D’Ambrosio, B. S., Kastberg, S. E., & dos Santos, J. R. (2010). Learning from student approaches to algebraic proofs. Mathematics Teacher, 103 ( 7), 489-495.
This article discusses the idea that students are not well trained in using algebraic methods to write or create a sufficient proof. Educators can discover if this is the case for their own students by asking them to write up their own ideas on a general statement or theorem. What each student writes will give the educator an idea of the level of understanding the class has reached on proving that particular concept. A study was conducted where the students were given the assignment to write a general statement regarding a pattern that results from squaring numbers with a 5 in the ones place. The students were struggling, so they were each giving a hint consisting of the binomial (10n + 5)^2. Most students thought the statement was obvious and found no point in proving it, so they just wrote specific examples of when it is true. Others set the binomial equal to zero and solved for n. Few students actually used the binomial correctly to algebraically prove the statement. This evidence shows that the students are not experienced in creating sufficient proofs through algebraic means.
If students are more familiar with algebraic proofs they will be more likely to have the ability to create their own sufficient proofs. Through the study conducted above, it was obvious that the students who were tested were uncertain how to connect algebra with written work. In order for students to become familiarized with these proofs, the educator must take the time to see how much knowledge they already have on the subject. As stated in the article, this information can be obtained through written proofs on statements they have never seen proven before. When the educator understands where they students are in the understanding process, they will know which proofs to expose them to, so the students will be better prepared to create their own proofs.
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Kelli,
ReplyDeleteI like how clearly you stated the main idea and walked me through what the article was about. However, after reading just the first paragraph, I felt that the article was just stating a problem and no solution (which might just have been because of what I read and not what the article actually said). However in your second paragraph you went into more detail about what it means to know that students don't know how to do proofs. So I guess that part should have been included in the first paragraph so then in the second paragraph you could have said if you agreed or not and why.
Thanks for your post!
I think that the main idea that you have identified in the topic sentence of your summary paragraph is not a surprising finding. Research has consistently shown that students have difficulty writing and reading proofs, even those who have taken proof courses in college. Because students' difficulties with proof are so well documented, I wonder if the authors were trying to make a different point and using the students' difficulties with this particular proof as evidence. What do you think?
ReplyDeleteI agree that students can benefit from exposure to proofs. But students need much more than just exposure to be able to create their own proofs. Did the authors present any ideas on how teachers might promote students' reading and writing of proofs?
Great topic sentence! I feel like I understand what this article was trying to explain and I think that the topic covered is very true. I felt like the example given in the first paragraph is not enough to determine whether or not students can do proofs. Did the author give any other examples or research to help justify his/her claim? I think the ideas may have been more clear to me if there were more cases studied rather than just one. Awesome job!!
ReplyDeleteI felt that your summary was good, but it left me with questions still. I couldn't really see the conclusion and connection of the example problem that you talked about in the article. I also agree with what Dr. Siebert said, and I wonder if the author was trying to make other points other than students "don't get" proofs, which is fairly obvious. I thought your ideas in the second paragraph were well structured, and well said.
ReplyDeleteThanks for the great post!