Commentary on Chapters 8 to 10: Teachers’ Knowledge and Flexibility—Understanding the Roles of Didactical Models and Word Problems in Teaching Integer Operations

The crucial role of teachers in introducing integers to children is highlighted in chapters 8–10, comprising this section. The three chapters discuss (prospective) teachers’ conceptions of integer equations, of children’s thinking about integer expressions, and of the role of some didactical models used in teaching integer addition and subtraction. These different aspects of teacher knowledge and conceptions draw an important picture of characteristics and issues that should be taken into account by teacher educators in preparing teachers for teaching integers. In the first part of our commentary we highlight the main contributions of each of the chapters, focusing on the central findings and on important issues brought up by each chapter. The second part offers a meta-perspective of some of the issues by discussing more general educational implications. In this part we also take the opportunity to express our own insights emerging and associated with the ideas presented in the three chapters.