There can be many advantages to a classroom with a constructivist mindset like the one put for by Warrington. We see that all of Warrington's students were confident in their learning. Each of them created ideas and took responsibility for their own understanding, we learn that the students never gave the typical response of “I don't know how to do this,” indicating that instead of giving up they were willing to keep moving forward. We also see that in addition to creating ideas, these students have come to the desire to have a sound understanding of what everyone else believes. The class discussion comes to a point where only one student does not agree with what the class believes, Warrington tells us that she would not accept the class’s theory until it made sense to her. Something that Warrington does not directly say but eludes to when explaining that one of the students had assigned meaning to a basic arithmetic problem, is that the students gain an understanding of what the number they are using really mean and how they relate to “the real world.” A constructivist classroom yields nicely to a solid, relational understanding.
Of course, like everything, there are bound to be disadvantageous also. Some disadvantageous I came across while reading come mostly from trying to find a balance for this constructivist teaching style. Towards the end of the paper we see that the children asked Warrington “which answer is right?” Since Warrington does not include whether or not that question is answered, it concerns me that the students may never come to a sound understanding if they do not happen to reach the correct answer in their discussions in class. I would think that Warrington would correct the theories of the students if they arrive at an incorrect conclusion, but since this doesn’t happen in the paper, I am left to wonder how far in the wrong direction the class discussions would be allowed to go. If there is no guidance by Warrington in the discussion, because the students are to be their own mathematic authority, the students could very easily construct false ideas about any subject, like we saw with Erlwanger’s study of Benny. If discussions going in the wrong direction are not corrected, great confusion would result. This confusion would not only affect them with their immediate learning but it is highly probable, like in the case with Benny, that students will continue to have a difficult time with future learning. Although constructivism leads to a relational understanding, a classroom with such extremist views may not lead to correct knowledge.
You did a very nice job organizing your blog entry. You had good, clear topic sentences and did a great job following the prompt. You also had good insights into the advantages and disadvantages.
ReplyDeleteAs a student, I think sometimes we want the "fail proof" way to solve a problem. This is how you do it, all the time, hands down, it's right. If students are given that, often they will turn off their brains and stop thinking about what they are doing. The relational understanding is gone and they can't apply what they've learned in a different situation. As a teacher, it's part of our job to decide when to let class discussion continue on its own, and when to step in. I think that if, after awhile, all of the class was convinced of the wrong answer, Warrington would have given them another problem to work through that would make them question what was done in the past. Teachers do need to learn the delicate balance of when to step in.
I agree with the advantages of students who are willing to move forward as oppose to just giving up if they cannot get the right answer the first time. I also agree witht he disadvantage of how far in the wrong direction (away from the right answer and right concepts behind them) might the class discussion go before the teacher steped in. I think this has the potenetial to create a very sandy foundation for the children on of which when later in their education when a teacher tried to build on, would create problems for the student and the teacher.
ReplyDeleteI wonder though if the teacher would really let it get that far. I feel the article sort of left that open. So we might be able to assume the other way that the teacher would step in bfore the class disscussion got too bad.
I completely agree with the point you make about the disadvantage of how much Warrington was involved with the class discussion. The one example where one student was able to persuade the rest of the class was good because the student was correct in their reasoning about the problem. However, like you said, there still is the chance that the students could be wrong, and the discussion could confuse many students. The fact that Warrington didn't say whether she corrected the discussion or not gives cause for worry.
ReplyDeleteOne point that I included, which you mentioned somewhat, is the fact that there even is a discussion. Most math classes don't have much a discussion but rather a teacher who lectures with the occasional question from a student. It's remarkable to me that the students were willing enough to share their ideas. I have never had that experience before.