Mathematics: Explaining and modeling content – TeachingWorks Resource Library

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Making mathematics topics and practices explicit

Novices learn the definition, key moves, and considerations for determining whether and when to use modeling to make mathematical practices explicit to students. They practice modeling the use of area models and the number line to solve problems.

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Adapted from:
McDonald, Kazemi, and Kavanagh, 2013; Lampert et al., 2013;
Teacher Education by Design

Introduce

"Modeling" means many things, and if misused, it can rob students of opportunities to do complex cognitive work. Novices are introduced to the practice's definition, and they learn considerations for deciding whether and when to use modeling to make mathematics practice explicit.

Prepare

Novices plan and practice modeling a grade 1 math task in peer run-throughs and a rehearsal

Enact

Novices film themselves modeling a grade 4 math task using an area model.

Analyze

Novices independently annotate video of themselves modeling, then write guided reflection on the moves they used and ways to continue refining their practice.

Activity 1

Examining common definitions of modeling

Activity 1

In this introductory activity, novices will examine definitions of modeling that exist in the education field and work to clarify what is and is not meant by modeling in the work of explaining and modeling content, practices, and strategies.

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Activity 2

Comparing the work of demonstrating, explaining, and modeling

Activity 2

In this activity, novices learn the distinction between demonstrating, explaining, and modeling by analyzing video examples of each and identifying key modeling moves.

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Activity 3

Considerations for determining when to model

Activity 3

Novices will learn a set of considerations that will help them to determine whether modeling is an appropriate instructional strategy for their students at a given time, or if modeling at that time would prevent students from engaging in cognitively demanding work. They will then apply the set of considerations to multiple scenarios.

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Activity 4

Peer practice and rehearsal

Activity 4

In this activity, novices will work first with peers to use a set of planning questions and a planning tool to design and try out the work of modeling subtraction on the number line. After working with their peers, one novice will rehearse modeling with coaching from the teacher educator.

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Activity 5

Modeling a mathematics task

Activity 5

Novices recompose the practice of modeling using an area model to multiply. Unlike typical enactment, this task involves novices filming their practice without students present.

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Activity 6

Analysis of multiplication modeling

Activity 6

In this activity, novices independently watch and annotate their modeling video to identify specific moves the made and ways they can continue to refine their practice.

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