This glossary of hands-on manipulatives was created to help teachers learn about and use manipulatives in their regular classroom settings.
Though there are dozens of different manipulatives that can be used to educate students, the pedagogical basis for using one is the same: firsthand interaction with manipulatives helps students understand mathematics. Manipulatives provide concrete ways for students to bring meaning to abstract mathematical ideas. They help students learn new concepts and relate new concepts to what they have already learned. They assist students with solving problems.
When students explore with manipulatives, they have the opportunity to see mathematical relationships. They have tactile and visual models that help develop their understanding. Without these concrete references, students are too often lost in a morass of abstract symbols for which they have no concrete connection or comprehension.
Teachers need to learn how to make use of concrete manipulatives so that students learn the how and why of mathematics concepts. Students’ thinking and reasoning must be the top priorities when they are engaged in learning with manipulatives. The concrete manipulatives and the activities for which they are used are only as valuable as the students’ reflection on the mathematical concepts.