The Proper Use of Manipulatives in the Math Classroom
Visit any math classroom today and you are sure to find shelves filled with a variety of objects. Some of these objects will be as commonplace as buttons and sticks, while others may include counting frames and Cuisenaire rods. Objects used by students which enable them to actively learn a concept are called manipulatives.
The use of manipulatives in the classroom has been studies for years. Research journals print glowing reports of the success of teaching math with manipulatives. Many teachers obtain manipulatives for their classroom, but their students fail to achieve the promised success. The problem lies in the teacher not knowing when and how to use the manipulatives.
Manipulatives are frequently used only for counting in the lower grades; however, this is a very limited use. Manipulatives are important to all students, kindergarten through high school. The younger students will need more time and activities with these concrete objects, but students of every age will benefit from them.
Another common use of manipulatives is with the remedial student who does not understand a concept after the teacher has explained it several times. Manipulatives are important for the remedial student, but not as a last resort. Manipulatives need to be an integral part of every math class, not merely a remediation technique. A builder does not wait and use his nails after the boards of his house are collapsing. Instead, he carefully hammers each nail in a strategic place to give the house stability and strength. If manipulatives are used correctly and frequently, students will have a strong conceptual math foundation.
Manipulatives should be provided when a new concept is introduced to students and when reteaching is necessary. A perceptive student may not always need manipulatives to be successful, but they will enhance his understanding of the concept. For those students who do not understand the concept when it is introduced, using manipulatives when reteaching is important. Often these students are given more and more practice, when they really need reteaching. (I.e., a student who does not understand the concept of renaming one ten as ten ones will not benefit from being assigned extra subtraction problems for practice. This student needs reteaching using a bundle of sticks, Cuisenaire rods, or an abacus. After the student understands the renaming concept, he can them benefit from practicing the process.)
There is a variety of different types of manipulatives that students can use. Classification skills can be learned before a student is able to count. Given a bag of buttons, a student can sort them according to color, size, or shape.
Geometric shapes are easily learned if a student is able to feel and count the edges of cardboard and foam shapes. Later the student can make his own shapes by gluing toothpicks onto paper. With manipulative activities like these, it won't be long before the kindergarten student will be identifying pentagons and octagons.
Many students have a difficult time understanding fractions. It is important for students in the early grades to cut and color parts of a whole when naming or adding fractions. It is just as important for the older student to manipulate fractions when multiplying and dividing them. Before multiplying 1/2 x 1/3, let the student fold a paper into thirds and color two- thirds of the paper. Then re-fold the paper into halves and color one-half a different color. The overlapping colors will be the product 1/6. This activity will help most students understand why the product of two fractions is smaller than one or both of the factors.
Manipulatives are important when you teach for the understanding of math concepts. They are the concrete objects you provide in order to transfer understanding to the abstract level. Don't place them on a desk or table and wait for a student to discover what to do with them. Demonstrate the manipulatives letting the students use them while you teach. Provide specific activities so your students know how to use the manipulatives by themselves. Manipulatives can be a valuable teaching tool if they are properly used.