In Warrington's paper she describes her experience of creating fifth and sixth grade class environments in which the students develop understanding of division of fractions without first being given algorithms from the teacher. The results were fascinating and as far as the reader can tell from the article, very successful.
Some advantages of this teaching style as demonstrated in the article are the fact that the students' minds are free to explore and develop without being "shackled" by rules. Another clear advantage is demonstrated by the girl who disagreed with the rest of the group. Warrington describes her as having "intellectual autonomy", which is considered something positive out in the world. Overall the most important advantage is the extended understanding they develop as they work together and can't give up and ask the teacher. They build off of each others' ideas until what that come up with makes sense. After long discussions and heavy thinking, they develop deep and long-lasting understandings of fractions.
A disadvantage could be that some students might lead the discussions; ones who are further along or simply better at division of fractions might continue to grow and construct knowledge while the students not quite as proficient might just tag along and listen to the others without ever grasping how to do it on their own. I also question if the group could have come to a confident conclusion that was incorrect without knowing. If it weren't for the autonomic girl who pointed out that the last part was wrong, they might have stuck with their previous answer; so not being given the correct answer could be a problem.
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I like how you pointed out that the girl that stood up and noticed a problem with the class answer. She was firm in her belief and held strong. I am not sure that the students that don't actively participate in class discussions are those that don't understand the material though. The shy ones can also construct their knowledge, but they may be more reserved in doing so. Altogether, good job :)
ReplyDeleteEven though this assignment didn't require an introductory paragraph at the beginning, I like that you added one. It makes the subsequent comments much clearer.
ReplyDeleteI agree with the advantages that you identified. I would have appreciated if each had been illustrated with an example from the paper. I also share your concern about the disadvantages you identified. I wonder if there might ways to change the class structure so that more students would be required to participate. I also think that Warrington would probably have stepped in and assigned additional tasks to uncover students' wrong answers if students had come to and settled on an incorrect answer.
Very well done! I agree that students receive all of the advantages you listed, and you backed it all up with evidence which is great! Although,I think that Warrington purposely talked about the example with the autonomous girl because that is normally how the class operates. It seems like Warrington is trying to point out that because the students are building their own reasoning, they will eventually come up with the correct answer. Especially since they have a good foundation of what fractions are and so forth. Great post though!
ReplyDeleteI agree that never giving a correct answer could pose problematic to the students. I agree that this is a disadvantage because students may never know that they are right, and what if they are wrong and are not told?
ReplyDeleteIn explaining that students may fall behind I might include something like that if a student at least has a procedure to follow, they are more likely to begin to understand from that point rather if they have no idea what is going on in a classroom such as Warringtons and have no procedure at all.
I agree with the disadvantages that you mentioned. Originally I hadn't thought about the drawback of having children who dominate the class discussion, but it is very true and very common that this happens.
ReplyDeleteIn the last sentence you mentioned that not being given the correct answer could be a problem if they had stuck with their previous answer. I agree with this, but I don't think the teacher would leave them completely on their own with no correct answers.