Deborah Schifter, Virginia Bastable, and Susan Jo Russell

PLEASE NOTE: This product can only be purchased via NCTM's Online catalog. Non-web payment methods, such as POs, cannot be used to purchase this item. If you have questions, please call NCTM's Customer Service Department at 800-235-7566. NCTM does not accept returns on digital content purchases. All purchases are final.

Making Meaning for Operations is the second module in the seven-part 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 think through the meaning of each of the four operations on whole numbers, how they are related to each other, what kinds of situations they model, how each can be represented, and how these meanings must be extended and deepened to accommodate fractions.

The primary goal of Making Meaning for Operations 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: Making Meaning for Whole Number Addition and Subtraction
Session 2: Making Meaning for Multiplication and Division
Session 3: When Dividing Doesn’t Come Out Evenly
Session 4: Greater Than, Less Than, Equal To
Session 5: Combining Shares, or Adding Fractions
Session 6: Taking Portions of Portions, or Multiplying Fractions
Session 7: Expanding Ideas About Division in the Context of Fractions
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 Making Meaning for Operations 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 MMO and those who piloted the first MMOprograms.

To sample all that Making Meaning for Operations has to offer, click here for a preview of Session 2.