Geometry: Measuring Space in One, Two, and Three Dimensions Facilitators Package
Deborah Schifter, Virginia Bastable, and Susan Jo Russell
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Measuring Space in One, Two, and Three Dimensions (MS 123) is one of the seven modules in the Developing Mathematical Ideas Series. It consists of a casebook (sold separately) and this online facilitator’s package that contains everything necessary to prepare for and lead the seminar, including access to the casebook content and classroom videos. Under the guidance of the facilitator, participants examine different attributes of size, develop facility in composing and decomposing shapes, and apply these skills to make sense of formulas for area and volume. They also think through the conceptual issues of length, area, and volume and their complex interrelationships.
The primary goal of Measuring Space in One, Two, and Three Dimensions 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 curriculum also offers teachers opportunities to explore mathematics in collaborative lessons led by facilitators, to share and discuss the work of their own students, to view and discuss video clips of mathematics classrooms, and to read an overview of related research.
The facilitator’s package consists of an Introduction, Preseminar Preparation for the facilitator, and eight sessions:
Session 1: Different Aspects of Size
Session 2: Composing and Decomposing in One, Two, and Three Dimensions
Session 3: Measuring Length: What Is a Unit and How Is It Used?
Session 4: Measuring Area: Structuring Rectangles
Session 5: From Rectangles to Triangles and Trapezoids
Session 6: Measuring Volume: Structuring Boxes
Session 7: Same Shape, Different Measures
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 Measuring Space in One, Two, and Three Dimensions 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 MS 123 and those who piloted the first MS 123 programs.