"I hear, and I forget. I see and I remember. I do, and I understand"
Experiential education is based on the idea that active involvement enhances students' learning. Applying this idea to mathematics is difficult, in part, because mathematics is so 'abstract'. One way of bringing experience to bear on students' mathematical understanding, however, is the use of manipulatives. Manipulatives are small, usually very ordinary objects that can be touched and moved by students to introduce or reinforce a mathematical concept. Manipulatives come in a variety of forms, from inexpensive, simple buttons or empty spools of thread to tangrams and pattern blocks. Typically, it has been the primary grades' teachers who have generally accepted the importance of manipulatives.
"Both Pestalozzi, in the 19th century, and Montessori, in the early 20th century, advocated the active involvement of children in the learning process. In every decade since 1940, the National Council of Teachers of Mathematics (NCTM) has encouraged the use of manipulatives at all grade levels. Every recent issue of the "Arithmetic Teacher" has described uses of manipulatives". "Arithmetic Teacher" articles feature monthly articles describing the usefulness (as well as the why, when, what, how and with whom) of manipulatives.
Research indicates that manipulatives are particularly useful in helping children transition from the concrete to the abstract level. It is key for the teacher, however, to select the appropriate activities/manipulatives to support the transition. The transition often reflects the developmental process. Further research, in a review of activity-based mathematics learning, indicates that mathematics achievement increased when manipulatives were used.
"Children learn best when they are active rather that passive learners" . According to Spikell most learners, whether adults or children, will master mathematical concepts and skills more readily if they are presented first in the concrete/pictorial or with symbols. Manipulatives are concrete objects used to teach a concept. By using manipulatives, pictures and symbols to model or represent abstract ideas, the stage is set for learners to understand the abstractions they represent.
Just recently, while teaching an Extended Day 5th grade Mathematics class, I presented each student with a set of tangrams (ancient Chinese 7-piece tile set). The students had an opportunity to explore the tangrams, reconfiguring the pieces to create new shapes and designs. After 'playing' with the tangram pieces one student commented that she felt as though she was back in Kindergarten. I felt sad to think that a 5th grade student's memory of working with manipulatives in a Mathematics class took her all the way back to Kindergarten. Research also shows that long-term use of manipulatives was more effective than short-term use.