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Some of the electronic materials I have reviewed seem to be designed to "trick" students into absorbing the material without their really noticing that by trying to make it fun and easy. Some ideas are deeper than that, however, and take work and long periods of thought to understand. It is important for the students to recognize when they are learning and what they have to do to make learning happen. If all they do is gain facts subliminally as part of an entertaining activity, they will not be able to generate appropriate conditions for their own future learning. The ability to organize and separate valuable information is a critical part of learning, and they need to be aware of it when they do it.

I try to address this issue directly with my students, by talking about learning and encouraging them to think about how they go about it. For example, I added a page to my "advice for students" web site that asks the students to look closely at how they learn new material. At issue is the fact that learning is a destructive as well as a constructive process: one must frequently tear down old ideas and replace them with new ones. All too often, students seem to accept only those concepts that fit in with their existing world view, and simply ignore any that conflict with that as irrelevant. In a math course, for example, this may mean that whatever their first impression is of some new object being defined, that is the meaning they will use through the rest of the course even if it is incorrect or grossly incomplete. One result is that I correct the same mistake over and over again for the same student; he never seems to go back and re-evaluate (in light of new information) the things he thinks he knows to be true.

Real learning involves measuring ourselves against the ideas we encounter, and when we come up lacking, that may mean changing ourselves in some fundamental way. I find that many students seem unprepared to do this; indeed they seem virtually unaware of the possibility at times. As I become more sensitive to this, I try to be clearer with my students about ways they can be more effective at self-evaluation, and the roles that homework and study can play in bringing those changes about.

As an educator, my function is not simply to give the students more information, but to change them: to change their idea about what mathematics is; to change their preconceptions of what is important and why; and to change them into citizens who can make informed decisions based on reasoning and understanding. In short, to give them the tools they need to continue their learning throughout the rest of their lives.

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Created: 08 Sep 2001
Last modified: 07 Jan 2002 06:56:20
Comments to: dpvc@union.edu
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