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One Point of View: Manipulatives Are Good Mathematics!Author(s): Elizabeth HerbertSource: The Arithmetic Teacher, Vol. 32, No. 6 (February 1985), p. 4Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192548 .Accessed: 14/06/2014 20:08

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One Point oF '7iGCO

Manipulatives Are Good Mathematics!

By Elizabeth Herbert Houston Independent School District, Houston, TX 77027

4 OCIA

lo 4

When asked, "Do you like mathe- matics? Why or why not?" at the be- ginning of each school year, a startling 80 to 85 percent of my middle school students would reply that they did not like mathematics because it was bor- ing and because they did not under- stand it very well. Their negative at- titudes appeared to stem from a lack of understanding based on plain bore- dom with uninteresting classes.

For fifteen years, this informal sur- vey yielded the same answers on the first or second day of school. By week three, the same students no longer dreaded mathematics. To their sur- prise and my delight, they were en- joying mathematics. Why? Manipu- latives.

Manipulatives can and should be used on a regular basis in the mathematics classroom, along with a variety of other tools and methods. On the basis of my experience as a teacher, mathematics department head, instructional super- visor, and workshop leader, I strongly advocate the use of manipulatives for three reasons: manipulatives motivate students; manipulatives stimulate stu- dents to think mathematically; and ma- nipulatives informally introduce "big" ideas in mathematics.

Teachers often claim that not enough time is available to use manipulatives, that their use is the same as playing games, and that they are difficult to manage with large numbers of stu- dents.

Yes, using manipulatives takes time. Isn't it better to take time at the be- ginning of a unit to motivate students and spark their thinking than to take time during a unit to bore them - and yourself - with endless drills and

worksheets? Thinking time is time well spent.

Yes, using manipulatives feels like playing games. Teachers and students having fun thinking and discovering together is what makes teaching so re- warding. We must be ready to share ourselves, our thought processes, our own mistakes, and our sense of fun with students.

No, manipulatives are not difficult to manage with large numbers of stu- dents. First, explain to the entire class the purpose of the manipulative. Show them how it works and then pose a problem or situation. Divide the class into small groups and supervise them as you would any group activity. Cir- culate among them, help any who really need assistance, but try to let them struggle and experiment. Don't solve problems for them. If any students start flipping rubber bands or throwing rods, isolate them and make them work out of the textbook.

Conquer the fear of losing control of the class. A little noise can be ex- pected when students work together. A few "ahs," "wows," and "I un- derstands" will be music to your ears. Invite the principal to observe. If you're lucky, the principal will join a group and try to help solve a problem.

A favorite definition of mathemat- ics states, "Mathematics is discover- ing relationships and expressing those relationships in symbolic form." What better way to introduce young children to mathematical thinking than to have them use Cuisenaire rods or fraction bars t discover the algorithms for adding and subtracting fractions? Mid- dle school students can use geoboards to discover and write the formulas for

finding the areas of polygons. Algebra students can feel challenged and in- terested when they are confronted with this proposal: "Let's find a way to determine the distance between these two points on your geoboard." The students use the Pythagorean

theorem and then discover,. /V>>* write, and use the distance formula.

In each example, the manipulative provides the situation from which real mathematical thinking arises. The stu- dents gain the understanding that may have come using traditional methods after hours of drill and practice. Ef- fective thinking in mathematics de- pends on understanding, not on re- membering words and phrases from a text.

A confining, narrow textbook ap- proach to teaching mathematics is in- adequate and inappropriate in today's schools. It does motivate students - to take as few mathematics courses as possible - and often does not help them to become independent, confident problem solvers.

Textbooks transmit known mathe- matics; they tend to simplify learning by emphasizing the mastery of small, isolated steps. Mathematical thinking is riot done in small, isolated steps using finished definitions from a text. Rather, it starts with situations that draw mathematical responses from the students. Manipulatives allow teach- ers to create those situations and in- volve the students actively in the cre- ation of mathematics, resulting in improvements in motivation, involve- ment, understanding, and achieve- ment - overwhelming reasons to be- lieve that manipulatives are good mathematics, w

4 Arithmetic Teacher

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Article Contentsp. 4

Issue Table of ContentsThe Arithmetic Teacher, Vol. 32, No. 6 (February 1985), pp. 1-68Front MatterBy Way of Introduction [pp. 2-3]From the File [pp. 3-3]One Point of View: Manipulatives Are Good Mathematics! [pp. 4-4]Readers' Dialogue [pp. 6, 57]Let's Do ItPromoting Mathematical Thinking [pp. 7-13]

The Role of Questioning [pp. 14-16]Research ReportQuestions? [pp. 18-18]

Mathematical Symbols: Insight through Invention [pp. 20-22]Mathematical Games: Antithesis or Assistance? [pp. 23-26]Instructional Computing [pp. 27-30]Ideas [pp. 31-36]Estimation [pp. 37-41]Mental Computation [pp. 43-46]The Role of Problem Solving [pp. 48-50]Geometry [pp. 52-56]From the File [pp. 56-56]Research on the Role of Structure in Thinking [pp. 58-60]From the File [pp. 60-60]Problem Solving: Tips For Teachers [pp. 62-63]Reviewing and ViewingComputer MaterialsReview: untitled [pp. 64-64]Review: untitled [pp. 64-64]Review: untitled [pp. 64-65]Review: untitled [pp. 65-65]Review: untitled [pp. 65-65]

New Books for PupilsReview: untitled [pp. 66-66]Review: untitled [pp. 66-66]Review: untitled [pp. 66-66]Review: untitled [pp. 66-67]

New Books for TeachersReview: untitled [pp. 67-67]Review: untitled [pp. 67-67]

EtceteraReview: untitled [pp. 67-68]Review: untitled [pp. 68-68]Review: untitled [pp. 68-68]

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