of Math Education

(Bitte auf deutsch)

We present a sample -- DEMODISK1 -- on our future mathematics teaching material and ideas. Our material can be used as part of a multimedia package as well as independently.

These are the themes of the animation programs available on DEMODISK1 ( Click for still picture samples):

- Algebraic curves from (rotating straight lines) (27 kb) (J. Steiner)
- Envelopes from coupled circular motions and (rotating straight lines) (23 kb) (J. Steiner)
- Orbits in central fields (Newton) (23 kb)

- Conics as Lissajous curves
- Conics in the frame of Apollonius (23 kb) famous contact problem
- Astroid and evolutes of conics

- Cardioid (18 kb): seven different generations
- Circles of momentaneous rotation and of curvature (45 kb) (using Euler's theorem about moving rigid bodies)
- Cycloid (36 kb): Roberval's and Huygens' ingenious ideas

- Trajectory of a cannon ball (Galilean Parabola) (23 kb)
- Circular motion around a sink (Archimedean Spiral) (27 kb)
- With constant angle by candlelight (Cartesian Spiral) (18 kb).

Our teaching materials are designed to be part of the long overdue revision of school and freshman mathematics. They start with new aims from some genuinely unifying points of view.

In contrast to the verbally posed problems found in common textbooks computer technology allows for visual communication. These pictures and animations are a nonverbal invitation to ask relevant questions and to look around for answers -- possibly making use of sources such as 'Mathematica', 'Maple', Dictionaries,.... common sense and friends.

The power of visual communication is used for an efficient revitalising of geometric and analytic problem solving.

The rich concept of a 'curve' serves as a common focus for isolated parts of school mathematics: Geometry, Algebra, Trigonometry, Analytical Geometry, Calculus. Using computer graphics and animation, geometrical methods, particularly so called obsolete precalculus methods of the 17th century, will gain renewed educational importance. The material on curves in Newton's Lucasian Lectures on Algebra, or the problems in the Calculus textbooks of Johann Bernoulli can be exploited using kinematic computer representations like the ones on DEMODISK1.

Download one of the DOS-based animation program samples:

- cardioid animation program 1 (68 kb)
- cardioid animation program 2 (59 kb)
- cycloid animation program (59 kb)
and see for yourself, how you can use beauty as a strong motivator for learning ....

The full DEMODISK1 can be ordered for 15 dollars by E-mail at stowass@math.tu-berlin.de