ONE POINT OF VIEW: Using Manipulatives SuccessfullyAuthor(s): Jeane M. JoynerSource: The Arithmetic Teacher, Vol. 38, No. 2 (OCTOBER 1990), pp. 6-7Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194687 .

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ONE POINT OF VIEW

Using Manipulatives Successfully Jeane M. Joyner

curriculum with goals for

students of valuing mathematics, being confident in their abil- ities, making mathe- matical connections,

becoming mathematical problem solv- ers, and learning to reason and com- municate mathematically is a call for classrooms in which students are ac- tively involved in learning. It is a call for teachers to establish environments that encourage the use of manipula- tives to assist students in attaining these goals proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989). A major difficulty, however, is how to manage the materials effi- ciently.

The recognition of the need for ac- tivity-oriented lessons to assist stu- dents in learning mathematical skills and concepts is not new. Most educa- tors subscribe to the notion that stu- dents are better able to internalize concepts and visualize ideas when they work with a variety of models. Why then do so many classrooms re-

Jeane Joyner is the elementary mathematics consultant for the North Carolina Department of Public Instruction, Raleigh, NC 27603. Readers are encouraged to respond to this ed- itorial by writing to the authors with copies to the Arithmetic Teacher for consideration for publication in "Readers' Dialogue.'' Please double-space all letters that are to be consid- ered for publication. Editorials from readers are welcomed.

6

main havens of pencil-and-paper drill to the exclusion of experiential learn- ing?

For the teacher who has never per- sonally learned mathematics in an ac- tive manner, the teacher who relies on pages of written work to teach con- cepts, and the teacher who tried once to use manipulatives only to have chaos, what is needed is not another creative idea but specific guidance in

the management of materials. Strate- gies that are simple and obvious to teachers who successfully use manip- ulative materials are major hurdles for many instructors.

The following guidelines are gener- ic; they apply to all materials and to all grade levels. And although they seem obvious, they are the missing strategies for many teachers.

Free exploration is a necessity whenever new materials are intro- duced. Because students' desire to in- vestigate in their own manner is stron- ger than their desire to follow the teacher's directions, lack of explora-

tion time will jeopardize the best- planned mathematics activity.

To facilitate distribution of the ma- nipulatives, package the materials ac- cording to the purpose of the lesson. Students do not wait well. If individ- uals must count out cubes while oth- ers are waiting their turns, those at the end of the line will find other ways - usually unacceptable to the teach- er - to entertain themselves. Geo- boards are easy to distribute, for example, if they are prestrung with rubber bands. Patterning blocks sorted for fraction lessons or boxes with all equipment for an experiment make the distribution of materials go smoothly. Having students help orga- nize the materials can be a learning opportunity. Wise teachers store ma- terials so that students can distribute and put them away with little direc- tion.

When students are involved with hands-on lessons, it is important that clear expectations be established for both lesson goals and how students may use the materials. Teachers must be able to articulate their purposes in using the manipulatives. If they do not have a clear understanding of why the materials are important to the lesson, they are unable to help students make the connections from models to an in- ternalized idea. Students build under- standings through their experiences. They must be encouraged to summa- rize their activities and talk about the ideas they discover through the use of the materials.

Students also need simple but clear guidelines for what is acceptable and

ARITHMETIC TEACHER

Teachers need management guidelines.

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what is not acceptable when using ma- nipulatives. "The cereal is for the graphing activity; you may eat it at the end of the lesson." "When you return your cubes to the shelf, please snap them into sticks of ten."

Finally, teachers should model the use of materials and "think aloud" about what they represent. When they see their instructors using manipula- tives, students are more likely to value manipulatives and to use them in their own explorations.

Active lessons in which students explore and discuss mathematical ideas are not easy to plan and carry out; assigning a page or two in the book is an easier way to fill the time designated for mathematics in the daily schedule. Teachers who are not currently using activity-oriented les- sons need specific ideas on using ma- nipulatives. They need reassurance that the time invested in hands-on les- sons is not wasted and will lead to an understanding of relationships be- tween ideas and symbols. Most im- portant, however, staff-development leaders must recognize that teachers who are not comfortable with activity- centered lessons need management guidelines and assistance in organiz- ing their classrooms so that mathe- matics involving the use of manipula- tive materials can be implemented effectively.

Bibliography Focus Issue on Manipulatives. Arithmetic

Teacher, February 1986. National Council of Teachers of Mathematics,

Commission on Standards for School Mathe- matics. Curriculum and Evaluation Stan- dards for School Mathematics. Reston, Va.: The Council, 1989. W

OCTOBER 1990 7

Assigning a page in the

book is easier.

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