Number and Operations, Part 1: Building A System of Tens Facilitators Package
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Deborah Schifter, Virginia Bastable, and Susan Jo Russell
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Building a System of
Tens, the first module in the seven-part Developing Mathematical Ideas Series, 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 explore the base-ten number structure, consider how that structure is exploited in multidigit computational procedures, and examine how basic concepts of whole numbers reappear when working with decimals.
The primary goal of Building
a System of Tens 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: Students’ Addition and Subtraction Strategies
Session 2: The Base-Ten Structure of Numbers
Session 3: Making Sense of Addition and Subtraction Algorithms
Session 4: Multiplication of Multidigit Numbers
Session 5: Division with Multidigit Numbers
Session 6: Place-Value Representation of Numbers Less than 1
Session 7: Multiplying and Dividing with Decimals
Session 8: Wrapping Up
For each session, there is an overview, summarizing the main mathematical themes of the session, a facilitator preparation checklist plus 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 Building a System of Tens 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 BST and those who piloted the first BSTprograms.
Even if you’re not from the “Show Me” state, we would like to show you Session 2 by clicking here.