Virginia Bastable, Deborah Schifter, and Susan Jo Russell

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Geometry: Examining Features of Shape (EFS) 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 the casebook content and classroom videos. Examining Features of Shapeparticipants examine aspects of 2-D and 3-D shapes, develop geometric vocabulary, and explore both definitions and properties of geometric objects. The seminar includes a study of angle, similarity, congruence, and the relationships between 3-D objects and their 2-D representations.

The primary goal of Examining Features of Shape 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: Describing 2-D and 3-D Objects

Session 2: Developing Meaning for Geometric Terms

Session 3: Making Sense of Angles

Session 4: Creating and Applying Definitions

Session 5: Comparing Shapes

Session 6: 2-D Images of a 3-D World

Session 7: Reasoning in Geometric Contexts

Session 8: Highlights of Related Research

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 Examining Features of Shape 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 EFS and those who piloted the first EFS programs.

To sample all that Examining Features of Shape has to offer, click here for a preview of Session 2.