Problem-solving situations that lead to developing diagrams or constructing physical models with manipulative engage students in exploring mathematical ideas and forming mental images about those ideas (Petit, Laird, and Marsden 2010).
These mental images support the development of number sense (Greeno 1991).
When discussing student-developed models, it is important for teachers to pose questions that spotlight key mathematical ideas embedded in students’ work (Petit, Laird, and Marsden 2010).
Because students do not automatically see the mathematical ideas embedded in their models, discussions should guide students to pay attention to particular mathematical underpinning inherent in their work.