The Making Of Mathematics
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Making Mathematics Practical: An Approach To Problem Solving
Author: Tin Lam Toh
language: en
Publisher: World Scientific Publishing Company
Release Date: 2011-03-08
This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms.This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed.
The Making of Mathematics
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Making Images with Mathematics
This textbook teaches readers how to turn geometry into an image on a computer screen. This exciting journey begins in the schools of the ancient Greek philosophers, and describes the major events that changed people's perception of geometry. The readers will learn how to see geometry and colors beyond simple mathematical formulas and how to represent geometric shapes, transformations and motions by digital sampling of various mathematical functions. Special multiplatform visualization software developed by the author will allow readers to explore the exciting world of visual immersive mathematics, and the book software repository will provide a starting point for their own sophisticated visualization applications. Making Images with Mathematics serves as a self-contained text for a one-semester computer graphics and visualization course for computer science and engineering students, as well as a reference manual for researchers and developers.