How Teacher Educators Can Use Manipulative Materials with Preservice TeachersAuthor(s): Sharon L. YoungSource: The Arithmetic Teacher, Vol. 31, No. 4 (December 1983), pp. 12-13Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192296 .

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Teacher Education How Teacher Educators

Can Use Manipulative Materials

with Preservice Teachers By Sharon L. Young

Louisiana State University, Baton Rouge, LA 70803

Not long ago I was observing Mar- tha Peterson, a preservice teacher from my methods course, as she was teaching the subtraction algorithm to some third graders. Martha was using base-ten blocks to show how the physical exchange of a "long" for ten ■'units," in relation to a written step in the algorithm, when Johnny ex- claimed, "So that's why you cross out the tens!" As we left the classroom, Martha was elated and said, "Did you hear Johnny? The base-ten blocks really helped him understand. I didn't think manipulative materials would really work, but now I do."

Scenarios similar to this occur fre- quently when manipulative materials are fully integrated into a methods course. My own experiences have shown me that methods instructors can use a variety of activities to intro- duce preservice teachers to manipula- tive materials. Some activities pre- pare preservice teachers to use the materials and others have the students use the materials in actual instruction- al situations.

The preparatory activity should fo- cus on the definition of manipulative materials. The following definition is one that I have used with my stu- dents: manipulative materials are ob- jects which represent mathematical ideas that can be abstracted through physical involvement with the ob- jects. With such a definition, preser- vice teachers can evaluate various in- structional aids to determine whether or not they are manipulative materi- als. For example, they might deter- mine that a bead abacus and colored rods are manipulative materials for

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teaching addition but that flash cards are not.

Many different manipulative mate- rials can be used to teach a single mathematical concept or skill. It is important that preservice teachers learn which materials are appropriate for which of the various levels of mathematical understanding, as some may require children to think in more abstract ways than others. A useful activity is to have students rank a variety of materials according to the level of abstraction required to use them for a particular concept or skill. For example, among place- value ma- terials the easiest to think about are objects that can be grouped into tens by hooking together (plastic connect- ing cubes) or bundling (wooden sticks). Materials that involve a trad- ing process, such as base-ten blocks, require a greater degree of abstraction in thinking, and colored chips (for chip trading) require a higher degree of abstraction than base-ten blocks.

In the previous activity, the preser- vice student learned that a variety of materials can be used to teach a single concept or skill. The next activity "reverses" the approach by focusing on the many skills and concepts which can be taught with a single manipula- tive material. Whenever I introduce preservice teachers to a manipulative material for the first time, I have them use the material with a specific skill or concept, and then I also have them identify other mathematical ideas that can be taught through the use of that material. For example, students can discover that base-ten blocks can be used to teach the four basic algo-

rithms for whole numbers and decimal fractions as well as place value.

It is important that preservice teachers learn how to help children connect the physical manipulation of materials with written symbols. One activity that focuses on building bridges between materials and sym- bols is to have your students develop specific, step-by-step teaching proce- dures that will enable a child to see that written symbols are simply a way to record the results of manipulating materials. For example, fraction tiles could be used to show children how to add fractions with unlike denomina- tors on a concrete level and then in written form.

Preservice teachers also need to discover that manipulative materials and textbooks can form a working partnership. The first instructional lesson plan that my students write focuses on this important notion. I have them develop a plan to teach a specific lesson from a current text- book. Manipulative materials must constitute a major portion of the in- structional time in the plan, and some link must enable the child (and, there- fore, the preservice teacher) to see the connection between the materials and the textbook.

With today's limited school budgets it is important for preservice teachers to learn to develop inexpensive ma- nipulative materials. One activity is to brainstorm ways to make inexpensive models of manufactured materials. For example, paper clips can be hooked together in lieu of plastic con- necting cubes, base-ten blocks can be cut from graph paper, and tangrams

Arithmetic Teacher

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can be cut from colored posterboard. For a related activity, students- are assigned a specific skill or concept for which they are to design a lesson using items from a "junk" box. An- other activity is to have students make their own manipulative materi- als. Beansticks, fraction kits, geo- boards, and stick abaci can all be made easily and inexpensively. Stu- dents are often amazed at their own ingenuity and learn that inexpensive materials can be as effective as pur- chased manipulative materials.

Instructors of methods courses are interested in whether or not preser- vice teachers can effectively use ma- nipulative materials to teach concepts and skills. This concern can be ad- dressed by observing students in peer- teaching situations. Students can pre- pare lessons that use manipulative materials and teach the lessons to one or more preservice teachers. These microteaching situations can be vid- eotaped so that students can observe their own teaching.

Of all the activities that train preser- vice teachers to use manipulative ma- terials, the most beneficial one is teaching children. As a part of the field-experience component of the course, I have my students prepare and teach lessons to children in ele- mentary school classrooms. The les- sons must incorporate the use of ma- nipulative materials, and they must also fit in with the classroom teacher's ongoing plan for mathematics instruc- tion. Several years ago I did not re- quire my preservice teachers to use manipulative materials with children. When given a choice, many preser- vice teachers did not use the materi- als, despite extensive work with them in the methods course. Now that I require the use of manipulative mate- rials in actual teaching situations, most preservice teachers become "sold" on their use.

Another useful teaching activity is to have preservice teachers use ma- nipulative materials with children for purposes of evaluation. As an exam- ple, the methods students can use materials such as connecting cubes or base-ten blocks to determine how well children understand the concept of

December 1983

addition or the skill of subtracting two-digit numbers. Such evaluation can be diagnostic or for postassess- ment.

Preservice teachers can synthesize the information and skills they have obtained in the previous teaching ac- tivities when they develop a project in which they prepare an instructional unit for a specific skill or concept. The project requires that the student inte- grate manipulative materials with the textbook or other printed material and use manipulative materials within the framework of long-range objectives. The project can also reinforce the use of inexpensive materials by requiring the incorporation of at least one teacher-made manipulative material.

Teachers must be selective in their choice and use of manipulative mate- rials. Constraints on budgets and classroom space limit the teacher's inventory of such materials. Given such limits, teachers should make their selections based on the age and interest of the children, the appropri- ate mathematical content, and their own personal teaching styles. A previ- ous article in this journal (Reys 1971) offers additional pedagogical and physical criteria for selecting manip- ulative materials. In an activity that prepares preservice teachers to select appropriate materials, the methods in- structor can have students specify the type and quantity of purchased and teacher-made manipulative materials needed to teach mathematics for a hypothetical class. It is specifically suggested that this activity be used toward the end of the course, as it requires preservice teachers to syn- thesize and apply their knowledge about manipulative materials.

Using manipulative materials with preservice teachers can be a reward- ing experience for the instructor of mathematics methods. The following are some managerial suggestions that will be of help when using materials in a methods course.

• Assign students to work with ma- nipulative materials in groups, when appropriate. Small groups encourage the participation of all students, not just those who are highly vocal. Group decisions can be shared with

other groups. • Seat students around tables when

using manipulative materials. This gives needed work space that individ- ual slant-topped desks cannot provide and encourages students to work to- gether. • Give students time to explore new

materials. As with children, students need time to acquaint themselves with materials before they use them for specific purposes. • Give students access to materials

outside of class. This goal can be accomplished through a mathematics laboratory, an instructional materials center, or by having students pur- chase a materials kit, much as they would purchase a textbook for the course. • Use one of the many methods

textbooks that emphasize the use of manipulative materials.

When teacher educators introduce their preservice teachers to manipula- tive materials, they should use a com- prehensive approach that will maxi- mize the students' opportunities and experiences. The activities described above are a necessarily brief sample of many techniques that can be used to expose preservice teachers to the value of using manipulative materials to teach children.

Reference

Reys, Robert. "Considerations for Teachers Using Manipulative Materials." Arithmetic Teacher 18 (December 1971):551-58. W

Professional Dates

NCTM 62d Annual Meeting 25-28 April 1984, San Francisco, Calif.

NCTM 63d Annual Meeting 17-20 April 1985, San Antonio, Tex.

NCTM 64th Annual Meeting 2-5 April 1986, Washington, D.C.

For a printed listing of local and regional meetings, contact NCTM, Dept. PD, 1906 Association Dr., Reston, VA 22091, (703)620-9840.

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