4. Thinking and Spreadsheets

This chapter highlights the dynamic nature of mathematical knowledge over time. Spreadsheets are able to illustrate concrete mathematics for younger students (pets, hair and eye color, favorite ice cream, etc.) into the more advanced abstract form (number) on the same chart. Spreadsheets provide a dimensional perspective of numerical thinking.

Reminding the reader that Euclid described geometry in the fourth century and Gallileo in the Middle Ages invented the telescope, proving the the Earth rotates around the Sun, the author displays many photographs of the famous astronomer and some of the concepts he saw. Whole new mathematical preception and disciplines emerged.

Also illustrated was the Mandelbrot Set of photographed fractals. Fractals are nonsymetrical, geometric shapes. Recently they were difficult to measure because of their uneven sides, but now scientists can. A modern mathematician, Cythia Lanius of the National Order for
Educational Statistics for Kids, wrote the article about fractals. Non-linear mathematics is an example of a new discipline. Many of these studies could not be represented until the discoverors became digitally literate. In the future, software that converts numerical data to 2D and 3D may be available.

As teachers, we can point out to students that mathematics is important, powerful, growing and exciting. It provides another language of expression. We should also make every effort to show them. And if it is not in our personal expertise, we should find local sources to visit. There is, for example, an observatory in Otto from which beautiful colored photographs from space have been taken. Examples of these photographs can be seen at Three Eagles Outfitters in Franklin. The outdoor center also sells professional telescopes and equipment.