In von Glasersfeld's article about constructivism, he argues how people "construct" knowledge through their experiences. People do not acquire knowledge in a classroom or through lectures. As we live each day, we go through different experiences. From these experiences, we draw conclusions about different subject matters. One does not learn to shoot a basket without having the experience of standing before the basket with a ball and learning the proper technique to shoot the ball. After one has experienced how it feels to stand correctly and shoot, one constructs a knowledge of how to shoot. One also learns how not to shoot, and this also becomes part of the constructed knowledge. Everyone will learn different things from the same or similar situation. Not everyone will draw the same conclusions from their experiences.
In mathematics education, it is important to remember that everyone learns different things from the same situation. When a teacher defines a word or teaches a principle, not every student will understand the word or principle in the same way. Mathematics, as von Glasersfeld states with constructivism, is an individual learning experience. To teach my students, I would instruct them on how to do a certain problem, teaching them why it works and how it works, and then allow them time to do many example problems so they can construct their own understanding of the principle. To ensure they did the problems right, I would review their work thoroughly and give them feedback.
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You did a really nice job noticing how everyone will learn different things from the same situation because of our past experiences. This was a key idea and you were able to express it in clearly and simply. Additionally, you nicely connected this idea to mathematics teaching today.
ReplyDeleteI am unsure about mathematics being an individual learning experience. I understand that we each learn in our own way (or individually), but we benefit and still learn from experiences from others. I need some clarification about the implications of that sentence.
von Glasersfeld would argue that people never "acquire" knowledge in the sense they never get exactly the understanding that is intended. This is because any experience they have is filtered through their theories for how the world works and what is true. Thus, it's not possible to have an objective experience; it is always colored by a person's existing knowledge. People area always "constructing" knowledge, or make meaning of what they experience, by applying their preexisting knowledge. Thus, "acquiring" knowledge is not possible in any circumstance, not just in classrooms or lectures.
ReplyDeleteI feel like your implication of Von Glasersfeld's theory of knowledge is clearly stated and feel like you tied the two together well. I actually wrote along the same lines for my blog entry and agree that students need the opportunity to teach themselves and learn from their own experience.
ReplyDeleteI really liked what you had to say and felt you explained your implication very well. I agree that people learn differently from situations and that each student will then take different ideas from mathematics taught to them. I would like to know more on what type of problems you would provide the kids, how you would review their work, and also what type of feedback you would give them. Though, overall I completely agree with your idea!
ReplyDeleteYou basketball example is a great way to explain aspects of contructivism. I hadn't really thought of applying it in that way to explain it. Also, I think that personally student's work may be a little more time consuming that other things you could in the classroom to make sure students are understanding the material you're teaching. You could have students work in small groups or partnerships, you could play games in the classroom, you could have students teach aspects of the lesson. I just think there are more effective ways for students to learn aside from getting feedback on their homework.
ReplyDeleteI liked the way you created the example of basketball to illustrate your ideas. I also liked how your structure was easy to follow and flowed nicely. I did not quite agree with some of the descriptions of constructivism. Because von Glasersfeld described all experiences teaching us including lectures and classroom settings. Hands-on activities are not the only things we learn from but also everything we experience.
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