Computational Experiment Approach to Advanced Secondary Mathematics Curriculum

1. Front Matter

   Pages i-xv

   PDF

2. Theoretical Foundations of Computational Experiment Approach to Secondary Mathematics

   • Sergei Abramovich

   Pages 1-23

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

   • Sergei Abramovich

   Pages 25-62

4. Computationally Supported Study of Quadratic Functions Depending on Parameters

   • Sergei Abramovich

   Pages 63-113

5. Computational Experiment Approach to Equations with Parameters

   • Sergei Abramovich

   Pages 115-163

6. Inequalities with Parameters as Generators of New Meanings

   • Sergei Abramovich

   Pages 165-205

7. Computational Experiments in Trigonometry

   • Sergei Abramovich

   Pages 207-252

8. Advancing STEM Education Through TEMP: Geometric Probabilities

   • Sergei Abramovich

   Pages 253-285

9. Exploring Topics in Elementary Number Theory Through A Computational Experiment

   • Sergei Abramovich

   Pages 287-315

10. Back Matter

    Pages 317-325

    PDF

This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, the book addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book’s pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession.

• collateral learning
• engineering applications of mathematics
• mathematical modelling
• mathemics learning through computational experiment
• pedagogical approaches to use of digital tools
• teacher preparation for use of modern technology in education
• learning and instruction

“This is a comprehensive, well-written, and meticulously organized text on computing technology for secondary mathematics teacher education.” (Steven C. Althoen, zbMATH 1295.97001, 2014)

• State University of New York at Potsdam, Potsdam, USA

  Sergei Abramovich

Policies and ethics