In "Learning as a Constructive Activity" von Glasserfeld describes how we come to know what we know through constructivism. von Glasserfield defines construct knowledge as a process of how we come to know things through experience. The term 'constructing' is used rather than 'acquire' because our knowledge is built through reasoning and experience, not simply gained or acquired through hearing it. As in the view of constructivism, we all gain knowledge through our own experience, von Glasserfeld explains that because of this our own personal knowledge is more of a theory because we do not know if what we know about a subject is the same as what someone else knows. This all can come into play with how teachers teach mathematics today.
As according to constructivism, if we gain knowledge through our experiences, then students must be actively involved in the learning process. If they will not learn simply through hearing, they must have more doing and practicing with mathematics so that they can gain more experience and reasoning with the material. As a teacher I would do this by having more in class assignments where the students can work together while practicing a concept and reasoning together about what is being taught. I would also make it possible for them to ask me questions about their homework assignments so that their reasoning and learning could be guided. Through these ways I would hope they could have more meaningful experiences with mathematics material.
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I really enjoyed reading your implication that constructivism has on teaching mathematics. Your ideas were very clearly laid out and explained thoroughly. I agree that if students can create their own experience with mathematics, then they will come to more fully learn the material. You also mentioned that by asking questions their reasoning and learning could be guided, which I think is a good point. One question I have is how else are your ideas connected to constructivism besides students being actively involved?
ReplyDeleteYou are right that the term "construct" is related to learning from experience. von Glasersfeld's point is that when we experience something, we use our theories of how the world works, what things mean, and what is true to make sense of the experience. We can't just absorb the "innate" meaning in the experience, because we have no way of knowing what that innate meaning is supposed to be. Instead, we try to make sense of the experience and determine what it might mean to us. As we interpret the experience, we are "constructing" knowledge of what that experience is about and its implications for our previously constructed theories.
ReplyDeleteI completely agree with what you said about students working together to reason through problems. Getting students to talk to each other helps train them to be able to communicate ideas and validate their own thinking. However, although I am all for "hands on" learning experiences and student involvement, I feel that constructivism implies that learning happens constantly and that students can and do learn from just hearing. Even during lectures, our understanding is either being confirmed or contradicted.
ReplyDeleteI very much agree with what you had to day, and I appreciated that it was clearly explained. Your view on it was not one that I had thought of and I like the idea of letting students work together to help in the learning process. I see how it does connect to constructivism, because of the road block idea, however I probably would have described the connection a little better if I were to use this point. It sounds great, but to me it isn't completely clear. Really good idea though. Great job.
ReplyDeleteYou did a great job! I thought your implications were very well thought out and clear. I thought that that the part about how your plan for teaching would foster constructive learning was a little unclear but other than that it was great.
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