I think Erlwanger's most important point in this paper is that the individualism of the IPI program is the biggest downfall of its mathematical teaching system. By taking the reader on a journey with what Benny has learned about mathematics, Erlwanger exposes how individualistic the program is and how mathematics, if learned properly, demands a true teacher to teach students relational mathematics. After spending 4 years learning mathematics through IPI, Benny had learned on his own to distrust the teacher and the answer key by making up his own (false) rules for mathematical basics, especially when dealing the fractions and decimals. Thus, Erlwanger believes that learning individually is not how mathematics should be taught.
I believe that learning should not be an individual experience, which leads me to argue that this point of Erlwanger is applicable in teaching mathematics today because it shows how important a proper math teacher is in today's society. We, as math teachers, need to be trained well enough to teach students relational mathematics, stopping any kind of individual (false) learning as fast as possible in a child's learning lifetime. So not only is it valid to understand that the value of teachers becomes higher as individual learning becomes disintegrated, but we must use stories like Benny's to re-inspire us to continue our mathematical education to help prevent any other child suffering through an individualized program in mathematics.
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Annalee, I really liked what you picked out as the main point. You did a fantastic job using the article and finding Erlwanger's reasoning on why individual learning of mathematics is terrible. The student cannot be expected to teach themselves fractions, and being in this class we get to experience how brutal learning fractions is (and we get the help of a whole class) I really like that you said this is why we are becoming teachers. That really brings this whole story full circle.
ReplyDeleteI really can't think of anything to suggest, so I will just add to your main point that also the teacher needs to give reasoning behind rules. Obviously Benny didn't have that when he made his own rules, and that would have helped him greatly in the long run.
Thanks, Haley Bly :)
You did a very nice job about describing the important role that we have as teachers. I especially liked how you talked about being re-inspired by stories such as Benny's to continue our mathematical education because it is so true. As teachers, we cannot simply stop learning after college, rather we will be continually learning through our daily lives and career. It is so important for us as teachers to recognize that responsibility and adhere to it.
ReplyDeleteI was a little confused by the word proper. To me, proper concerns someone's manner rather than a teaching style. As a result, I wonder if there is another word that better describes an important math teacher in society today or if the word proper could be clarified.
Your paragraph was really good and clearly pointed out the idea that you were trying to argue. I really like how you talked about how Benny's story can motivate us right now as we are pursuing our math education majors. It brought Erlwanger's ideas close to home.
ReplyDeleteThe only thing that I can think of that might help strengthen your paragraph is to use specific evidence/examples other than just Benny in order to be even more convincing that this continues to be a valid concern today. Really great job though :)
I think that you have identified a main point of the article. I also think that you have identified some of the evidence that Erlwanger has used to discredit IPI. At the same time, however, Paragraph 1 was difficult for me to read because I wasn't sure what characteristics of the IPI instructional setting you were including under the term individualism. It would have been helpful to me if you first described what was individualistic, and thus problematic, about IPI instruction. Also, it wasn't clear to me what you meant by "true" teacher. I would also have benefited from a definition of this term.
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