Название: Mathematics Studies Through Technology: Precalculus, Calculus, And More
Автор: Vladimir Nodelman
Издательство: World Scientific Publishing
Год: 2025
Страниц: 621
Язык: английский
Формат: pdf (true)
Размер: 50.0 MB

This book caters to both prospective and current mathematics educators at the school and university levels, along with their students and anyone intrigued by the possibilities of integrating software into mathematics education.

Mathematics, being a unified science, is best comprehended when its cohesive nature is emphasized and demonstrated to students. Educational software assumes a pivotal role in achieving this pedagogical goal.

The book outlines the author's methodology in utilizing educational software for developing and applying computer models, grounded in a thorough analysis of the subject matter. This approach is vividly illustrated through examples employing a non-profit authoring program (VisuMatica) provided with the book, enabling users to:

- Visualize formal mathematical concepts and their interrelations in theorems,
- Effortlessly explore and uncover features through a user-friendly interface,
- Construct models of the studied material without the need for specialized syntax or programming skills.

Through the guidance of this book, students will discover mathematics as clear, visible, friendly, and enjoyable. In this book, we consider computer software as an educational aid in teaching and learning mathematics, as an organic element of the entire system.

The following types of software are used in teaching mathematics:
• software of general purpose;
• professional software for mathematicians and engineers:
a) Computer Algebra Systems (CAS);
b) Interactive Geometry Software (IGS)/Dynamic Geometry Environments (DGEs);
• software designed specifically for teaching mathematics.

Software of general purpose (PowerPoint, Excel, etc.) is often publicly available and familiar to most students. It can be applied in the study of mathematics, although in the vast majority of cases, it does not support in-depth learning of the subject. On the other hand, the lack of mathematical orientation of this type of software allows to focus students’ attention on typical mistakes and ideas for their correction. Big packages, for example, Microsoft Office, often include support for the possibility of their expansion and adaptation, thanks to the presence of built-in programming tools like Visual Basic for Applications (VBA). With their help, one can develop easily and quickly specialized program modules for studying concrete mathematical subjects.

Computer Algebra Systems (CAS) (Mathematica, Maple, MATLAB, etc.) is software with the ability to create and manipulate mathematical expressions, execute some tasks, and present results in a user-friendly way. Some of them support links with other software products, for example, Wolfram CloudConnector for Excel.

Interactive Geometry Software (IGS)/Dynamic Geometry Environment (DGE) (Cabri, The Geometer’s Sketchpad, Cinderella, Geometry Expression, GeoGebra, etc.) are computer programs that allow us to create mainly geometric constructions and interactively and dynamically manipulate them.

Software, specially designed for teaching mathematics (Autograph, applets, and similar modules), is naturally better than others for this purpose.

The author exemplifies this approach by focusing on the functional line of mathematics, spanning from school basics to advanced university courses in higher mathematics. Importantly, the assimilated ideas and techniques are readily applicable to teaching and learning other areas of mathematics.






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