Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed—Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features:
- Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts.
- Practice Problems provide opportunities to apply what has been learned and complete proofs.
- Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students.
Changes in the Second Edition
- New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination
- New problems, simpler proofs, and more illustrative examples
- Answers and hints for selected problems provided
Table of Contents
Notes to the Reader/Professor
What is New in the Second Edition
Chapter 1 Intuition and Proof
Chapter 2 Basics of Number Theory
Chapter 3 Theory of Equations
Chapter 4 Measurement: Area and Volume
Chapter 5 The Triangle: Its Study and Consequences
Chapter 6 Introduction to Non-Euclidean Geometry
Chapter 7 Constructions and Three Problems of Antiquity
Chapter 8 Building the Real Number System
Chapter 9 Building the Complex Numbers
Chapter 10 Functions and Modeling
Chapter 11 Geometric Transformations
Chapter 12 Trigonometry
Chapter 13 Data Analysis and Probability
Hints and Answers for Selected Problems
Alan Sultan is Professor of Mathematics at Queens College of the City University of New York, USA.
Alice F. Artzt is Professor of Secondary Mathematics Education at Queens College of the City University of New York, USA.