How to Motivate Students to Learn Math?
Date: 03/06/2008 at 09:50:25 From: Cara Subject: properties of special quadrilaterals I am a teacher and need to give students a compelling why for learning about properties of special quadrilaterals. In other words, how would learning about properties of special quadrilaterals help students apply this knowledge to a previous use, a current use, or a future use? I need a reason to motivate students to participate in the geoboard activity I have planned. I do NOT want the reason to be because it will help to know when you get to higher math classes or to do well on tests like the state assessment or SAT. Please help.
Date: 03/06/2008 at 11:18:47 From: Doctor Ian Subject: Re: properties of special quadrilaterals Hi Cara, You wrote: >I am a teacher and need to give students a compelling why for >learning about properties of special quadrilaterals. You mean, apart from fun, or making it easier to learn more mathematics later? You might be in trouble there. >In other words, how would learning about properties of special >quadrilaterals help students apply this knowledge to a previous use, >a current use, or a future use? Probably it won't. Any situation I can think of where you would use this information could also be handled without knowing it. >I need a reason to motivate students to participate in the geoboard >activity I have planned. I do NOT want the reason to be because it >will help to know when you get to higher math classes or to do well >on tests like the state assessment or SAT. Please help. It's just my opinion, but in my opinion, the harder you try to "motivate" students this way, the more it works against you, because their experience will tell them that you're not being straight with them. That is, any one of them could go to a public place, like a mall, in a relatively affluent neighborhood, stop 100 randomly-selected people, and ask them what they know about the properties of special quadrilaterals. They would find that only a handful would even know what a "special quadrilateral" is; even fewer would be able to name a property of one; and still fewer would be able to name some practical use for that information. And yet, the majority of these people would be leading relatively successful lives. Which would say a lot about the ostensible "value" of this information. Your students know this, and pretending that they don't just undermines your credibility. Except to a very small number of people, the properties of special quadrilaterals aren't of any importance at all. What IS important, though, is learning how you go about solving a problem that you haven't seen before. If the focus of your activity is on that, and not on the particular results, then you have an easier sell. I like to use this analogy: When you were very young, you spent a lot of time doing things like stacking objects up so you could knock them over. That's not a skill you use anymore, but the time wasn't wasted. The point was never to learn a particular skill, but to develop hand-eye coordination, which is useful in lots of different contexts. Math is the same way. Scientists and engineers use it as a tool for understanding and designing things, but for most people the value of math is that it's like a little jungle gym for the mind. It's a medium in which we can set up problems of increasing complexity, so that students can get practice at learning to solve problems using both creative and organized thought. Once the particular problems have been solved, most people can just forget about the solutions, at least once they graduate. The valuable residue isn't the math itself, but the ability to do things like break problems into sub-problems, the ability to follow a logical chain of reasoning (and detect breaks in the chain), the ability to work backwards from a desired state ("If I knew this, then I could solve the problem; so how can I find that out?"), the ability to abstract or simplify a problem to make it simpler to work on ("What if I had only a dozen of these, instead of several thousand?"), and so on. What's unfortunate is that many teachers emphasize the answers rather than how to deal with the questions; so their students, once they get out of school and forget the answers, are left with nothing. To put it briefly: There's no real reason to know this material, or even to learn it; but there's great value in getting practice at facing a problem that you haven't seen before, and working your way through it. Because that IS something you're going to be doing over and over in your life. To put it another way: The point of solving math problems isn't to be able to remember or use the solutions. It's that by solving lots of math problems, you get a chance to develop strategies for solving ANY kind of problem, and to learn how to work with your own personal strengths and weaknesses as a problem-solver. Buddhists have a metaphor for this: You use a boat to get you across a river, but then you leave the boat behind. You don't continue to carry it with you. It's done its job. Having said all this, there are, I think, three good reasons for learning as much math as you can, including properties of special quadrilaterals. The first is that you just never know what's going to turn out to be useful: Math is Power? http://mathforum.org/library/drmath/view/62716.html The second is that once you realize that math is really just a game, it opens up a lot of possibilities for fun that are hidden if you view it only as a set of tools: Why is Math Interesting? http://mathforum.org/library/drmath/view/52355.html The third, and perhaps the most important, is self-defense: The Importance of Math http://mathforum.org/library/drmath/view/52348.html Understanding Graphs http://mathforum.org/library/drmath/view/61632.html I hope this helps, even though it's probably not what you were hoping for. Write back if you'd like to talk more about this or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 03/13/2008 at 13:34:00 From: Cara Subject: Thank you (properties of special quadrilaterals) Doctor Ian - Thank you so much for your awesome response to my question. I am so impressed with the timeliness and depth with which you answered it! I showed it to my department head (who asked for a copy), and she was so mesmerized that she wanted me to tell you that she wants to marry you:) I also shared it with a professor of a graduate course that I am taking, and she had me share it with our entire class. My husband, an English teacher, also asked for a copy of your response, as it is so important that, as educators, we teach children how to think and problem-solve on their own. I appreciate how much time and thought you put into your remarks; it is nice to know that there are still people out there who take pride in their work and who take what they do seriously. This was my first experience with the "Ask Dr. Math" site. I will most definitely use it again thanks to you! Best wishes to you! ~ Cara
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