Many adults might not realize that young children first understand mathematical ideas through physical actions and concrete experiences, not abstract symbols. Manipulatives are grounded in learning theory, particularly Bruner’s (1966) framework of enactive (physical), iconic (visual), and symbolic (abstract) representations. This progression is essential: children manipulate objects, see and create patterns, and later connect these experiences to formal symbols and procedures (Bruner, 1966; Gravemeijer, 1999). Manipulatives serve as a bridge, making abstract concepts tangible and accessible.
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