In her paper, Warrington discusses some advantages to teaching students in a manner where they learn the material based on their own understanding and not a set of algorithms. The students were willing to solve problems using their prior knowledge and understanding as Warrington illustrates when she first put 1 divided by 1/3 on the board. This kind of teaching also encourages discussion in the classroom. Students debate with one another to discover the error of their reasoning and to come to the correct answer. Warrington's students believed that 1/(2/3) was either 6 or 3/2 and thus discussed the answer until they arrived at the correct answer. One girl solved a problem by doubling the original quantities. Warrington argues that this kind of thinking is not present in students that are told what to do. One student illustrates the autonomy that can be developed when she disagrees with all her peers answers and stands alone.
Although Warrington discusses many advantages to teaching in this manner, she does not discuss the disadvantages. As we saw earlier with Benny, some students who are left on their own to discover the principles do not learn correct principles. This will stunt their ability to learn deeper mathematics later on in life. Also, some students in the classroom will rely on the same students to do the problems and will not be learning at all. When it comes time to take a test they won't know how to proceed. I think it is important in mathematics teaching to teach with both relational and instrumental understanding. That way students know why something works and how it works.
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I agree with the disadvantages that you mentioned. I think that some students will definitely tend to rely on others and not be learning at all. It seems as though they just want to be done quickly rather than spend time understanding.
ReplyDeleteI also think that another disadvantage that could be included is that even if students learn the correct principles, they may never realize the quick algorithms and when they move on to other topics that build on this knowledge, they could spend lots of time on these steps that merely lead to the final result.
You did a great job using examples from the paper to back your points.
ReplyDeleteI think that there is less of a chance for a student to become completely lost in this classroom than there is in a traditional classroom. There's a lot of discussion and I think there is more of an environment to question something if you don't understand it.
Great post! I totally agree with you. You came up with some great ideas for disadvantages. I never thought about relating this idea to Benny. That is such a great connection! I think also that one important advantage of this type of classroom is that the students learn to think critically on their own. Awesome job!
ReplyDeleteI definitely agree about the disadvantages you wrote about. You made some good points. Some students would probably be left out of the discussion and rely on other students for the answers if they are left alone. Like you mentioned, they won't be learning. You seemed to hit all of the major points, but one that I might include is that it would be difficult for students to initially adjust to this kind of learning. The majority of classes don't teach this way so students wouldn't start thinking on their own and developing reasoning for awhile.
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