Effective mathematics instruction involves posing tasks that engage students in the mathematics they are expected to learn. Then, by allowing students to interact with and productively struggle with their own mathematical ideas and their own strategies, they will learn to see the connections among mathematical topics and the real world. Students value mathematics and feel empowered to use it.
[…]we have several objectives in the tenth edition of this textbook:
1. Illustrate what it means to teach mathematics using a problem-based approach.
2. Serve as a go-to reference for all of the mathematics content suggested for grades preK–8 as recommended in the Common Core State Standards (NGA Center & CCSSO, 2010) and in standards used in other states, and for the research-based strategies that illustrate how students best learn this content.
3. Present a practical resource of robust, problem-based activities and tasks that can engage students in the use of significant mathematical concepts and skills.
4. Focus attention on student thinking, including the ways students might reason about numbers, and possible challenges and misconceptions they might have. (Elementary and Middle School Mathematics: Teaching Developmentally 10th Edition; John Van de Walle, Karen Karp, Jennifer Bay-Williams; Pearson ; Preface: Page xiii)