Providing physical and virtual representations of numbers and math concepts helps activate mental processes. Learners understand more deeply through hands-on experimentation and exploration with manipulatives. Research has found that manipulatives are effective when students are in the concrete operational stage -- where seeing an actual object supports their ability to think about it. As students become able to think about an object without it being there (formal operational stage, which usually begins at 11 years or older), manipulatives start to become less effective but can still offer some cognitive support.
Watch how this middle school student uses manipulatives to practice equations and problem solving. By using dice and playing pieces, she demonstrates her thinking by talking through her problem solving process, further supporting moving these concepts and skills into Long-term Memory.
Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.
Learn how products such as DragonBox Numbers allow learners to playfully explore digital manipulatives to strengthen their number sense. Through various games using the manipulatives, learners can build Geometric Reasoning and enhance Algebraic Thinking.