D'Ambrosio, B.S., Kastberg, S.E., Viola dos Santos, J.R., (2010). Learning from student approaches to algebraic proofs. Mathematics Teacher, 103 (7), 489-495.
I think one of the main points that authors are trying to make is that analyzing students work is not only a way, but an important way, to learn the depth of students understanding. They use the example of 12 grade math students and their understanding of algebraic proofs. They go into detail with one question in particular. Prove that if a number ends with a 5 that the number squared will result in an answer that ends with 25. They then give a hint that should start students on an algebraic proof of this topic. They show the work of many different students and they analyze the work of each of the students, and they show what you can learn about each students understanding of how to do an algebraic proof.
I agree that students work should be analyzed in order to ensure that what the teachers are teaching is getting through to the students. It is obvious from the paper that students are having a difficult time understanding specific parts of algebraic proofs. They are having a hard time with understanding the purpose of a variable in an algebraic proof, and they are giving explanations in some places where they could be showing arithmetic. Analyzing the mistakes they make will make a large difference in the teachers ability to help correct the mistakes that the students are making.
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Great summary and analysis of the main point. However I would have liked to seen your own experience in the second paragraph so that it was more personal. Maybe think about a teacher you've had who applied this or give specific examples of what you will do in your classes to implement and learn from this idea. Great job!
ReplyDeleteI think that the first paragraph clearly communicates the main idea. I thought your topic sentence was strong and was clearly supported by the points in the rest of the paragraph. I thought that the summary could have been strengthened further, though, by briefly describing some of the thinking that their analysis of students' work uncovered. You get at some of this in your critique paragraph, but I thought it would be nice if you introduced it in the first paragraph and referred back to it in the second paragraph.
ReplyDeleteYour stance toward the main point of the paper was clear in your critique paragraph. I'm not sure that you really have three main reasons that back up your position. I see the second and third sentences getting at the exact same point. The last sentence also seems very closely related. What other reasons could you give besides the data included in the article for why you agree with the main point? Anything you could use from some of the papers we have read in class? From your own personal experience?
I think you did a really good job explaining the main point of the article. It was a good idea to put in an example of what teachers analyzed, but it would have been stronger if you had put information with it. Maybe some results of the student's proofs. You got me interested in reading the article. Good job :)
ReplyDeleteI was quite interested in the article you talked about in your blog. I felt there could have been some transition phrases (etc.) in your first paragraph when explaining what the article was about, but I liked how you explained the arithmetic proofs described in the article.
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