the relationship of mathematics anxiety and mathematical knowledge to the learning of mathematical...

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The Relationship of MathematicsAnxiety and Mathematical Knowledgeto the Learning of MathematicalPedogogy by Preservice ElementaryTeachersMichael T. Battista

The quality of mathematics instructionat the elementary school level dependson the preparation ofpreservice elemen-tary teachers to teach mathematics.Without sufficient knowledge of mathe-matics and mathematical pedagogy, it ishighly unlikely that preservice elemen-tary teachers will be able to deliversound mathematics instruction to theirpupils. However, there has been a greatdeal of concern expressed lately aboutthe low level of mathematical knowl-edge and the negative attitudes towardmathematics possessed by pre- and in-

service elementary teachers. This concern is based on the belief that the lack ofknowledge of and poor attitudes toward mathematics exhibited by many pre-service elementary teachers may inhibit their learning and later use of effectivemethods for teaching mathematics. It is also based on the belief that teachers’negative attitudes towards mathematics may be transmitted to their pupils (Lar-son, 1983), or may negatively affect their pupils’ mathematics achievement(Schofield, 1981).

Based on these concerns, many teacher educators believe that developing posi-tive attitudes toward mathematics should be a major goal of both mathematicsand mathematics methods courses for preservice elementary teachers. They alsobelieve that preservice elementary teachers must be adequately prepared inmathematics in order for a mathematics methods course to be fully effective.The present research report examined how preservice elementary teachers’

School Science and MathematicsVolume 86 (1) January 1986

Mathematics Anxiety and Knowledge 11

mathematical knowledge and mathematics anxiety affect their success in amathematics methods course. It also examined the hypothesis that a mathemat-ics methods course can reduce the mathematics anxiety of preservice elementaryteachers.

Procedure

The subjects of the study were 38 preservice elementary teachers from two sec-tions of a mathematics methods course taught by the experimenter. At the begin-ning of the semester and before any instruction was given, the experimenter ad-ministered first the Mathematics Anxiety Rating Scale (Suinn, 1972), then a testof mathematical competence. The Mathematics Anxiety Rating Scale (MARS)was administered again at the end of the semester. Prior to enrolling in the meth-ods course, the preservice teachers had taken either one or two college mathe-matics courses.

During the methods course, the preservice teachers participated in lecture-discussion sessions, small group activities that familiarized them with the use ofvarious concrete materials commonly utilized in mathematics teaching, and afive-week field experience performed in the local schools. During the field expe-rience, each preservice teacher taught a small group of elementary school pupilsfour days a week during the time slot regularly scheduled for mathematics. Eachpreservice teacher taught the same small group of pupils for the entire five-weekperiod. The field experience was supervised by both a university faculty memberand the elementary school pupils’ full-time teachers. The preservice teacherswere required to write detailed daily lesson plans describing all their planned in-structional activities for the field experience. A midterm exam was given beforethe field experience; a final exam was given at the end of the semester.

In addition to the pre- and post-test scores on the MARS (MARS1 andMARS2, respectively) and pretest score on the test of mathematical competence(MATHT), several other scores were recorded for each preservice elementaryteacher. These were a combined score for the two course exams (EXAMS); thepreservice teacher’s field experience teaching evaluation that was developed by auniversity supervisor and the elementary pupils* regular teacher (TEACHING);a grade for all lesson plans written during the field experience (LPLANS); a finalgrade (FGRADE) for the methods course which was the average of the EXAMS,TEACHING, and LPLANS scores; and an average grade for previously takencollege mathematics courses (MATHC). Two additional scores obtained were aMATH score, which was the average of the percent scores received for theMATHT and MATHC scores, and a spatial ability score SA. The latter scorewas recorded because spatial ability has previously been shown to be related tomathematics achievement and mathematics anxiety, and it was thought that itmight also be related to learning concrete and pictorial embodiments for mathe-matical ideas�an essential component of the mathematics methods course.


12 Mathematics Anxiety and Knowledge

In addition to obtaining results on the original 38 preservice teachers taught bythe experimenter, partial results were obtained for two mathematics methodscourses taught by another instructor (N = 36). The experimenter and other in-structor covered approximately the same material for the methods course, hadpreservice teachers participate in the same field experience, and based the meth-ods course grade on the same three equally weighted factors�exam grades, fieldexperience teaching, and lesson plans. The two instructors differed in that the ex-perimenter gave the MARS pretest before the mathematics test, whereas theother instructor gave the MARS after the mathematics test; also, the experimen-ter gave a midterm and a non-comprehensive final exam, whereas the other in-structor gave only a comprehensive final exam.

In addition to examining pre- to post-test decreases on the MARS, scores onall variables were intercorrelated in an attempt to discover how different meas-ures of achievement in the mathematics methods course were related to mathe-matical knowledge and mathematics anxiety. The group of preservice teachersfrom classes taught by the experimenter was labeled Group 1; the group taughtby the other instructor was labeled Group 2.

Measurement Instruments

Mathematics Anxiety Rating Scale (MARS): mathematics anxiety was measuredby the Mathematics Anxiety Rating Scale (Suinn, 1972). Scores on the MARScan range from 98 to 490, with high scores indicating a high level of mathematicsanxiety. Richardson and Suinn (1972) have reported a Cronbach alpha of .97 forthe MARS.

Mathematical Competency Test (MATHT): the mathematical competence ofthe preservice teachers was measured by a 50-item multiple choice test that wasdeveloped at Kent State University to assess preservice elementary teachers*knowledge of mathematics (Speer, 1975). The test covers operations on fractionsand decimals, elementary algebra, problem solving, geometry, reading graphs,set theory, percents, ratio, and measurement. The Kuder-Richardson formula 20reliability of the test was .87.Purdue Spatial Visualization Test (SA)’. spatial ability was measured by a

modified version of the Purdue Spatial Visualization Test: Rotations (Guay,1977). The modified test is timed (8 minutes) and consists of 20 multiple choiceitems designed to measure the ability to mentally rotate three-dimensional ob-jects depicted in drawings. The KR-20 reliability of the test was .75.

Field Experience Teaching Evaluation (TEACHING): the preservice teachers*teaching performance during the field experience was evaluated by their universi-ty instructor and the regular teacher of the elementary pupils they were teaching.The same written evaluation form was used by both the teacher and the universi-ty instructor, and the two numerical scores derived from the forms were aver-



aged to arrive at a teaching score. Each of the following categories was rated ona 4-point Likert scale: teaching methods, instructional materials, rapport withpupils, provisions for individual- differences, organization, planning, clarity,knowledge of mathematics, questioning, professional conduct.

TABLE 1Means and Standard Deviations of Variables (N = 38)

Group 1

Variable

MARS1MARS2MARSDMATHTMATHCMATHSAEXAMSTEACHINGLPLANSFGRADE

Mean

205.84171.3434.5031.212.76

65.757.53

83.3790.0389.1887.55

StandardDeviation

53.6542.9242.787.84.94

17.453.365.353.491.902.72

PossibleRange

98-49098-490

(-392)-3920-500-40-1000-200-1000-1000-1000-100

Results

The means and standard deviations for all variables measured for the classestaught by the experimenter (Group 1) are given in Table 1. Intercorrelations forthese variables are given in Table 2. It can be seen from Table 2 that there was asignificant negative correlation (p < .05) between preservice teachers’ enteringlevel of mathematics anxiety (MARS1) and all three measures of mathematicalknowledge (MATHT, MATHC, MATH). However, preservice teachers’ mathe-matics anxiety (MARS1) was not significantly related to their final grade in themethods course (FGRADE) nor any of the three measures of achievement for themethods course (EXAMS, TEACHING, LPLANS). Also, there was a signifi-cant positive correlation (p < .05) between all three rreasures of mathematicalknowledge and preservice teachers’ EXAMS scores or the methods course.However, none of the measures of mathematical knowledge correlated signifi-cantly with the two other measures of achievement in the methodscourse�TEACHING and LPLANS. Preservice teachers’ EXAMS scores werepositively correlated with their TEACHING and LPLANS scores, but only thelatter correlation was significant. Although mathematical knowledge as meas-


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ured by the mathematics test did not correlate significantly with the final gradein the methods course, mathematical knowledge as measured by grades in previ-ous college mathematics courses and the overall measure of mathematicalknowledge, MATH, did (p < .05). Spatial ability correlated positively (p < .01)with all three measures of mathematical knowledge, and negatively (p < .05)with pretest and post-test anxiety measures. Spatial ability did not correlate sig-nificantly with any of the performance measures from the methods course. Ascan be seen from Table 1, the average decrease in mathematics anxiety from pre-test to post-test (MARSD) was 34.50. This represents a significant reduction inanxiety (paired t-test, t = 4.97,p< .001).

TABLE 3Means and Standard Deviations of Variables (N = 36)

Group 2

Standard PossibleVariable Mean Deviation Range

MARS1MARS2MARSDMATHTEXAMSTEACHINGLPLANSFGRADE

211.25192.8118.4432.1160.729.8310.223.42

54.9067.4943.948.369.391.781.35.69

98-49098-490

(-392)-3920-500-861-131-130-4

The means, standard deviations, and intercorrelations for those variablesmeasured for the other instructor (Group 2) are given in Tables 3 and 4. As canbe seen from the tables, the initial mathematics anxiety for this group was some-what higher and seemed to correlate negatively to a greater degree with MATHTthan for the experimenter’s preservice teachers. Table 4 indicates that, similar tothe results for the preservice teachers taught by the experimenter, the mathemati-cal knowledge of preservice teachers taught by the other instructor was signifi-cantly (p < .01) and positively correlated with preservice teachers’ performanceon the methods course exams but not with their performance in the field experi-ence or on written work. For the other instructor, preservice teachers’ finalgrades in the methods course were positively correlated (p < .05) with theirmathematical knowledge as measured by the mathematics test, but did not sig-nificantly correlate with their anxiety scores. Finally, Table 3 indicates that theaverage decrease in mathematics anxiety from pretest to post-test for Group 2(MARSD) was 18.44. Although this reduction in anxiety was significant (pairedt-test, t = 2.52, p < .05), it was only about half as large as the reduction in anxie-ty observed for Group 1.


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As can be seen from Tables 2 and 4, the decrease in mathematics anxiety waspositively correlated with preservice teachers* initial mathematics anxiety forboth groups of preservice teachers (p< .01 for Group 1 and p< .05 for Group 2).This result can be interpreted as indicating that the higher a preservice teachersinitial level of mathematics anxiety, the greater the reduction in anxiety duringthe methods course. In order to further investigate this finding, the overall meanfor both groups was calculated. Then, for each group, the pre- to post-testdecrease in MARS was calculated for those preservice teachers whose MARSpretest was greater than or equal to the mean (above average initial anxiety) andfor those preservice teachers whose MARS pretest scores were below the mean(below average initial anxiety). As can be seen from Table 5, for both Group 1and Group 2, there were noteworthy decreases in mathematics anxiety for theabove average initial anxiety subgroups, but only slight decreases for the belowaverage subgroups.

TABLE 5Pre-to Post-test Decreases in Mathematics Anxiety for Above and

Below Average Initial Levels of Anxiety

Pretest MARSGroup N MARS Decrease t

Group 1above averageMARS1 20 250.60 57.20 5.50**

Group 1below averageMARS1 18 156.11 9.28 2.34*

Group 2above averageMARS1 16 260.06 38.63 3.19**

Group 2below averageMARS1 20 172.20 2.30 31

*p < .05**p<.01

Discussion

One goal of the present study was to examine whether preservice elementaryteachers* mathematical knowledge affects their performance in a mathematicsmethods course. The study found that the preservice teachers’ mathematicalknowledge was indeed significantly related to their learning of mathematical


18 Mathematics Anxiety and Knowledge

pedagogy as measured by methods course exams, but was not related to theirteaching performance in an extensive field experience conducted during themethods course. The former result seems consistent, and the latter result incon-sistent, with the results ofSchofieId (1981) who found first year teachers’ knowl-edge of mathematics during their final year of college to be positively related totheir pupils’ mathematics achievement. Since there was some indication that thepreservice teachers’ knowledge of mathematical pedagogy as measured bymethods course exams was related to their performance in the field experience asmeasured by the TEACHING and LPLANS scores, and since mathematicsknowledge was related to performance on the methods course exams, it could beconjectured that there is a relationship between mathematical knowledge andteaching performance, but that the measurement instruments utilized in the pres-ent study were not powerful enough to detect the relationship.A second goal of the present study was to examine the hypothesis that preserv-

ice elementary teachers’ mathematics anxiety may inhibit their performance in amathematics methods course. Although the pretest anxiety scores did correlatenegatively with three out of four of the measures of performance in the methodscourse (EXAMS, LPLANS, FGRADE), none of these correlations was signifi-cant. Thus, the data did not support the hypothesis that mathematics anxiety in-hibits preservice elementary teachers’ learning of mathematical pedagogy.The third and final goal of the present study was to examine the effect of a

mathematics methods course on the mathematics anxiety of preservice elemen-tary teachers. The results of the present study indicated that the mathematicsanxiety of preservice elementary teachers can be reduced by a mathematics meth-ods course, and agree with the results ofSovchik, Meconi, and Steiner (1981). Infact, at the conclusion of the methods course, the overall mean of the anxietyscores for the preservice teachers had been reduced to a level that was somewhatlower than the average for humanities majors (Suinn, 1972; Richardson andSuinn, 1972). Furthermore, the results indicated that for those preservice teach-ers who entered the methods course with above average mathematics anxiety,there was generally a noteworthy decline in anxiety during the course. The de-creases in MARS scores for these groups (57.20 for Group 1 and 38.63 for Group2) compare favorably with the 50-70 point reductions in MARS scores reportedfor clients of behavior therapy who were being treated for mathematics anxiety(Richardson and Suinn, 1972; Suinn, Edie, Nicoletti, and SpineIIi, 1972).Two possible factors for the observed reduction in anxiety may be hypothe-

sized. First, since it has been suggested in the literature that mathematics anxietycan be reduced by making students aware of the personal usefulness of mathe-matics (Benton, 1979; Brush, 1979; Sherard, 1981), it could be that the methodscourse, especially the field experience, illustrated to the preservice teachers theusefulness and importance of mathematics in their future teaching careers.



Second, mathematics anxiety seems to be related to self-confidence in dealingwith mathematics (Sherard, 1981; Tobias and Weissbrod, 1980), so perhaps themethods course, and in particular the field experience, convinced the preserviceteachers that mathematics is not something that should be feared, but is some-thing they can deal with effectively. As one preservice teacher wrote about thefield experience in her log, ’This (field) experience has helped me develop theconfidence I needed in myself to teach math, and I finally realized that math isnot something to be feared."

It is suggested that future research in this area attempt to examine more care-fully the teaching performance of preservice elementary teachers in order to fur-ther investigate the relationship between preservice teachers’ mathematicalknowledge and their teaching performance.

References

1. Benton, B. Math Avoidance and Pursuit of Fantasy Careers. Paper presented at theAmerican Educational Research Meeting, San Francisco, 1979.

2. Brush, L. R. Why Women Avoid the Study of Mathematics: A Longitudinal Study.Washington, D.C.: National Institute of Education, 1979.

3. Guay, R. Purdue Spatial Visualisation Test: Rotations. West Lafayette, IN: PurdueResearch Foundation, 1977.

4. Larson, C.N. Techniques for Developing Positive Attitudes in Preservice ElementaryTeachers. Arithmetic Teacher, 1983, 8-9.

5. Richardson, F. C. and R. M. Suinn. The Mathematics Anxiety Rating Scale: Psycho-metric data. Journal of Counseling Psychology, 1972, 551-554.

6. Schofield, H. Teacher Effects on Cognitive and Affective Pupil Outcomes in Elemen-tary School Mathematics. Journal of Educational Psychology, 1981, 462-471.

7. Sherard, W. H. Math Anxiety in the Classroom. The Clearing House, 1981, 106-110.8. Sovchik, R., L. Meconi, and E. Steiner. Mathematics Anxiety of Preservice Elemen-

tary Mathematics Methods Students. School Science and Mathematics, December1981,643-648.

9. Speer, W. R. Mathematics Test. Kent State University, 1975.10. Suinn, R. M. Mathematics Anxiety Rating Scale and Information for Users manual.

RMBSI.Inc., 1972.11. Suinn, R. M., C. Edie, J. Nicoletti, and R. Spinelli. The MARS, A Measure of Mathe-

matics Anxiety: Psychometric Data. Journal of Clinical Psychology, July 1972, 373-375.

12. Tobias, S. and C. Wiessbrod. Anxiety and Mathematics: An Update. Harvard Educa-tional Review, 1980,63-70.

Michael T. BattistaKent State UniversityKent, Ohio 44242


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