Math Forum Internet News

Volume 2, Number 35

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1 September 1997                                 Vol. 2, No. 35


Math & Children's Lit | Real Analysis - Wachsmuth | What is Algebra?


Reviews of books for kids, ideas for ways to use them in the
classroom, and collections of math books and activities.

Articles and sections from Carol Hurst's professional books
for teachers and librarians have been reformatted to create
an interactive collection of information. The activities and 
discussions are most appropriate for those working with
students in grades K-4. Included are:

    - Math Out Loud: Math and the Oral Traditions
    - Time and Time Travel Fantasies
    - Math Month in the Library
    - Books in the Math Program

  Sample Chapters
    - Math and My Place in Space
    - Math and Mud Flat Olympics
    - Patterns and Picture Books
    - Data Gathering and Picture Books
    - Computation and Picture Books

  Picturing Math - a book by Carol Hurst and Rebecca Otis.
    - Using Picture Books in the Math Curriculum, for
      Pre-K through 2nd Grade.

Other curriculum areas and professional topics can be found
on Carol Hurst's Children's Literature site at:





    An online, interactive textbook for Real Analysis or
    Advanced Calculus in one real variable. Chapters include:

       - Sets and Relations
       - Infinity and Induction
       - Sequences of Numbers
       - Series of Numbers
       - Topology
       - Continuity and Differentiation
       - The Integral
       - Sequences of Functions
       - Metric Spaces

    "Historical tidbits" are also provided for the following

       - Abel
       - Archimedes
       - Bernoulli
       - Bolzano
       - Cantor
       - Cauchy
       - De Morgan
       - Euclid
       - Euler
       - Peano
       - Weierstrass
       - Zeno of Elea

    A glossary rounds out the presentation.

    Bert G. Wachsmuth is Assistant Professor of Mathematics
    and Computer Science at Seton Hall University, South
    Orange, NJ.



The TI-92 now has an algebraic manipulator; what implications
does this have for the algebra curriculum?

After a talk given at the Association of Mathematics Teacher
Educators' Conference Within A Conference during the April
NCTM meetings in Minneapolis, Blake Peterson initiated this
discussion on the AMTE list. He began the conversation with
some initial thoughts and comments:

 - Algebra is to Calculus as the alphabet is to reading.
 - Why do we still teach factoring - what is the underlying
   idea of factoring polynomials?
 - Now that the TI-92 can symbolically solve equations, do
   we still continue to have students solve pages and pages
   of them? What is the underlying idea of solving equations?

A small part of the discussion follows, and we think you'll
enjoy the rest:

 - Algebra is a powerful symbolic way of modeling situations
   in the world. It has value and beauty in its own right.
                                     - Cathy Wick

 - Is it possible to engage in algebraic thinking/reasoning
   without using algebraic symbols?
                                     - Libby Krussel

 - Just recently I opened a webpage that integrates functions.
   One feature allowed me to select a function at random and
   with the click of a button its integral would appear.
   (It had been over 30 years since I had seen many of these
   functions.) As I experienced this "magic" I was suddenly
   struck with the question, "How do I know these are correct?"
                                     - J. Wendell Wyatt

 - ...about the use of the TI 92... students who know the
   material find the technology beneficial, but students who
   do not know the material find the technology to be an
   additional impediment which acts as a barrier to learning.
                                     - Steve Wilson

 - We can't teach algebra in a vacuum. We need to give
   students meaningful situations early where algebra can be
   used to model and clarify those situations.
                                     - Barbara Muenster

For subscription information and a link to the Math Forum's
AMTE discussion list archive, see:


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