your first paragraph.

ReplyDeleteIt would have been helpful in the second paragraph to have some examples of how teachers can avoid causing students to simply work for a grade.

I really liked how you connected both papers and talked about specific things Benny did to show his misunderstanding of math. It did seem to me that the topic sentence was how Benny thought that math had no reason, but ended up being an argument for how students work for grades instead of understanding. I think I would have worded my topic sentence a bit differently to include both valid points that were made in the paragraph.

ReplyDeleteI totally agree with what you said. Teachers need to be careful to make their math class more about learning math than about getting good grades. I would have liked to hear some suggestions regarding ways to help students focus more on learning math instead of focusing on getting good grades.

ReplyDeleteYou did a great job on your first paragraph. It was very clear and easy to read.

ReplyDeleteThe only thing I might add is perhaps a few reasons of why Benny's shaking reasoning came about.