Using Integer Manipulatives: Representational Determinism

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some instructionally employ representations potentially leaves students confounded and mathematical ideas unlearned. From the perspective of representational determinism, this paper explores the appropriate uses and misuses of concrete representations in respect to integer operations.