Their purpose is to help students understand and learn mathematics with addition and subtraction operations, place value, geometric shapes, measurement, patterns, ect...
Concrete manipulatives connect to the work of Piaget for his theory of equilibration. When students can't find a solution to a familiar problem, he/she is in a state of confusion, disequilibrium. Concrete manipulatives help children construct (constructivism), their own knowledge, resolving the problem finding a state of equilibrium in the process of equilibration.
From this assignment I learned that