The Examining Features of Shape Casebook was developed as the key resource for participants’ Developing Mathematical Ideas seminar experience. The thirty-three cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session’s investigation into the concepts of geometric shape and teaching strategies.

Reading and discussing the cases under the guidance of the facilitator actively engages participants in their own learning enterprise as they—

• learn to recognize the key mathematical ideas with which students are grappling;
• consider the types of classroom settings and teaching strategies that support the development of student understanding;
• become aware of how core mathematical ideas develop across the grades;
• work on mathematical concepts and gain better understanding of mathematical content; and
• discover how to continue learning about children and mathematics.

The casebook is composed of eight chapters: the first seven consist of classroom cases from kindergarten through grade 7; chapter 8 is an essay providing an overview of the research related to the situations described in the first seven chapters. The chapters are as follows:

Chapter 1: Describing 2-D and 3-D objects

Chapter 2: Developing meaning for geometric terms

Chapter 3: Making sense of angles

Chapter 4: Creating and applying definitions

Chapter 5: Comparing shapes

Chapter 6: 2-D images of a 3-D world

Chapter 7: Reasoning in geometric contexts

Chapter 8: Highlights of related research