Deborah Schifter, Virginia Bastable, and Susan Jo Russell,

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Patterns, Functions, and Change (PFC) is one of the seven modules in the Developing Mathematical Ideas Series (DMI), a professional development curriculum designed to help teachers think through the major concepts of K–grade 8 mathematics and examine how children develop those concepts. Under the guidance of the facilitator, participants investigate mathematics content, analyze cases in the casebook as well as recorded classroom lessons, and inquire into the understanding of their own students.

The module consists of a casebook (sold separately) and an online facilitator’s package that contains everything necessary to prepare for and lead the seminar, including access to casebook content and classroom videos. In the course ofPatterns, Functions, and Change,participantsdiscover how the study of repeating patterns and number sequences can lead to ideas of functions, learn how to read tables and graphs to interpret phenomena of change, and use algebraic notation to write function rules. While its particular emphasis is on linear functions, the seminar also provides opportunities to explore quadratic and exponential functions and to examine how various features of a function are seen in graphs, tables, or rules.

The primary goal of Patterns, Functions, and Change is to help elementary and middle school teachers learn the mathematics content they are responsible for teaching in a profound way. To this end, the program asks participants to make sense of the content, recognize where and how the content of their grade is situated in the trajectory of learning from kindergarten through middle school, build connections among different concepts, and analyze student thinking from a mathematical perspective. Through this work, teachers learn how to orient their instruction to specific mathematical goals and to develop a mathematics pedagogy in which student understanding takes center stage.

The facilitator’s package consists of an Introduction to DMI, Preseminar Preparation for the facilitator, and content for eight sessions:

Session 1: Using Patterns to Determine What’s Ahead

Session 2: Representing Situations with Tables, Diagrams, and Graphs

Session 3: Finding Formulas

Session 4: Comparing Linear Functions

Session 5: Does Doubling Work?

Session 6: Examining Non-Constant Rates of Change

Session 7: Functions Without Formulas

Session 8: Wrapping Up

For each session, there is an “Overview,” summarizing the main mathematical themes of the session, a facilitator preparation checklist and mathematics background notes, a “Detailed Agenda,” and “Maxine’s Journal,” a narrative account of the session from the point of view of a facilitator.

The facilitator’s checklist for each session links to all the readings, including those from the casebook, and downloadable materials the facilitator will need to complete or prepare before leading that session. For those sessions that include a video, the checklist also contains a link to that video.

The “Detailed Agenda” describes each activity of a session and the recommended amount of time for that segment. There are three versions of the Detailed Agenda that the facilitator can access: (1) the “reading” form to prepare for giving the seminar, (2) an MS Word document that can be downloaded and annotated by the facilitator, and (3) the “In-Class Agenda” that not only can be scrolled through during a session but also has the video for that session embedded within, providing easy access to the video for displaying to the participants.

“Maxine’s Journal” was created to convey a sense of what a Patterns, Functions, and Change seminar might be like—the type of discussions that might take place, the type of lessons participants might draw from the sessions—and how it might feel to facilitate one. Maxine is a composite character as are the teachers in her seminar. Though she is fiction, Maxine’s journal describes events and individuals observed and recorded by the developers of PFC and those who piloted its first programs.

To sample all that Patterns, Functions, and Change has to offer, click here for a preview of Session 1.