Manipulatives represent one possible teaching tool for building a child's conceptual foundations. Once mathematical ideas are experienced at the concrete level, they must eventually be matched to a symbolic expression. In this way, conjectures can be explored and verified.
No teaching tools enable mathematics to jump magically into the child's mind and immediately enable him or her to reason mathematically and solve mathematics problems. The teacher must make decisions about the lesson and use the available materials in a manner beneficial to all children. Generally, this goal means that the teacher must carefully plan and prepare the lesson. Manipulatives are not always the best approach - manipulatives do not teach. Manipulatives, however, offer the teacher a method to afford children opportunities to discover and explore various mathematical ideas.
When manipulatives are the best approach, the teacher must demonstrate to the students how they are expected to use - not abuse - the materials. While the children work at their desks with their desk-manipulatives, the teacher models with the demonstration materials a preferred method of use. This process enables the child to see the teacher's suggestion before embarking on his or her own solution. For example, when creating patterns, the teacher might use pattern blocks for the overhead projector to demonstrate a particular pattern while the children use their desk-manipulatives to mimic and extend the pattern. Then, a child might model the extension of the pattern for the class using the demonstration materials. When the student shows his or her solution, the teacher-demonstration materials clarify the solution.
Overhead projector. The overhead projector offers an easy and efficient medium for demonstrating manipulatives. Many companies specializing in educational materials sell overhead manipulatives. Wiebe (1990) related an example of using transparencies or old report covers to create overhead manipulatives at a fraction of the commercial cost.
Metal chalkboard. A chalkboard made of metal offers another medium for demonstrating manipulatives. The absence of a metal chalkboard can easily be overcome by purchasing a sheet of metal, such as an old television tray, or by using the side of a metal filing cabinet. Poster board and adhesive magnetic strips will be sufficient for creating these tools. By using a scaling factor of 5, teacher-demonstration manipulatives can be constructed. After the manipulatives are cut from the poster board, the magnetic pieces are secured to the back.
These large, magnetic teaching manipulatives have many advantages. …