# One-Variable Equations and Inequalities: The Unity of Computational Experiment and Formal Demonstration

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## Abstract

This chapter concerns Type II applications of computing technology to one-variable equations and inequalities. It shows how in the context of TEMP there is a need not only to justify the results of such applications by using theory but also to use theory in order to fill in missing parts left from experimentation. Consequently, the chapter argues for the importance of mathematical knowledge the teachers of mathematics need in order to provide students with Style II assistance in the context of TEMP. The chapter demonstrates how TEMP may include a transition from problem solving to problem posing so that the ACA framework can support Type II technology applications to mathematics teaching. Finally, the chapter shows how the use of technology in the context of experimentation with mathematical concepts can develop entries into the history of mathematics through which connections between the classic concepts and their representations through the modern tools can be established.

## Keywords

Equation Inequality Algebra Graphing Monotone behavior Two-variable inequalities Problem posing Parameterization Proving Arithmetic mean Geometric mean Folium of Descartes Historical perspectives Spreadsheet modeling*The Geometer’s Sketchpad*the

*Graphing Calculator*

*Maple*

*Wolfram Alpha*