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Research Based Math Manipulative Strategies

The use of manipulatives in math teaching is based, in part, on the work of Jean Piaget, a noted figure from the constructivist school of thought in developmental psychology. According to Piaget, humans pass through four distinct stages in cognitive development: Infants do not use symbols; toddlers use symbols, but think in a non-logical way; elementary age children begin to display intelligence related to concrete objects; and adolescents and adults have the ability to think logically and relate symbols to abstract concepts. Thus, introducing math concepts to younger children using concrete objects aims to instruct in a developmentally-appropriate way.
  1. Construction of Knowledge

    • According to constructivist thinking, a teacher's role is not to give information, but to guide students in constructing their own knowledge based on their experiences. A major strategy in the use of manipulatives, therefore, is not to outline an activity step by step, but to frame it as a problem that the student solves under the guidance of the teacher. In this problem solving approach, the teacher gives a student pattern blocks, for example, and tells the student that the goal is to create a hexagon, but does not tell him exactly how to do it. The teacher does not walk away, of course, but stays to give hints and answer questions when necessary.

    Bridge to Abstract Thinking

    • Does a student who has built hexagons with pattern blocks have an advantage when he is learning how to calculate the area of a hexagon with a pen and paper in higher grades? This is not automatically the case. Learning with manipulatives only translates into a better grasp of abstract concepts if the teacher takes care to build bridges that span the range of understanding from concrete to abstract. For example, an activity with pattern blocks may be followed by a less concrete activity using pictures of geometric figures in a way in which the connection between the two is made clear. This will pave the way for the student to eventually make a connection between the blocks and figures and mathematical representations.

    Appropriate Use

    • Research suggests that overuse of manipulatives may be counterproductive. Some students may become too dependent on them while others -- namely, those more used to pencil and paper activities -- may find them unhelpful. Manipulatives should be used to support the teaching of concepts and not as the main teaching tool. While some amount of free play is beneficial, the teacher should make the goal of each activity clear while explaining and modeling how to use the manipulatives. Without this, students may end up just playing with blocks or straws and miss the point of the activity.

    Higher Grades

    • While use of manipulatives in the classroom, based on Piaget's theories, is common in elementary grades, it is far less prevalent at the secondary level. There are programs such as those that use tiles to teach algebra, but not much formal research has been done to evaluate their effectiveness. More of the research has focused on students with disabilities who have been found to benefit from the use of manipulatives.

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