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The Effect of Problem Type and Common Misconceptions onPreservice Elementary Teachers5 Thinking About Division

Dina Tirosh

Anna 0. Graeber

School of EducationUniversity of Tel AvivTel Aviv, Israel 69978

Department of Curriculum & InstructionUniversity of MarylandCollege Park, Maryland 20742

Current reform movements in mathematics educa-tion emphasize problem solving and conceptual under-standing as outcomes of instruction. A logically neces-sary condition for instruction that achieves suchoutcomes is teachers with conceptions of fundamentaloperations that are relatively rich and misconceptionfree. Since many of tomorrow’s teachers are today’spreservice teachers, the conceptions preservice teachershold of fundamental operations should be of concernto teacher educators. Graeber and Tirosh (1988) havepreviously suggested that preservice teachers’ explicitstatements about operations and even successful calcu-lations can mask misconceptions about division. Thesemisconceptions do, however, become apparent inword problem-solving situations.The main purpose of this study was to determine

whether preservice teachers’ success in solving divisionword problems was effected by: (a) the type of divi-sion problem or (b) by the common misconceptionsrelated to primitive models of division. Of particularinterest was the relative effect of problem type andmisconceptions on preservice teachers’ ways of think-ing about division.

Type of Division Word Problems

Although a number of different categorizationshave been suggested for division word problems, twotypes of division word problems have been especiallywidely discussed in the literature�measurement andpartitive (e.g. Glennon & Callahan, 1968; Greer &Mangan, 1986; Kouba, 1986; Paige, Theissen, &Wild, 1982; Vest, 1978). Kouba described measure-ment type problems as those in which the "number ofsets or groups is the unknown" (p. 4). She describedpartitive type problems as those in which "the numberof elements in a set is the unknown" (p. 4). Greer andMangan (1986) formalized the definitions, describingpartition as division by the multiplier and quotition(measurement) as division by the multiplicand.A number of studies indicate that young children

are more successful in solving measurement thanpartitive problems. Gunderson (1953) and Zweng(1964) found that second-grade students found mea-surement division problems easier than partitive divi-sion problems. Kouba’s (1986) data on first, second,and third graders indicated that a greater proportionof the students selected successful strategies using

manipulatives to solve measurement than partitivedivision problems.

Less is known about the effect of the problem typeson teachers’ performance on word problems. Vest’s(1978) data showed that when preservice elementaryteachers were asked to write a division word problem,they wrote partitive problems more frequently thanmeasurement ones; however, when they were asked toindicate a preference between two problems (onepartitive and the other measurement). Vest found thattheir choices were almost equally divided between thetwo types. In Vest’s report, there was no informationabout preservice teachers’ performance on these twotypes of word problems. Greer and Mangan (1986),who investigated Irish preservice teachers’ perfor-mance in solving partitive and measurement wordproblems, found that the preservice teachers’ perfor-mance was slightly better on measurement problems;however, a previous study (Graeber, Tirosh, &Glover, 1989) suggested that while preservice teachersseemed to access the partitive model more readily thanthe measurement model, their ability to write expres-sions for both types of word problems seemed to beabout equal.

Since children’s introduction to division is fre-quently with a measurement model and since divisionby a fraction or decimal is most readily comprehensi-ble in terms of a measurement interpretation, it seemsimportant that teachers, and therefore preserviceteachers, understand both of the problem types.Furthermore current instructional theories (Case,1985; Driver, 1987) emphasize the importance ofproviding instruction that takes into account thelearners’ current understanding of a concept. Thus, itwould be beneficial if teachers were adept at recogniz-ing and using both models of division.

Common MisconceptionsRelated to Primitive Models

In probing the sources of errors made in selectingthe operation to solve division and multiplicationword problems, Fischbein, Deri, Nello, and Marino(1985) described two primitive models of division, oneassociated with measurement type problems and theother with partitive type problems. These primitivemodels incorporate constraints that do not alwaysmatch those of the formal mathematical operation.

Volume 91 (4), April 1991

158Thinking About Division

Fischbein et al. (1985) stated that the behavioralnature of the primitive partitive model imposes threeconstraints on the operation of division. First, thedivisor must be a whole number. Second, the divisormust be less than the dividend. Finally, the quotientmust be less than the dividend. The only constraintimplied by the primitive measurement model is thatthe divisor must be less than the dividend.

Fischbein et al. (1985) found that the errors adoles-cents made in writing expressions to solve divisionword problems were consistent with misconceptionsabout division that are logically equivalent to theconstraints of these primitive models of division. Theyhypothesized that adults are also influenced by thesesame constraints. The data from another study(Graeber, Tirosh, & Glover, 1989) suggested thatpreservice teachers do as well in writing expressionsfor word problems that conform to the primitivemeasurement model as they do in writing expressionsfor problems that conform to the primitive partitivemodel. The same study found that preservice teachersperformed better with problems that conformed to theprimitive partitive model than they did with partitiveproblems that have decimal divisors or divisors largerthan the dividend; however, the study did not investi-gate preservice teachers’ success with measurementproblems that violated the constraint of the primitivemeasurement model, that is, had divisors greater thanthe dividend. Data collected in this study determinedthe relative effect of the two factors (problem type,conformity to the primitive models) on preserviceteachers’ success in writing expressions to solve divi-sion word problems.

Method

SubjectsThe subjects were 80 female college students en-

rolled in one of the mathematics content or methodscourses for early elementary education majors in alarge university in the southeastern United States.Students typically enter the 2-quarter methods se-quence as juniors having completed at least the firstof the 2-quarter content courses.

InstrumentsEach of 80 preservice teachers was given two

paper-and pencil-instruments.

Writing an Expression for Word Problem. Preser-vice teachers were asked to write an expression thatwould lead to the solution of each given wordproblem. Problems used in the study included addi-tion, subtraction, and multiplication problems alongwith 16 division problems, eight of which weremeasurement type problems and eight of which werepartitive type problems. Four of the division problemsfor each type included data that conformed to thecorresponding primitive model and the remaining fourproblems included data that violated the "the divi-

dend must be greater than the divisor" constraintcommon to both primitive models. In constructing thedivision word problems, an attempt was made to useproblems with similar contexts and similar numericaldata. The division word problems were interspersedwith the other problems to reduce the likelihood thatcorrect answers would result from guessing. The totalof 32 problems was divided between two tests formsin order that each subject would have a reasonablenumber of questions to complete. One-half of thepreservice teachers in each of the four classes receivedone form and the other half received the other form.The division word problems are shown in Figure 1.

Writing Division Word Problems. Four divisionexpressions: (a) 6 - 3, (b) 2 - 6, (c) 4 � .5, and(d) .5-4 were presented to the preservice teachers,and they were asked to write a word problem foreach. The types of problems written were used to gaininsight into the preservice teachers’ preference for andaccess to the types of division word problems. Theresponses on this instrument were also used to assessthe effect of the common misconceptions. Correctword problems for the expressions 2-6 and .5-4must counter the misconception "the divisor must beless than the dividend" common to both primitivemodels.

Interviews

Each of the 33 preservice teachers enrolled in oneof the four mathematics methods classes was inter-viewed in order to obtain more information about theconceptions she held and the reasoning she used.Typically, the preservice teacher would first be givenproblems similar to those she missed on the writteninstrument and asked to write expressions that couldbe used to solve them. Then, she was asked to explainwhy she responded the way she had and how shecould check her work. Systematic data on the audio-taped interviews is not presented here, but someresponses are included to illustrate preservice teachers’thinking.

Results

Effect of Problem Type

As can be seen in Table 1, preservice teachers weremore successful in writing expressions for partitivetype word problems than for measurement problems.Approximately 60% to 80% of the word problems

written for Expressions A, B, and D were appropriatepartitive type problems (see Table 2). This was truedespite the fact that these expressions can be inter-preted just as readily with a measurement type prob-lem. Only 44% of the preservice teachers wrotecorrect measurement type problems for the expres-sion, 4 - .5; 18% of the respondents incorrectlywrote reversed (.5 - 4) partitive word problems forthis expression.

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Thinking About Division 159

Figure 1. Division problems used.

Partitive Problems That Conform to the PrimitiveModel119. It takes 5.25 meters of ribbon to wrap 3 pack-

ages of the same size. How many meters ofribbon are required to wrap one of thesepackages?

131. The Yale Desk Encyclopedia is shipped threecopies to a box. If 3 of the copies weigh 13pounds, how much does each copy weigh?

108. Five friends bought 15 pounds of cookies. If thecookies were equally shared, how many poundsdid each person get?

116. Five bottles contain 6.25 liters of rootbeer. Howmany liters of rootbeer are in each bottle?

Partitive Problems That Do Not Conform to thePrimitive Model114. It takes 3.25 meters of ribbon to wrap 5 pack-

ages of the same size. How many meters ofribbon are required to wrap one of thesepackages?

102. Necklaces are shipped 13 to a box. If 13 of thenecklaces weigh 3 pounds, how much does eachnecklace weigh?

125. Five pounds of cookies were equally shared by15 friends. How many pounds did each personget?

117. Five bottles contain .65 liters of perfume. Howmuch perfume is in each bottle?

Measurement Problems That Conform to the Primi-tive Model110. You prepared 5.25 liters of punch. You have

punch bowls that hold 3 liters. How many punchbowls can you fill with the prepared punch?

104. A paperhanger needs 3 rolls of paper to do aroom. How many similar rooms can the paper-hanger do with 13 rolls of the same wallpaper?

121. Five French Francs are needed to buy 1 Ameri-can dollar. How many dollars can you buy for15 French Francs?

132. Girls club cookies are packed .65 pounds to abox. How many boxes can be filled with 5pounds of cookies?

Measurement Problems That Do Not Conform to thePrimitive Model107. You prepared 3.25 liters of punch. You have a

punch bowl that holds 5 liters. How much of thepunch bowl can you fill with the preparedpunch?

129. A paperhanger needs 13 rolls of wallpaper tofinish a job. How much of the job was donewith 3 rolls of wallpaper?

112. Fifteen Austrian Schillings are needed to buy 1American dollar. How many dollars can you buyfor 5 Austrian Schillings?

101. Peanuts are shipped in 5 pound boxes. Howmuch of a box is filled with .65 pounds ofpeanuts?

Table 1

Distribution of Responses to Division Problems

Problems Conforming tothe Primitive Model

Problems Not Conforming tothe Primitive Model

Item/Form

Partitive Probi119/B131/B108/A116/AAverage

Measurement ProblemsHO/A104/A121/B132/BAverage

Opera

’ems(5.25(13 -(15 -(6.25

(5.25(13 -(15 -(5 -

ition

- 3)3)5)- 5)

- 3)3)5)

.65)

%Cor

93901009294

7795885278

%NR

00000

00031

%Inc

710086

235124521

Item/Form

114/A102/A125/B117/B

107/A129/B112/A101/A

Oper

(3.25(3 -(5 -(.65

(3.25(3 -(5 -(.65

ation

- 5)13)15)- 5)

- 5)13)15)- 5)

%Cor

8744726567

4132412635

%NR

20000

23

1325

%Inc

1156283533

5765467260

The base used in calculating the percent correct (Cor), percent of nonresponses (NR) and the percent incorrect(Inc) was the number of respondents to the form involved, i.e., 39 for Form A and 40 for Form B.

Volume 91 (4), April 1991

160ThinkingAbout Division

Table 2

Percent of Word Problems Written for Given Division Expressions

Responses byProblem Type

Correct Word ProblemsPartitiveMeasurement

Incorrect Word ProblemsReverse Partitive*Reverse Measurement*Other

No response

(A) 6 -

783

1103

5

3 (B) 2 -

741

1106

8

Given ]

6

Expressio

(C)

n

4 - .5

044

18016

22

(D) .5 -

633

11

13

19

4

*Reverse is used to describe cases in which the role of the divisor and the dividend were reversed.

The interviews strengthened the belief that themajority of the preservice teachers have access only tothe partitive interpretation of division. Preserviceteachers were asked to interpret the expression 6-2.Almost always, they offered a partitive explanation.When asked to offer another interpretation, most ofthem were unable to do so without many cues andprompts from the interviewers. The following excerptis typical of the responses offered by preserviceteachers who were asked to write a word problem forthe expression 6�2:

S: There are 6 apples and 2 kids. They divided theapples evenly among them. How many applesdid each one get?

I: Is there any other division problem that you canwrite?

S: Yes. Instead of 6 apples and 2 kids, I can use 6marbles and 2 boys, or ... 6 dolls and 2 girls.Is this what you meant?

I: That’s fine. Now could you think about anotherproblem? A different type of division problem?

S: (thinking . . . ) No.I: Are there any other types of division problems

other than sharing things evenly?S: (long silence)I: Try to think about division. What does it mean

to you?S: For me, division means sharing.I: Is there anything else?S: (thinking . . . ) Not anything that I can think of

Many preservice teachers presented with simpleexpressions that easily lent themselves to a measure-ment interpretation were unable to find the quotientwithout resorting to the standard division algorithm.They were also unable to translate 4 - .5 into thequestion, "How many five-tenths are there in four?"Presented with a measurement interpretation of divi-sion, they reacted as if it were a completely new ideafor them.

Effect of Common Misconceptions

Table 1 gives information about the effect thatcommon misconceptions appear to have on preserviceteachers’ success in writing expressions for wordproblems. Comparing the percent of correct responsesin the left-hand column with those in the right-handcolumn it can be seen that the preservice teachers weremore successful with word problems that did notchallenge common misconceptions than with wordproblems that challenged the misconceptions.The expressions the preservice teachers’ wrote indi-

cated that many of them may have been effected bythe constraint of both primitive models, "the divisormust be smaller than the dividend." For example,56% of the students wrote the expression 13 - 3 forthe partitive problem: "Necklaces are shipped 13 to abox. If 13 of the necklaces weigh 3 pounds, howmuch does each necklace weigh?" Similarly, 65% ofthe students wrote the expression 13-3 for themeasurement problem: "A paperhanger needs 13 rollsof wallpaper to finish a job. How much of the jobwas done with 3 rolls of wallpaper?"

Preservice teachers’ statements during the interviewsindicated that the constraints of the primitive partitivedivision model dominated their thinking even whenthey solved measurement type problems. Thirty per-cent of the preservice teachers had incorrectly writtenthe expression .65 x 5 for the problem, "Girls clubcookies are packed .65 pounds to a box. How manyboxes can be filled with 5 pounds of cookies?" Anumber of interviewees explained that they rejecteddivision as the appropriate operation because theyknew that the answer ought to be larger than five.Interviewees from among the 8% who wrote theexpression .65 - 5 claimed that the divisor must be awhole number. These commonly voiced misconcep-tions, "Division always makes smaller" and "Thedivisor must be a whole number," are constraints ofonly the primitive partitive model.

If the misconceptions associated with the primitive

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Thinking About Division 161

models effect preservice teachers, it seems reasonableto assume that their performance in writing wordproblems for expressions that do not challenge themisconceptions would be better than their perfor-mance in writing word problems for expressions thatchallenge the misconceptions associated with one orboth of the primitive models. The data in Table 2 donot support this assumption. The preservice teachers’performance on the two expressions that violate the"divisor must be less than dividend" constraintshared by both models, 2-6 and .5-4, wasslightly poorer than their performance on one of theexpressions (6 - 3) that conformed to both models;however, their performance on the expression with adivisor less than the dividend, 4 - .5, was evenpoorer. The dismal performance on this expressionmay have resulted from violation of the "divisor mustbe a whole number" misconception associated withthe primitive partitive model.

The Relative Effect of Problem Typeand Common Misconceptions

Data on the preservice teachers’ success in writingexpressions for word problems was used to comparethe relative effect of common misconceptions with theeffect of problem type on preservice teachers’ perfor-mance in writing expressions for word problems. A 2x 2 analysis of variance was performed using percentof correct responses for each item as the unit ofanalysis. There were two problem types (partitive,measurement) and two states related to commonmisconceptions (don’t challenge misconceptions, chal-lenge misconceptions).The analysis (see table 3) showed that both the type

of problem and a problem’s status with respect tomisconceptions had significant effects on the preser-vice teachers’ performance in writing expressions forword problems. The interaction for problem type byconformity to primitive models was not significant.The F values indicate that status of conformity to themisconceptions has a larger effect on preservice tea-chers’ performance on this task than does problemtype.

Discussion and Implications

SummaryIt was found that when preservice teachers are

asked to write expressions for division word problems,they are more successful with word problems that donot challenge common misbeliefs than they are withproblems that challenge the misbeliefs. Data from thepresent study also indicate that preservice teachers aremore successful in writing expressions for partitivetype than for measurement type problems. Further-more, when asked to write word problems for givenexpressions they almost unanimously wrote partitivetype problems.

Table 3

F Statistics/or Analysis of Variance Main Effects andInteraction

SourcedfFP

Main EffectsProblem typePrimitive models

12.1126.08

.0001

.0001

InteractionProblem type xPrimitive models 1.49 .246

Another question addressed in the present studyconcerned the relative effect of the two factors�problem type and conformity to misconceptions. Theeffect of these two factors appeared to vary with thetype of task being attempted. For the task of writingexpressions for a given word problem, the preserviceteachers’ success is more effected by conformity to themisconceptions than by the problem type. For thetask of writing word problems for given expressions,the preservice teachers’ success seemed more effectedby the compatability of the expressions with thepartitive interpretation of division than by their adher-ence to the constraints imposed by the primitivemodels. This suggests that when the preservice teach-ers were placed in the position of having to attachmeaning to a division expression, they tended to giveit a partitive interpretation.

Implications

The results of this study indicate that many preser-vice teachers are familiar with the partitive interpreta-tion of division but have limited access to the mea-surement interpretation. Previous research hassuggested that young children find measurement divi-sion problems easier to solve than partitive ones.Teachers need to be proficient with the measurementmodel so that they can utilize children’s existingconceptions during instruction. Moreover, the situa-tion raises concerns about the preservice teachers’ability to explain measurement type problems and todemonstrate solutions in a manner consistent with theproblem type. In early elementary grades, the mea-surement model of division is frequently used tointroduce children to the operation of division. In themiddle and upper grades, the preservice teachers’limited access to the measurement model may alsomake it difficult for them to explain division expres-sions with decimal divisors less than one. The mea-surement model provides a relatively simple way ofendowing such examples with meaning (for instanceexplaining 4 -r .5 as the number of halves there are infour).

If conceptual understanding and problem solvingare highly valued curricular goals for mathematics

Volume 91 (4), April 1991

162ThinkingAbout Division

education, teacher educators must attempt to assurethat preservice teachers have the requisite understand-ings of fundamental operations such as division.Certainly preservice elementary teacher should beaware of the existence of both types of divisionproblems and of the apparent difference in difficultythe two types hold for young children. Preserviceelementary teachers should also be able to:

1. match division expressions with compatible inter-pretations,

2. provide meaningful explanations of division bydecimal and fractional divisors (especially for divisorsless than one), and

3. explain the steps of the division algorithm in amanner that reflects the type of division word prob-lem (measurement or partitive) from which the com-putation stems.

If preservice teachers are to acquire these competen-cies, it seems clear that they must overcome theirmisconceptions about division. Past studies haveshown that misconceptions are not easily monitoredor changed. It is essential that instruction for preser-vice teachers include:

1. Word problem solving sessions in which thecommon misconceptions about division are madeexplicit in discussions concerning reasons for writing aspecific expression to solve a problem. For example,students will say they wrote 13-3 for the necklaceproblem because problems are always that way, "biginto little." Some researchers (e.g.. Bell et al., 1985;Driver, 1987; Fischbein, 1987) suggest that reasons forholding the misconceptions should be discussed, newconceptions clarified, and opportunity for applicationprovided.

2. Explicit discussion of the primitive models andthe corresponding constraints and misconceptions.Driver (1987) and Semadeni (1984) have suggestedthat part of instruction must include a time to discussa misconception, why it is held (for example, in whatdomain is it true and in what domain is it not true),and what the correct conception is. Thus, preserviceteachers’ attention should be focused on those in-stances in which calculations produce results contraryto the common misconceptions.

3. Wider use of the measurement model. A numberof researchers who have studied instruction designedto change conceptions argue that appropriate modelscan be an effective way to helping students build newschemes or revise old ones in order to incorporateconcepts that were previously antithetical to them(Bell et al., 1985; Driver, 1987). The measurementmodel is one simple way of giving meaning toexpressions with divisors less than one. Since themeasurement model involves only one constraint,emphasis on its use, along with continued use of thepartitive model, might also help to eliminate a numberof misconceptions. For instance, students can beasked to provide solutions to relatively simple prob-

lems such as .25)2 without using the division algo-rithm, i.e. without renaming the division example asan equivalent example with a whole number divisor.Such solutions should be required both before andafter standard algorithm has been taught. The factthat the quotients in these cases are greater than thedividends should be stressed. The similarities and thedifferences between division with whole numbers anddivision with non-negative decimals less than oneshould be explored, made explicit, and applied.

References

Bell, A., Swan, M., Onslow, B., Pratt, K., & Purdy,D. (1985). Diagnostic teaching: Teaching for longterm learning (Report for an ERSC Project). Not-tingham, England: Shell Centre for MathematicalEducation.

Case, R. (1985). Intellectual development: Birth toadulthood. New York: Academic Press.

Driver, R. (1987). Promoting conceptual change inclassroom settings; The experience of the children’slearning in science project. In J. Novak (Ed.),Proceedings of the Second International Seminar onEducational Strategies in Science and Mathematics,Vol. 2, (pp. 96-107). Ithaca, NY: Cornell Univer-sity.

Fischbein, E. (1987). Intuition in science and mathe-matics. Boston, MA: D. Reidel.

Fishbein, E., Deri, M., Nello, M. S., & Marino,M. S. (1985). The role of implicit models in solvingproblems in multiplication and division. Journal forResearch in Mathematics Education, 16, 3-17.

Glennon, V., & Callahan, R. (1968). A guide tocurrent research: Elementary school mathematics.Washington, DC: Association for Supervision andCurriculum Development.

Graeber, A. & Tirosh, D. (1988). Multiplication anddivision involving decimals: Preservice teachers’performance and beliefs. Journal of MathematicalBehavior, 7, 263-280.

Graeber, A., Tirosh, D., & Glover, R. (1989). Preser-vice teachers’ misconceptions in solving verbalproblems in multiplication and division. Journal forResearch in Mathematics Education, 20, 95-102.

Greer, B., & Mangan, C. (1986). Choice of opera-tions: From 10-year-olds to student teachers. InProceedings of the Tenth International ConferencePsychology of Mathematics Education (pp. 25-30).London, England: University of London Instituteof Education.

Gunderson, A. G. (1953). Thought patterns of youngchildren in learning multiplication and division.Elementary School Journal, 55, 453-461.

Kouba, V. (1986, April). How young children solvemultiplication and division word problems. Paperpresented at the National Council of Teachers ofMathematics Research Presession, Washington, DC.

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Thinking About Division 163

Paige, D., Theissen, D., & Wild, M. (1982). Elemen-tary mathematical methods. New York: Wiley andSons.

Semandeni, Z. (1984). A principle of concretizationperformance for the formation of arithmetical con-cepts. Educational Studies in Mathematics, 15,

379-395.Vest, F. (1978). Disposition of pro-service elementary

teachers related to measurement and partitive divi-sion. School Science and Mathematics, 78, 335-339.

Zweng, M. (1964). Division problems and the conceptof rate. Arithmetic Teacher, 11, 547-556.

SCHOOL SCIENCE AND MATHEMATICS ASSOCIATIONASSOCIATION OFFICERS FOR 1990-1991

ROBERT L. MCGINTY (1990-1992)President:Professor of Mathematics, Department of Mathematics, Northern MichiganUniversity, Marquette, Michigan 49855

DOROTHY L. GABEL (1990-1991)Past-President:Professor of Science Education, Indiana University, Bloomington, Indiana47401

LARRY G. ENOCHS (1989-1994)Journal Editor:Associate Professor of Science Education, Science Education Center, 247Bluemont Hall, Kansas State University, Manhattan, Kansas 66506

Executive Secretary: DARREL W. FYFFE (1981-1993)Associate Professor of Science Education, Bowling Green State University,126 Life Science Building, Bowling Green, Ohio 43403-0256

BOARD OF DIRECTORS FOR 1990-1991

Terms Expire in 1991LLOYD BARROW, College of Education, University of Missouri, Columbia, Missouri 65211PATRICIA BLOSSER, Science Education, The Ohio State University, Columbus, Ohio 43210

Terms Expire in 1992DONNA BERLIN, Department of Education, The Ohio State University�Newark, Newark, Ohio 43055DIANA M. HUNN, College of Education, University of Akron, Akron, Ohio 44325

Terms Expire in 1993FRANCES LAWRENZ, Department of Curriculum and Instruction, University of Minnesota, Minneapolis,Minnesota 55455

BONNIE LITWILLER, Department of Mathematics and Computer Science, University of Northern Iowa,Cedar Falls, Iowa 50614

Volume 91 (4), April 1991