Building Conceptual Understanding through Using Manipulatives and Models in Math
Explore how the intentional use of manipulatives and visual models can deepen students’ conceptual understanding of mathematics through the Concrete–Representational–Abstract (CRA) instructional framework. Rather than using tools as a means for answer-getting, participants will engage in learning experiences that position manipulatives as sense-making tools that support reasoning, discourse, and connections across representations.
Teachers will experience and analyze tasks that model key mathematical concepts using physical manipulatives (concrete), visual and drawn representations (representational), and symbolic equations and numerical representations (abstract). Throughout the session, participants will examine how purposeful transitions between representations support students in building meaning, justifying their thinking, and developing flexible understanding of mathematical ideas.
The learning will also address practical classroom considerations, including routines for distributing, using, and collecting manipulatives; setting expectations for productive struggle and student talk; and anticipating common misconceptions. Teachers will leave with ready-to-use instructional tasks, strategies for managing materials, and a clearer vision for how connecting multiple representations can strengthen equity, access, and understanding for all learners.
June 25, 2026
8:30 AM-3:30 PM CT
GRREC Event Center
230 Technology Way
Bowling Green, KY
- Explain the role of manipulatives within the CRA framework as tools for developing conceptual understanding rather than shortcuts for procedures or answer finding.
- Use concrete manipulatives to model key mathematical concepts and intentionally connect those models to visual representations and abstract equations.
- Identify and implement routines and structures for managing manipulatives that promote productive student engagement, discourse, and sense-making.
- Analyze how connecting multiple representations supports deeper understanding and reduces misconceptions for all learners.
