The goal of Erlwanger's paper is to show the danger of learning math strictly on your own, the problems of not teaching the 'why' behind the 'how', and the faulty conclusions that students obtain from not learning correct principles. According to the IPI system of mathematics, Benny was one of the more advanced students in the program, but upon investigation, Erlwanger discovered many false conceptions that Benny had with regards to math. The fact that Benny in effect 'worked the system', or put down the answer he knew was wanted as opposed to what he felt was correct is a good example of this. By working by himself, Benny had come to many false conclusions with regards to many fundamental parts of math such as fractions and decimals. Because Benny didn't understand why fractions worked the way they do, he made many mistakes. Also, the fact that he didn't have someone checking his work was a large contributor to his coming up with incorrect ideas of math. Had someone been more involved in the learning process, they could have corrected many of his erroneous assumptions.
A main argument that is still valid today is that of the danger of learning math strictly on your own. It's still a valid argument because of the fact that math is a difficult subject to learn and if you have to teach yourself it is easy to create false ideas of how and why math works. I currently am a tutor for some students who are taking some online math classes, and I really don't know how they are expected to learn all the material without someone to explain it to. The language of the text is difficult to understand, the homework is challenging and tests the limits of the concepts, not the basics, also, it's easy to get rules confused and use the wrong rule in a situation. Having witnessed first-hand what not having a teacher does to a student, I know it's SO important to have someone involved in the learning process.
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It is clear from the entry that you have read the article, have understood many of the points made in the article, and have connected these points to your own personal experience. In other words, I think that you have read and understood this paper deeply.
ReplyDeleteIn Paragraph 1, however, your understanding of the paper does not come across to make a clear, coherent argument. The topic sentence lists three main points of the paper, but it is not clear from this sentence or the paragraph how these points are related. Certainly Erlwanger would have made some connection between these ideas. Furthermore, the structure of the paragraph does not seem to follow the structure of the topic sentence. In other words, I don't know if all of these three things get discussed. Without evidence to show that these ideas were discussed in detail in the paper, it leaves me wondering if they were really main ideas, or if they were smaller ideas that were proposed to support a larger, more encompassing main idea.
I also agree that trying to learn math strictly on one’s own can lead to one learning false concepts. Even though it can work really well for some people, it is not an affective teaching style to apply in schools. I liked how you used some personal experiences to show how your argument is still applicable today. I could have used more detail about what you meant by dangerous. Maybe some more examples of how it is dangerous to students.
ReplyDeleteI thought what you wrote was very clear and it made a lot of sense to me. I agree that it is difficult to learn math without a teacher and that it can cause a lot of misconceptions of mathematical rules. I also believe, however, that students learn in different ways. Some may learn a new concept by struggling with it a little bit at first and then figuring it out on their own. I think learning styles depend on the individual student.
ReplyDeleteYou took a different point than a lot of the other blogs. I agree that teachers are so vital to the learning process. This is why students make such a big deal about whether or not they like their math teachers.
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