Deborah Schifter, Virginia Bastable, and Susan Jo Russell

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