The main idea of Erlwanger's paper was that the IPI form of mathematics was not effective because it taught math in a way that forced students to work only individually and to react to situations rather than contemplate them. Erlwanger defended this topic by using examples of his interactions with Benny. Benny's explainations showed that he had to determine the rules of mathematics for himself rather than be taught by a trained teacher. Because of this Benny's conception of math was often wrong. Benny's responces also proved that this form of teaching math made students only seek out the answer the key provided rather than think about how to solve the problem rationally.
One part of Erlwanger's paper that I thought was very applicable for today was his opinion of the role of a teacher. According to IPI mathematics, teachers hardly have a role at all, in fact it is some what ironic that they are even called teachers because they don't actually teach the students. IPI mathematics tries to have the students learn individually. Erlwanger emphasized the importance of a teacher in helping children to understand a concept more fully and to assist when needed. I think this idea of teacher participation is very important in a classroom. Students are better able to understand concepts when a teacher is there to explain it to them, or show them what they are doing wrong and how to fix it. I think a lot of people think they are naturally not good at math, while this may be true for some people, I think that the majority of the time this opinion is formed because an individual had a teacher that did not help or encourage them. I think teachers should be more a part of student learning.
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I think that you have identified the main idea of the paper, namely that IPI is not a good instructional method. I agree with you that the two reasons you list for why IPI fails are reasons Erlwanger gives in the paper. The topic sentence does a good job of preparing me for these two reasons, and the paragraph follows through by talking about these reasons.
ReplyDeleteI think that this paragraph could be even stronger if more description of the context had been included. For example, a description of what things Benny did during a unit might have helped clarify where the problems were. This is particularly true if someone who had not read the paper closely was reading this paragraph. Consider, for example, the statement, "this form of teaching math made students only seek out the answer the key" would make more sense if it was preceded by a description of how Benny's competency was assessed in the class, and the occasional inaccuracies in this assessment.
I agree with you completely that a teacher is a necessary part of mathematics learning. I have seen in many classrooms that students do learn better when a teacher is there to instruct them. I believe that there are many arguments to support having a strong teacher who cares about his or her students' improvement and learning. I would be more convinced of the validity of your statement in today's world if you elaborated more on the arguments in favor of having a teacher instruct.
ReplyDeleteI agree with you as well that teachers need to be a part of the learning process for children and students. You brought out some great points with why students may think they aren't good at math. Teachers can make a huge difference! Some of the things I read seemed obvious, like what IPI is, so I think that if you remember who your audience is (our class) then it will be a tighter paragraph. Great job though!
ReplyDeleteI really thought that your entry was very good and that you did an excellent job of finding a point from the article that still applies today. It was easy to find what your main point was just from reading your topic sentence and it was stated concisely. Although I understood your argument, I think I would have better believed your ideas if there had been more evidence to back up the ideas. I would consider using personal experience or something to solidify your good argument. Overall I enjoyed your entry.
ReplyDeleteO and I also agree, poor Benny.