Van de Walle J.A., Karp K.S., Bay-Williams J.M. Elementary and Middle School Mathematics: Teaching Developmentally

9^th Edition. — Pearson Education Limited, 2015. — 709 p. — ISBN13: 9781292097695This is the philosophy behind Elementary and Middle School Mathematics: Teaching Developmentally. John A. Van de Walle wrote this book to help students understand mathematics and become confident in their ability to teach the subject to children in kindergarten through eighth grade. Although he could not have foreseen the changes in mathematics teaching over the last three decades, he was at the forefront of the movement towards a constructivist view of teaching, or teaching developmentally. Constructivism says that children construct their own knowledge. They are not blank slates waiting to absorb whatever the teacher tells them. Teachers must understand both mathematics itself and how students learn mathematics in order to teach it effectively.
Learning through problem solving is another major theme of this book. Students solve problems not just to apply mathematics, but also to learn new mathematics. Effective problems will take into account where students are, the problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn and not be diluted by non-mathematical activities such as cutting or pasting, and the problem must require justifications and explanations for answers and methods. Learning then becomes an outcome of the problem solving process.Teaching Mathematics: Foundations and Perspectives
Teaching Mathematics in the 21st Century
Exploring What It Means to Know and Do Mathematics
Teaching through Problem Solving
Planning in the Problem-Based Classroom
Creating Assessments for Learning
Teaching Mathematics Equitably to All Children
Using Technological Tools to Teach Mathematics
Development of Mathematical Concepts and Procedures
Developing Early Number Concepts and Number Sense
Developing Meanings for the Operations
Developing Basic Fact Fluency
Developing Whole-Number Place-Value Concepts
Developing Strategies for Addition and Subtraction Computation
Developing Strategies for Multiplication and Division Computation
Algebraic Thinking, Equations, and Functions
Developing Fraction Concepts
Developing Fraction Operations
Developing Concepts of Decimals and Percents
Ratios, Proportions, and Proportional Reasoning
Developing Measurement Concepts
Geometric Thinking and Geometric Concepts
Developing Concepts of Data Analysis
Exploring Concepts of Probability
Developing Concepts of Exponents, Integers, and Real Numbers
Appendixes
Standards for Mathematical Practice
NCTM Mathematics Teaching Practices: from Principles to Actions
Guide to Blackline Masters
Activities at a Glance