The Patterns, Functions, and Change Casebook was developed as the key resource for participants’ Developing Mathematical Ideas seminar experience. The twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session’s investigation of how the study of repeating patterns and number sequences can lead to concepts of functions, the learning of reading tables and graphs to interpret phenomena of change, and using algebraic notation to write function rules.

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;
• deepen their own understanding of the Common Core standards for mathematical practice and how to engage their students in them; and
• discover how to continue learning about children and mathematics.

The casebook is composed of eight chapters: the first seven consist of classroom cases spanning the elementary grades; 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       Using patterns to determine what’s ahead

Chapter 2       Representing situations with tables, diagrams, and graphs

Chapter 3       Finding formulas

Chapter 4       Comparing linear functions

Chapter 5       Does doubling work?

Chapter 6       Examining non-constant rate of change

Chapter 7       Functions without formulas

Chapter 8       The Mathematics of Patterns, Functions, and Change for the
                          K–Grade 8 Classroom