Entry #5

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.

Entry #4

Von Glaserfeld’s theory of knowledge is based on experiences we have and understandings that we created based on those experiences. Von Glaserfeld talks about “constructing” knowledge, he doesn’t talk about “acquiring” or “gaining” knowledge. He does this because both terms, acquire and gain, have an implication that there is some standard of truth out in the world and we have to get that from someone or something else, but according to von Glaserfeld, our knowledge is constructed based on what we have experienced and how we perceive things. Our past experiences will continually affect the understanding that we embrace as knowledge. Von Glaserfeld talks about knowledge as being a theory because there is no way for any individual to really know that what they “know” is correct. We believe it to be true but it is not necessarily proven facts. We believe that the knowledge we have constructed is true until we encounter things that challenge our understanding and thus our perceived truth is no longer truth, and we construct a new knowledge for ourselves.

Constructivism is something that can play a huge role in classrooms. Since each student has had different experiences and has gained different knowledge, based on constructivism, it becomes very difficult to teach a large group of children. For this reason it becomes increasingly important to have a reliable way of evaluating a students understanding of a given concept. One way this evaluation could occur would be to have some sort of peer instruction. A simple way of doing this would be to have students explain the answer, and the process of getting the correct answer, on homework assignments to the class each day. Now, obviously every student would not be able to present every single day but a rotating schedule could be implemented. In my opinion this has many benefits, it gives students the opportunity to explain what they did, gives you as the instructor an opportunity to correct any misunderstandings they may have, it gives the rest of their peers the opportunity to hear another perspective, and finally when someone explains their work I believe it helps solidify the concept in their own minds.