Mathematics Anxiety in Upper Elementary School Teachers

499

in

William S.Department of Curriculum and Instruction

University of KentuckyLexington, Kentucky 40506-0017

Over the past fifteen years, mathematics educators have become keenlyaware of the importance of affect in the learning and teaching of mathematics(Aiken, 1970, 1976; Kulm, 1980; Reyes, 1987; McLeod, 1988). An affectivefactor of particular interest to both educational psychologists and mathematicseducators is mathematics anxiety, defined as "feelings of tension and anxietythat interfere with the manipulation of numbers and the solving ofmathematical problems in a wide variety of ordinary life and academicsituations" (Richardson & Suinn, 1972, p. 551). Recent research revealsparticularly high incidences of mathematics anxiety in preservice elementaryteachers (Battista, 1986; Kelly & Tomhave, 1985; Sovchik, Meconi & Steiner,1981). These findings raise two pertinent questions for mathematics teachereducators. Do elementary teachers with mathematics anxiety transmit it totheir students? Do these teachers teach mathematics differently than teacherswithout mathematics anxiety?

Several educators (Bulmahn & Young, 1982; Kelly & Tomhave, 1985;Lazarus, 1974) argue that elementary teachers transmit their avoidance andfear of mathematics to their students. Many teachers teach as they were taughtand thereby perpetuate mathematics anxiety in their students. Previousresearch on the effects of teachers attitudes toward mathematics and subjectmatter on student attitudes provides support for this argument (Aiken, 1970,1976; McMillan, 1976). On the other hand, Widmer and Chavez (1982) foundthat elementary teachers had generally positive attitudes toward teachingmathematics, and that the teachers felt secure in their mathematics teachingeven though they had developed some negative attitudes toward mathematicsas students. Teachers with mathematics anxiety seemed eager to break thecycle and to reduce mathematics anxiety in their students.

Purpose

This study investigated teacher mathematics anxiety as it related to (a)changes in student mathematics anxiety and achievement, (b) selected teachingpractices, and (c) various teacher characteristics. It also described differencesin selected teaching practices, student outcomes and characteristics of teacherswith and without mathematics anxiety.

School Science and MathematicsVolume 89 (6) October 1989

500 Mathematics Anxiety

Method

Subjects

The subjects of this study were 31 fourth, fifth, and sixth grade teachersand their students in six suburban elementary schools in a metropolitan schooldistrict in Kentucky. Of the 31 teachers, two were male. Upper elementaryteachers were chosen because (1) high incidences of mathematics anxiety havebeen found in elementary education majors (Bulmahn & Young, 1982; Kelly &Tomhave, 1985; Sovchik, Meconi, & Steiner, 1981) and (2) mathematicsanxiety is more easily measured in upper elementary students than in youngerchildren. The teachers, after being informed of the purpose of the study,volunteered and were paid a small stipend. Table 1 provides the followingteacher information: number of years teaching experience, number ofgraduate level mathematics and education courses, and scores on each sectionof the Iowa Test of Basic Skills. The means and standard deviations of thesedata are found in Table 6. Table 2 provides such class data as school, grade,size, and reported ability level.Although 739 students participated in pretesting and 707 students in

posttesting, only 584 students completed both batteries of tests. Data from the584 students were used for analysis.

Instruments

Teacher mathematics anxiety was measured using the 98-item MathematicsAnxiety Rating Scale (MARS) (Richardson & Suinn, 1972). The instrument iscomprised of brief descriptions of ordinary life and academic situationspertaining to mathematics which may arouse mathematics anxiety. Subjectsare asked how anxious a particular situation makes them feel and to recordtheir responses on a Likert scale with range from 1 (none at all) to 5 (verymuch). The item scores are summed to give a total range of 98 to 490, withhigher scores reflecting higher mathematics anxiety.

Student mathematics anxiety was measured using an adaptation of theadolescent version of the Mathematics Anxiety Rating Scale (MARS-A)(Suinn, 1979). The purpose of the adaptation was to make the scale moremeaningful to upper elementary students. Because some items of the MARS-Alacked meaning for upper elementary students, the reading level of the itemswas lowered and some items were omitted. The adaptation reduced thenumber of items from 98 to 75 giving a new range from a low of 75 to highof 375. To obtain an estimate of the reliability of the adapted MARS-A, twoclasses, one fourth-grade and one sixth-grade, were selected and administeredthe scale on a test-retest basis with a one week interval. The test-retestreliability coefficient obtained was r = .72, p < .0001.Achievement in mathematics was measured by the Mathematics Concepts

and Mathematics Problem Solving sections of the Iowa Test of Basic Skills(ITBS), Form 6 (Hieronymus & Lindquist, 1971). Students at each grade were


Mathematics Anxiety 501

Table 1

Teacher Data

TeacherNo

12345678910111213141516171819202122232425262728293031

YrsExp

176

212519111141

111214161014221114168

15015101424615171428

NumberGradMathCourses

0000

. 0

’’ 2; 01

1 00021111211000502110112

NumberGradEducCourses

101220010871051

2010129713188

2010100510109510101010

ITBSConcepts(45 items)

43424242444341424140404342424443424143413542403639434438423443

ITBSProb Solv(31 items)

30302829282826302829263028283029293028232826262826313022282929

administered their respective grade-level version. Teachers’ achievement inmathematics was measured using the sixth-grade versions of the ITBS.Audio-recorded mathematics lessons were coded using an investigator-designedLesson Coding Form intended to measure time and frequency of selectedteaching behaviors and classroom discourse. Instruction was described bytiming various instructional tasks and by classifying and tallying classroomquestions and the mathematics content of the lesson. The variables measuredand their definitions can be found in Table 3. All lessons were coded by the


502Mathematics Anxiety

Table 2

Class DataTeacher

12345678910111213141516171819202122232425262728293031

School

1112222222334444445555666666666

Grade

6445564546555456465444554665444

Level

AverageAverageAverageAverageAboveBelowAboveBelowAverageAverageBelowAboveBelowBelowAboveAverageAboveAboveBelowBelowAboveAverageAverageBelowBelowAverageAboveAboveBelowAboveAbove

r^

1818201819161921202414221620281720201413211720i516183017131624

denotes number of students taking both ore- and posttests

investigator. Three lessons were randomly selected to be coded by a secondperson to establish a coding reliability. A Pearson product moment correlationwas calculated by comparing all time and frequency categories of the threelessons of the investigator and second person. The correlation between thethree codings was r = .94, p < .0001.

Procedure

During the last two weeks of September, less than one month from the startof school, the investigator visited each of the 31 classes. During the visits, theteachers were administered the MARS and the sixth-grade ITBS, and the



Table 3

Definitions and Examples of Lesson DataVariablesDefinitions/Examples

Time Measures

checking home/seatwork

reviewing

development

seatwork

giving directions

playing game

problem solving

total lesson

whole class

small group

individualized

Frequency Measures

total questions

high-level question

low-level question

choral question

individual question

student-initiated question

concepts introduced

Teacher directs checking of home/seatwork by callingout answers, asking for answers, etc.

Teacher reviews information presented in previouslesson.

Teacher introduces new concepts, principles or skills tostudents.

Students practice or work individually at their seats.

Teacher gives directions for seatwork, homework,activity, etc.

Students play an instructional game.

Teacher poses or discusses a challenge or non-routinemathematics problem.

Entire time teacher devotes to mathematics instructionthat day.

All students involved in same tasks.

Groups of students collectively involved in differenttasks.

Individual students involved in different tasks.

Questions asked by teacher except during seatwork.

Question asked by teacher requiring analysis, inferring,judgement, transfer.

Question asked by teacher requiring rote memory.Giving examples, explaining procedures, applyingdirectly included.

Question asked by teacher to whole class or group ofstudents.

Question asked by teacher to particular student.

Question asked by student except during seatwork

New mathematics concepts (fraction, triangle)introduced during a lesson.



Table 3 (continued)Variables Definitions/Examples

concept behaviors Different behaviors (defining, giving examples/nonexamples, discussing properties, comparing andcontrasting) used by teacher to introduce new concept.

principles introduced New mathematics principles (Pythagorean Theorem,The sum of two odd numbers is an even number)introduced during a lesson.

principle behaviors

skill introduced

skill behaviors

Different behaviors (stating, paraphrasing, analyzing,applying, justifying) used by teacher to introduce newprinciple.

New^ mathematics skills (adding two-digit numbers,finding averages) introduced during a lesson.

Different behaviors (prescribing, demonstrating,justifying, making analogy) used by teacher tointroduce new skill.

students were administered the adapted MARS-A and their respective grade-level versions of the ITBS.Throughout the school year, the teachers were required to audio-record

typical mathematics lessons. On three separate occasions, once in October,January, and March, the investigator called the school before classes andasked the secretary to instruct the teachers to audio-record their mathematicslesson that day. If they were testing, reviewing or doing atypical activities thatday, they were instructed to audio-record the next typical mathematics lesson.The audiotapes were collected the following week. Two teachers had extendedabsences during one month and recorded one lesson at a later date. Oneteacher taped only two lessons. The Lesson Coding Forms were subsequentlycompleted on the audio-recorded lessons.During the last two weeks of May, the investigator again visited each

classroom to administer the battery of post-tests. The teachers were given theMARS; the students were given the adapted MARS-A and the ITBS.

Analysis

Residual gain scores for the adapted MARS-A and the ITBS were computedby regressing the posttest scores on the pretest scores. Class mean residualgain scores for each instrument were computed for each teacher. Table 4reports the class means and standard deviations for the adapted pre- and post-MARS-A and class means of the residual gain scores. Means for the codedcriteria of the three audiorecorded mathematics lessons were calculated foreach teacher to provide a profile of their teaching practices. Two separatestatistical analyses were performed with these data. First, Pearson productmoment correlations between the teacher postMARS scores and the means



from the coded lessons, as well as the teacher data and the class mean residualgain scores of the adapted MARS-A and ITBS, were calculated. Second,teachers were grouped by the average of their two MARS scores. One groupwas comprised of the seven teachers with the highest average MARS scoresand labeled mathematics anxious (MA) teachers. The second group wascomprised of the seven teachers with the lowest average MARS scores andlabeled non-mathematics anxious (NMA) teachers. Table 4 reports the teacher

Table 4

Teacher MARS Scores and Class Mean Residual Gain Scores

Teacher

I3

3̂4563789131011123131415s16"17131819202122233241325326273281329b3031

Teacher

Pre-MARS

143270190169216160196194239207217161162152118342280175243169177176121303140233100260282167233

Post-MARS

120215217213218144146200248212171140161172117316275155200150218170107334143209101274295179185

AdaptedMARS

-7.783.87

-5.08-11.35-6.750.96

-9.536.7716.0123.16-8.23-9.364.53

-3.745.65

-5.63-6.6715.36-4.1623.72-4.178.17

-24.762.81

-8.55-2.24-5.72-8.983.68

23.75-5.75

Class Residual

ITBSConcepts

-0.52-0.79-0.020.650.22

-0.50-2.13-0.452.043.59

-1.032.420.15

-0.482.196.32

-0.382.51

-0.410.01

-0.93-0.85-6.180.41

-2.63-0.800.78

-2.900.690.82

-1.85

Gains

ITBSProb Solv

0.040.731.611.37

-1.560.580.620.091.322.00

-1.64-0.43-2.99-1.302.00

-0.893.920.50

-2.02-2.28

1.203.15

-3.74-1.90

1.51-1.63-0.98-0.95-0.06-0.11

1.82

denotes teacher in NMA groupDenotes teacher in MA group


506Mathematics Anxiety

pre- and postMARS and ITBS scores, as well as the teachers selected for eachgroup. Analyses of variance comparing the MA and NMA teachers withrespect to the coded lesson means, nominal data and the class means of theadapted MARS-A and ITBS gain scores were conducted.

Results

The range of mathematics anxiety in the teachers of this sample was quitelarge�101 to 334 (Table 4). Table 5 compares the means and standarddeviations of the teacher MARS scores with the findings of other studies ofmathematics anxiety in elementary majors (Battista, 1986; Kelly & Tomhave,1982; Sovchik, Meconi & Steiner, 1981). The mathematics anxiety of theseteachers, even though they volunteered for the study, was not substantiallyless than the mathematics anxiety of prospective elementary teachers in otherstudies.

Table 5

Number, Means and Standard Deviations of Elementary Teachers andPreservice Teachers of Various Studies

Study

Present PreMARSPresent PostMARSKelly & TomhaveBattista PreMARSBattista PostMARSSovchik et al. PreMARSSovchik et al. PostMARS

Number

31314336365959

Mean

200.63193.71230.00211.25192.81200.76181.18

SD

57.0260.01

54.9067.4961.0656.40

Table 6 reports (I) the overall mean and standard deviation for eachvariable, (2) Pearson product moment correlations between MARS scores andvariables, (3) each variable’s contribution to the variance in MARS scores,and (4) results of the analyses of variance comparing MA and NMA teachers.Two significant correlations (p < .05) and one significant F value (p < .05)were found. Teacher mathematics anxiety correlated positively with timedevoted to whole-class instruction and negatively with the number of questionsasked by students during lessons. That is, MA teachers tended to spend moretime in whole-class instruction and have fewer students ask questions duringclass than did their NMA counterparts.The analysis of variance yielded one significant F value for number of

student-initiated questions. Analysis of the means revealed that students inclasses of NMA teachers tended to ask more than twice as many questions asstudents of MA teachers (7.19 questions per class to 3.10 questions per class).

Discussion

The contention that mathematics anxiety is transmitted from teacheis to



Table 6

Lesson Variable Means and Standard Deviations, r-values and Variance, andAnalysis of Variance between MA and NMA Teachers

R2

Lesson Time Spentchecking home/

seatworkreviewingdevelopmentseatworkgiving directionsplaying gameproblem solvingtotal lessonwhole classsmall groupindividualized

Questionstotal numberhigh levellow levelchoralindividualstudent initiated

Content Taughtnumber of conceptsconcept behaviorsnumber of principlesprinciple behaviorsnumber of skillsskill behaviors

Teacher Datayears teachinggraduate math

coursesgraduate educ coursesITBS Concepts scoreITBS Prob Solv score

Student DataMARS residualITBS Concepts

residualITBS Prob Sol

residual

X

10.07

3.0810.4223.013.482.18.047

52.2550.241.901.48

44.888.65

36.2413.6131.274.90

0.561.610.110.600.944.67

13.410.84

10.2541.2228.03

0.000.00

0.00

SD

6.24

2.476.059.491.985.551.575.6513.338.168.25

22.335.7219.4814.3915.592.94

0.903.220.281.710.523.59

6.501.05

6.132.472.01

11.292.18

1.79

r

-.18

-.03-.03

.16

.08-.14-.30-.09

.37*-.29-.23

-.15-.08-.14-.05-.16-.39*

-.09-.17

.00

.08

.20-.02

.13-.32

.06-.25-.04

.08

.30

.09

R2

0.19

0.030.010.110.000.070.130.000.120.070.07

0.070.020.000.090.020.41

0.000.030.000.020.170.00

0.000.20

0.000.120.04

0.240.01

0.01

F

2.65

0.380.101.390.000.851.610.021.440.890.85

0.870.240.901.060.197.72*

0.010.390.010.250.010.01

0.012.87

0.011.660.49

3.450.54

0.13

* p < 0.05



students (Bulmahn & Young, 1982; Kelly & Tomhave, 1985; Lazarus, 1974)was not supported by the results of this study. The correlation yielded nosignificant relationship between teacher mathematics anxiety and changes instudent mathematics anxiety, and there was not a significant difference inchanges in mathematics anxiety between students MA and NMA teachers.However, the adapted MARS-A residual obtained the second highest variance(R = 0.24) of all variables. This finding indicated a mild effect and meritsfurther investigation into the relationship between teacher and studentmathematics anxiety.The results yielded few significant relationships between teacher

mathematics anxiety and teaching practices. MA teachers, as a whole, did notappear to teach drastically differently than NMA teachers (Lesson Time Spentand Content Taught sections of Table 6). The findings, however, did indicatea slight tendency for MA teachers to be more traditional in their teaching.They tended (a) to devote more time to seatwork and whole-class instruction,(b) to devote less time to checking homework, playing games, problemsolving, small-group instruction, and individualized instruction, and (c) toteach more skills and fewer concepts. Nontraditional activities such as playinggames, problem solving, small-group instruction, and individualizedinstruction require teachers to take more mathematical and management risksin the classroom. Perhaps MA teachers, because of their mathematics anxiety,tended not to take such risks. In any event, the findings of this study were notstrong enough nor was enough time devoted to the non-traditional activitiesby the teachers of the study to draw definitive conclusions. Further researchconcerning the relationships between mathematics anxiety and teachingpractices is needed.The questioning techniques of MA and NMA teachers were not significantly

different. However, students of NMA teachers tended to ask more questionsduring lessons. Perhaps because non-anxious teachers were more comfortablewith mathematics, they were more receptive to questions from students.Perhaps non-anxious teachers established an environment which gave studentsmore opportunities to ask questions. The strength of this finding in both dataanalyses merits further investigation.The findings also provided some support for the assertions of Widmer and

Chavez (1982). Awareness seemed to be a critical factor in both this and thatstudy. No doubt the teachers were aware of their own mathematics anxietyand the mathematics anxiety of their students during the studies. Perhapsteachers who are aware of their own negative attitudes and their sources ofmathematics anxiety seek ways to provide students with a differentmathematics environment, and unaware teachers simply perpetuatemathematics anxiety. Further research on the effect of awareness is needed.The statistical analysis of this study was based in part on the comparisons

of means with classes as units of analyses. When means are compared,individual differences are lost in the analysis. Many individual exceptions to



the results of the statistical analyses conducted were noted in the data.Descriptive studies which focus on individual teachers and students, especiallyones with high levels of mathematics anxiety, are needed. A more in-depth,longitudinal analysis of mathematics anxiety in teachers and students w^ouldprovide useful information.

References

Aiken, L. R. (1970). Attitudes toward mathematics. Review of EducationalResearch, 40, 551-596.

Aiken, L. R. (1976). Update on attitudes and other affective variables inlearning mathematics. Review of Educational Research, 46, 293-311.

Battista, M. T. (1986). The relationship of mathematics anxiety andmathematical knowledge to the learning of mathematical pedagogy bypreservice elementary teachers. School Science and Mathematics, 86(\),10-19.

Bulmahn, B. J., & Young, D. M. (1982). On the transmission of mathematicsanxiety. Arithmetic Teacher, 30(3), 55-56.

Hieronymus, A. N., & Lindquist, E. F. (1971). Iowa Test of Basic Skills,Form 6. Boston: Houghton Mifflin.

Kelly, W. P., & Tomhave, W. K. (1985). A study of math anxiety/mathavoidance in preservice elementary teachers. Arithmetic Teacher, 32(5),51-53.

Kulm, G. (1980). Research on mathematics attitude. In R. J. Shumway (Ed.),Research in mathematics education (pp. 356-387). Reston, VA: NationalCouncil of Teachers of Mathematics.

Lazarus, M. (1974). Mathophobia: Some personal speculations. NationalElementary Principal, 53, 16-22.

McLeod, D. B. (1988). Affective issues in mathematical problem solving:Some theoretical considerations. Journal for Research in MathematicsEducation, 19, 134-141.

McMillan, J. H. (1976). Factors affecting the development of pupil attitudestoward school subjects. Psychology in the School, 13, 322-325.

Reyes, L. H. (1987, April). Describing the affective domain: Describing whatwe mean. Paper presented at the annual meeting of the National Council ofTeachers of Mathematics, Anaheim, CA.

Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety RatingScale: Psychometric data. Journal of Counseling Psychology, 19, 551-554.

Sovchik, R., Meconi, L. J., & Steiner, E. (1981). Mathematics anxiety ofpreservice elementary mathematics methods students. School Science andMathematics, 81, 643-648.

Suinn, F. M. (1979). Mathematics Anxiety Rating Scale-A (MARS-A). FortCollins, CO: RMBSI. Inc.

Widmer, C. C., & Chavez, A. (1982). Math anxiety and elementary schoolteachers. Education, 102, 272-276.


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Mathematics Anxiety in Upper Elementary School Teachers