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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

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?

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?

The third, and perhaps the most important, is self-defense:

  The Importance of Math

  Understanding Graphs

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

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
Associated Topics:
High School About Math
High School Euclidean/Plane Geometry

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