GeoGebra is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra view corresponds to an object in the graphics view and vice versa.
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… it is much of a challenge to demonstrate that functions, modelling, and problem solving are all types of generalizing activities, that algebra and indeed all of mathematics is about generalizing patterns.
p 103
The history of the science of algebra is the story of the growth of a technique for representing of finite patterns.
The notion of the importance of pattern is as old as civilization. Every art is founded on the study of patterns.
Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of patterns.(1996)
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