Math Forum Internet News

Volume 2, Number 15

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14 April 1997                                 Vol. 2, No. 15


Well Connected Educator | Building Model Surfaces | Why Trig?



     A publishing center and forum where teachers,
     administrators, parents, and others write about
     educational technology, join in conversations,
     and learn from one another.

Nominate your favorite classroom use or professional
development site for the Teachers' Choice Web selection
contest... join author Howard Rheingold in an on-line Forum
and discuss the varying quality of information, the dangers
of using old models, the opportunities of new models, and
how to move into the future... or earn a stipend by writing
about what you do in the classroom for publication on this

New articles and columns:

  - Can an email project create friendship links across
      the generations?
  - Can computers make language barriers disappear?
  - Who is best equipped to help students and teachers
      learn to use a 'library without walls'?
  - How does a teacher provide help with topics beyond
      his range of knowledge?
  - Does television mix well with school work?

A project of the Global SchoolNet Foundation.



At the Math Forum we're interested in the use of physical
models as aids in understanding three-dimensional surfaces.
Joan Hoffmann (Swarthmore '96) has created some pages for
building surfaces discussed in multi-variable calculus.
Using yarn, she shows how to:

  - trace a sine curve around the inside of a soda bottle;
  - construct a simple or economy (appropriate for group
      learning situations) hyperbolic paraboloid in a
      cardboard box;
  - using foam board, cardboard, a sharp X-acto blade, and
      glue, make f(x,y) = (x^2 * y) / (x^4 + y^2).

Do you have models of your own? Write up instructions for
building them and submit them to

       the Math Forum Internet Newsletter editors



   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:


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