When you are trying to solve a problem, it is convenient to have a teacher tell you correct answers, but their are advantages to a teacher not giving his/her students answers at all. For example, in Warrington's paper, she noted that the students never complained that they didn't know how to do the task at hand and they were eager to take risks. That is because the children weren't bogged down with remembering logarithms, they were then free to discover procedures for themselves. Essentially they were able to construct knowledge freely, and on their own. Another advantage is, students are able to build new knowledge from what they already know. For example, the students used their knowledge of dividing whole numbers to learn how to divide fractions.
Though mathematical discourse based on Constructivism beliefs has a lot of advantages, it also has some disadvantages. It is possible that students could make up procedures that are incorrect, like what Benny did. While some students may be able to connect what they are learning to what they have already learned, others may struggle with determining exactly what they are learning. They may just think of the class discourse as a big class discussion where they just talk about theories. It may be hard for some students to know that their method of procuring an answer is sound.
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I definitely agree with what you said about the potential for the students to get off track like Benny did because if they use their own method it has the potential to be wrong. I think your points were strong but I also think they could be strengthened by adding some more specific examples from the reading.
ReplyDeleteI really agree with the fact that students feel more free when they don't have to just memorize things but can explore the answers to questions. I think you had some really good ideas, but I would have liked to seen more information backing them up. Good job :)
ReplyDeleteI really like the fact you pointed out about how sometimes algorithms can bog students down and make them feel trapped. That's something that I hadn't ever really thought about. :) One thing that would have been nice would have been more development of your ideas. They're SO good, but I wasn't thoroughly convinced because I didn't feel as if there was enough support behind the claims.
ReplyDeleteI appreciated the topic sentences for both paragraphs. I also liked the structure of the first paragraph, because it was clear where the description of each advantage began and ended. With that said, I wondered what you had in mind for the first advantage. Was it that students don't complain, that they engage with any problem given to them, that they weren't boggled down with "logarithms" (you meant algorithms, right?), or that they were able to construct their own solutions?
ReplyDeleteThe structure in the second paragraph wasn't as clear to me, so I didn't know where the description of one disadvantage stopped and the next began. I agree with you that there is a risk of developing wrong solution methods. I doubt, however, that Warrington would let students end their investigation if they developed a wrong method. I also agree that students could easily think the class was a big talk session unless they were helped to see otherwise.