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Why Study Practical Geometry?

Date: 04/26/97 at 11:03:25
From: K. Superko
Subject: Secondary Math Practical Geometry

I am currently student teaching and my one section of Practical 
Geometry (a group of 11th and 12th graders) finds no use at all for 
the information that we are talking about. I have been stressing that 
Geometry is everywhere and that they may someday use it in their 
lives. I have had them do hands on activities to discover theorems in 
the class, I have them do scavenger hunts in and outside of the 
classroom to see that Geometry is everywhere, but they do not see 
this. What can I do to help them to see just how important Geometry 
and all Math is?

Date: 04/26/97 at 12:21:58
From: Doctor Sarah
Subject: Re: Secondary Math Practical Geometry

Hi there -

Well, we get questions regularly from people who are not able to solve 
problems they have about finding the amount of liquid left in a tank 
lying on its side, or how to cut carpet, or how to make a cone out of 
a rectangle, and we've catalogued them in the Practical Geometry 
section of our Dr. Math archives at   

That's one kind of answer.  However, it's interesting that your group 
of 11th and 12th graders thinks you have a crystal ball.  :-)  Given 
the speed of change in technology and the exponentially increasing 
need for mathematics in the workforce at all levels, from student 
teachers to machine toolmakers to people working with anything having 
to do with computers, to... it's pretty difficult to predict all the 
ways in which your students will profit from a good grounding in 
geometry and other math.  That's a big part of the excitement in 
learning right now - we just don't know!

And then on another level, we are now hearing about the building of 
neural pathways in the brain, and the improvement in thinking 
generally that learning things like math brings to human beings, so 
when you learn math you're learning how to think about other things as 
well as how pi is calculated.  We all need to have a better 
understanding of how the world works, probability, statistics, etc., 
to be able to sort through all the messages that come at us through 
the media.

Nevertheless, students keep asking and math teachers think they have 
to keep answering immediate questions about the utility of math.  In 
our Dr. Math FAQ we've put together some items that might help you 
open a conversation about this with your students - see   

and look toward the bottom of the page for "Why study math?"

You yourself might be interested in a discussion called "Why trig?" 
which we highlighted in the April 14 number of our electronic 
newsletter, the Math Forum Internet News - back issues and information 
on subscribing are at    

This conversation about why people might want to study trigonometry 
took place recently on the math-teach mailing list. Here's how we 
described it in the newsletter.


     You are teaching a group of skeptical high school
     students trigonometry and they want to know
     "Why do we learn Trigonometry?"
                                - Sharon Hessney

  Responses to this question ranged from concrete examples of 
  how trig is used to conversations about the validity and
  utility of the question as stated. Below are a few
  excerpts, and we encourage you to read the full discussion.

     Trig is easy to defend! Any physical situation where 
     two actors don't meet at right angles or are parallel 
     requires trig. This includes virtually any realistic 
     mechanics problem (cars on hills, the trajectory of a 
     baseball or rocket, bridge design, road design, TV 
     picture tube design, etc.) and many optics problems... 
     Taken a step further, understanding many kinds of 
     motion and vibration (sound, light "waves,"...)
     Now, try defending integration by parts...
                           - Tim Corica, The Peddie School

     Why is it that questions from students about different 
     bits of math cause so much agitation among teachers? 
     I wonder how often English teachers get "why should we 
     study Shakespeare?" ...I suspect their answer is that 
     people without passing knowledge of old Will are 
     ignorant...           - GYanos

     I think it is because there is a strong feeling that
     since there are some uses for mathematics, the study
     of mathematics needs to be justified in terms of its
     usefulness... [but what about] history or music or
     literature. Are teachers of those subjects providing
     their students with job skills?
                           - Jack Roach


  The Math Forum's gateway to these and other recommended math
  and education discussions, with directions for subscribing to
  mailing lists, can be found at:   

Good luck with your students.  Maybe they should be telling YOU why 
math will be important - at least to 21st century society generally, 
if not to each of them in particular.  :-)

-Doctor Sarah,  The Math Forum
 Check out our web site!   
Associated Topics:
High School About Math
Middle School About Math

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