There are many advantages to teaching mathematics without using algorithms. One is that the students have to use their own logic to come up with ways how to do things and how to make sense of it. They have to go through an understanding and discovering process rather than a using process, using meaning using different rules and equations. The advantage of the teacher not ever telling if the answer is right or wrong is that the kids will continue to second guess their logic until they have come to a conclusion that it could not be any other way. This kind of teaching is also beneficial because it gets kids involved and interacting rather than just sitting and listening to a lecture.
The disadvantage to this is that kids may come up with the wrong answer, even after much work and debate on it. If the teacher never tells them it's wrong, they'll continue to do things wrong. I think that the better way to approach this kind of teaching is to sit back and watch the kids construct ideas and learn interactively but when they are sure that they have the right answer, but it is really wrong, the teacher uses questions to have them think through the spots that they went wrong. That way the students are still are able to use their own logic because no particular answer or process was given to them, but they'll be able to construct the correct processes and knowledge.
Subscribe to:
Post Comments (Atom)
I agree with everything you have to say in your first paragraph, but we were also asked to relate our advantages to specific examples in Warrington's paper and I don't see that you have done that.
ReplyDeleteI see your point with the second paragraph, but I don't think it applies to the way Warrington was teaching. Even through she didn't let the students know whether the answers were right or wrong, she was still there to lead and guide her students with questions. So I think what you have specified as a disadvantage, doesn't apply in this case.
You've got strong topic sentences that capture the main point of each paragraph. I like that. I also really appreciated your discussion of the disadvantage. I agree that the teacher should step in and somehow direct the conversation toward further investigation if students settle on a wrong idea. I'm pretty sure that Warrington would have asked additional questions or posed additional problems to help them see the error.
ReplyDeleteI got a little lost on your first advantage. Oh, I just reread it and now I understand what you meant by "using meaning using different rules and equations." Perhaps there's a way to express this that might be easier to read?
I see your point with the disadvantage. Students can get lost arguing the wrong answer. I would say that even when the teacher interferes some students have been so convinced of the wrong answer they don't want to listen to their peer's arguments.
ReplyDeleteI think the one thing you can add to the first paragraph is support from the reading. That would make your argument much stronger.
I agree with a lot of what you have to say. I understand what you said about the advantages how children use their own logic to create answers. I also agree with your point on the disadvantages of not telling the children the answer at some point. But I also think it's good to point out how Warrington idea of teaching could take longer and be more difficult for some children. Kids all learn differently and it could take some longer than others to just think of the different procedures in their head.
ReplyDeleteI thought you did a wonderful job explaining the advantages and disadvantages to Warrington's type of teaching. I completely agree that teachers need to find some way of guiding their students to the correct ideas and answers in mathematics. It is important for a teacher to teach correct principles, otherwise we end up with a case like Benny.
ReplyDeleteHowever, I did get a little lost in the first paragraph when you talked about the "using process". I think it could have been worded a little better, and it could also have been explained better, and a few examples could possibly have been given.