Geometry: Examining Features of Shape Facilitators Package
Virginia Bastable, Deborah Schifter, and Susan Jo Russell
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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
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
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.