Mathematics Anxiety of PreserviceElementary Mathematics Methods Students

Robert SovchikL. J. MeconiandEvelyn Steiner

The University ofAkronAkron, Ohio 44325

INTRODUCTION

Recently, the term "mathematics anxiety" has become a popular edu-cational phrase. Articles have been published in the popular press attest-ing to the existence of this widespread phenomenon. Fear of mathemat-ics, avoidance of mathematics, even poor attitude toward mathematicsare often associated with the popular term "math anxiety."

Unfortunately, little research has been done to clarify the meaning ofthis term and to suggest effective therapeutic interventions (Aiken, 1970,1976). Thus the purpose of this study was to review some of the relevantliterature in an attempt to clarify the meaning of the term "mathematicsanxiety." A second purpose of this study was to field test an instrumentdesigned to measure mathematics anxiety. Finally, the change scores ofstudents enrolled in a preservice elementary mathematics methods coursewere analyzed to see if reductions in mathematics anxiety were observed.

REVIEW OF THE LITERATURE

The topic of anxiety has been studied by psychologists for many years.Speilberger (1972) estimated that between 1950 and 1970 over 5,000 arti-cles or books on anxiety were published. Different definitions of the termhave yielded a lack of established correlations and have reduced the prac-tical value of the global term "anxiety."

Because of the difficulty defining the global term of "anxiety," psy-chologists began to look at specific forms of anxiety, one form being testanxiety (Sarason, 1960; Hill and Sarason, 1966). In a five year study ofelementary school children, Hill and Sarason (1966) concluded that testanxiety and anxiety scores were increasingly and negatively related to in-dices of intellectual and academic performance. McCandless and Casta-neda (1956) investigated the relationship between anxiety and schoolachievement, finding that the more complex elementary school subjectssuch as reading and arithmetic were affected more by high levels of anxi-ety than the mnemonic skills such as spelling.

In summary, some psychologists began to study specific forms of anxi-ety such as test anxiety. Thus, the term "mathematics anxiety" can beviewed as an outgrowth of the movement to study specific forms of anxi-

643

644 School Science and Mathematics

ety. Also complex cognitive functioning had been shown to be adverselyaffected by high levels of anxiety.

MATHEMATICS ANXIETYVery little experimental work of mathematics anxiety has been done

(Aiken: 1970, 1976). Studies have been located which have related bothanxiety scores and mathematics anxiety scores to performance in mathe-matics. Szetia (1973) used Sarason’s Test Anxiety Scale for Children(TASC) and the Mathematics Debilitating Anxiety Scale to investigatethe relationship between test anxiety, mathematics anxiety and perfor-mance in an eighth grade mathematics class. Szetela found that the effectof test anxiety on mathematics performance was barely significant (p =

.05). The prediction that girls would report significantly higher mathe-matics anxiety than boys was upheld (p < . 0005).

Richardson and Suinn (1972) described the development of the Mathe-matics Anxiety Rating Scale (MARS). This 98 item instrument has beentested at the University of Missouri and Colorado State University, yield-ing test-retest reliabilities of .78 and .85. Data obtained to support theconcurrent validity of MARS has been reported with an inverse relation-ship observed with grades in mathematics (r = - .29, p. < .001) andnumber of years studying mathematics (r = -.44, p. < .001). Also, apositive correlation with reported dislike of mathematics has been ob-served (r == .39, p < .001). Thus, the reliability and validity of the MARSappeared promising when used with college subjects.

Although, the research literature describing mathematical anxiety israther sparse, there have been several articles regarding mathematicsanxiety in popular magazines and newspapers such as the Wall StreetJournal and Time magazine. For example, the March 14, 1977 issue ofTime described a study at the University of California at Berkeley whichrevealed that 57% of the male first-year students had taken four years ofmathematics while only 8% of the females had done so. Thus, 92% ofthe freshmen women could major in only 5 of 20 available fields becausethey lacked the necessary prerequisite skills. Females were excluded fromareas like premedicine and engineering because of their avoidance ofmathematics in high school.

In conclusion, few studies were located which clarified the term"mathematics anxiety." In the popular media the term "mathematicsanxiety" seemed to be associated with fear, avoidance, and dislike. Itwas taken for granted that this construct was well-defined and measur-able. If the psychological history is any precedent this assumption is un-supported. As has been previously noted, 5,000 journal articles and re-search studies have yielded little basic agreement on the origin, defini-tion, and treatment of anxiety within the psychological area. Theoriesrun the gamut from those emphasizing that anxiety has biochemicalorigins to others which say that anxiety is a learned response.

Mathematics Anxiety 645

Although the mathematics education literature is meager regardinganxiety when compared to the psychological literature, a common threadof using paper and pencil inventories in both areas was identified.Richardson and Suinn*s instrument (MARS) seemed particularly usefulas a means of operationally defining and measuring mathematics anxietyby means of scores on the instrument. Thus, it was deemed practical aswell as important to utilize the Richardson and Suinn instrument as ameans of measuring the mathematical anxiety of junior level elementaryeducation mathematics methods students. Also, the reliability of this in-strument was investigated again.

PROBLEM

Two basic research questions were asked during this study. Firstly,w^at was the reliability of the Mathematics Anxiety Rating Scale(MARS)? Secondly, did taking a mathematics methods course lessen thedegree of mathematics anxiety as measured by the MARS?The 98 item Likert type Mathematics Anxiety Rating Scale (MARS)

was administered on a pretest and posttest basis to 59 students enrolled ina mathematics methods course for prospective elementary school teach-ers during the Fall Quarter, 1978. This instrument requires students to re-spond by marking how much they are frightened by statements presentedin the test. For example, one item is stated in this way: "calculating asimple percentage, e.g., the sales tax on a purchase." Subjects are askedto respond whether this item elicits anxiety levels in these categories: notat all, a little, a fair amount, much, and very much. The scores given to aresponse range from one to five, with a score of five associated with aresponse of very much.The 59 elementary education students comprising the subjects of this

investigation were enrolled in three sections of a mathematics methodscourse at The University of Akron. Course syllabi, tests, textbooks andmethods of instruction in all three sections were similar.

Table I presents the data obtained during the pretest and posttest.

TABLEl

Pretest Posttest

Mean 200.76S.D. 61.06N = 59

Mean 181.18S.D. 56.40N = 59

A dependent measures t test (Glass and Stanley, 1970) yielded a t valueof 4.29 which was significant at the .05 level. Coefficient Alpha (Bron-bach, 1951), a generalized form of the Kuder-Richardson Formula 20,yielded a pretest reliability of 0.978 and a posttest reliability of 0.982.

646 School Science and Mathematics

Several tentative conclusions can be made from this study. First, thereliability of the MARS was quite high for both the pretest and the post-test. This occurence tends to confirm the results of other studies cited inthis paper.

Also the t value of 4.29 indicated a statistically significant mathematicsanxiety reduction from pretest to posttest.

Caution should be exercised here because the design of this investiga-tion was not a true experiment in the Campbell and Stanley (1970) sense.Lack of a control group and the absence of randomization force a tenta-tive view of this result. Nevertheless, since the mathematics methodscourse instructors utilized active learning approaches with concrete ma-terials, a hypothesis for further testing emerged. Specifically, what rela-tionship exists between mode of instruction and mathematics anxiety?

Finally, the data obtained in this study compare favorably to otherdata obtained from the MARS. For example, Richardson and Suinn(1977, personal correspondence) produced the following data for 109(Sample 1) and 80 (Sample 2) upper class students at a university:

TABLE 11

Sample 1 Sample 2Humanities 196.46 (63.9)* 187.40 (52.4)Social Sciences 176.72 (57.7) 169.40 (56.0)Physical Sciences 142.88 (39.5) 143.80 (33.4)

*Figures in parenthesis are standard deviations.

The Humanities students exhibited the highest scores on the MARS. Itseems reasonable to compare the elementary education major scores withthose of the Humanities students. Doing this reveals that the elementaryeducation majors scores of 200.76 and 181.18 are comparable to the Hu-manities students scores.

CONCLUSIONS

Three main questions were asked during this study. First, a survey wasundertaken of the research and popular literature dealing with mathe-matics anxiety. When compared to the psychological literature dealingwith anxiety the amount of mathematics anxiety research seemed mea-ger. It may be safely stated that mathematics anxiety is an illusive,ambiguous term in need of greater clarification. One vehicle for effectiveclarification might be to communicate more with psychologists who arestudying the construct of anxiety. For example, a list of proximal conse-quences of anxiety developed by Phillips, Martin, and Meyers (1972)might serve as a base for developing a behavioral list of mathematicsanxiety symptoms. Working within the psychological construct of anxi-

Mathematics Anxiety 647

ety Phillips, Martin, and Meyers developed the following list ofproximalconsequences of anxiety:

1. cautiousness, perseveration, rigidity, and dependency2. reduced responsiveness to the environment3. interference with a variety of cognitive and mediational processes4. increased drive or motivational level5. helplessness6. compulsive behaviors7. poor self image.

Behavioral checklists which specifically relate the above items tomathematics anxiety might prove useful in teaching and experimentalsituations. In short, greater communication between mathematics educa-tors and personnel trained in the area of psychology needs to be startedin order to clarify the meaning of the term "mathematics anxiety. *’

Although this study lacked a control group and randomizations, atentative finding seems to be that taking a mathematics methods coursereduces mathematics anxiety. Since this study was designed to suggesthypotheses rather than to exhibit rigid experimental controls, a need isevidenced to replicate this study utilizing proper experimental controls.In this way the experimenter might determine the effects of curriculum,instruction and other variables upon anxiety measurements. Some spe-cific questions are the following:

1. What relationship exists between the mathematics anxiety of teachers and students?2. What relationship exists between various instructional sequences and mathematical

anxiety?3. How does mode of instruction (i.e. concrete, semi-concrete, and abstract) interact

with mathematics anxiety?4. How do general anxiety measurements relate to specific mathematics anxiety meas-

urements?

Finally, the Richardson and Suinn Mathematics Anxiety Rating Scaleexhibited high reliability and reinforced other studies which suggested itspotential in the clinical identification and treatment of mathematicsanxiety.

REFERENCES

AIKEN, L. R. Nonintellective variables and mathematics achievement. Journal of SchoolPsychology, 1970, 8, 28-36.

AIKEN, L. R. Update on attitudes and other affective variables in learning mathematics.Review of Educational Research, 1976, 46,293-311.

CAMPBELL, D. T. & STANLEY, J. C. Experimental and quasi-experimental designs for re-search. Chicago: RandMcNally, 1966.

CASTANEDA, A., PALERMO, D. S.. & MCCANDLESS, B. R. Complex learning and perfor-mance as a function of anxiety in children and task difficulty. Child Development, 1956,27,327-332.

CRONBACH, L. J. Coefficient alpha and the internal structure of tests. Psychometrika,1951.76.297-334.

648 School Science and Mathematics

GLASS, G. V. & STANLEY, J. C. Statistical methods in education and psychology. Engle-wood Cliffs, New Jersey: Prentice-Hall, 1970.

HILL, K. T., & SARASON, S. B. The relation of test anxiety and defensiveness to test andschool performance over the elementary-school years: A further longitudinal study.Chicago: Society for Research in Child Development, 1966.

PHILLIPS, B. N. & MARTIN, R. P., & MEYERS, J. Interventions in relation to anxiety inschool in C. D. Speilberger (Ed.) Anxiety: current trends in theory and research^ NewYork: Academic Press, 1972, pp. 410-464.

RICHARDSON, F. C., & SUINN, R. M. The mathematics anxiety rating scale�psychometricdata. Journal ofCounseling Psychology^ 1972, 7P, 551-554.

SARASON, S. B. et al. Anxiety in elementary school children. New York: John Wiley, 1960.SPEILBERGER, C. D. Current trends in theory and research on anxiety in C. D. Speilberger

(Ed.) Anxiety: current trends in theory and reserach, New York: Academic Press, 1972,pp.3-23.

FREAK TORNADO

A University of Chicago expert says the April 4, 1981 tornado that stuck WestBend, Wisconsin, killing three people and damaging 150 buildings, was a "one-in-a-thousand" freak�and the most vicious of its type on record. It was a clock-wise-rotating tornado, and Professor T. T. Fujita says it was the first known tohave killed anyone."Many people used to think these clockwise tornadoes were weak," Fujita

says. But this was a strong one. We never thought a clockwise tornado couldreach this kind of intensity. On the Fujita scale, which assigns the number * *0’ * tothe weakest tornadoes and "5" to the strongest, the West Bend tornado was a"4". Fujita says clockwise tornadoes are so rare that their very existence was de-bated until 1975, when the first motion picture of one was taken.He explains that tornadoes in the Northern Hemisphere nearly always spin

their winds counterclockwise, while clockwise tornadoes from south of the equa-tor. Their rotations arise from the rotation of the earth.

Fujita and his research associate Roger Wakimoto studied the tornado’s windsby analyzing Wakimoto’s aerial photographs of its path of destruction. Theyshow that the tornado scattered debris in large arcs that stretch clockwise fromthe shattered buildings.

Fujita says that the West Bend tornado is unusual for another, and unexplain-ed, reason. While most tornadoes begin with wide funnels that become narrow-er, this tornado started with a diameter of less than 100 feet and grew to 1,000feet near the end of its 1.8 mile path.

Fujita also is not sure how these reversed tornadoes form, but in 1977, he andhis students succeeded for the first time in creating a clockwise tornado on Fuj-ita’s tabletop tornado machine. By combining a jet of air traveling near the sur-face with an updraft of air, the researchers created two tornadoes flanking thejet and rotating in opposite directions.

Wakimoto, who now has found five clockwise-rotating tornadoes, adds thatthe West Bend tornado also was formed from a much weaker thunderstorm�with a height of 28,000 feet rather than the normal 40,000 feet�than are mosttornadoes."The people who suffered from this tornado may not care that theirs was a

very unusual type," Fujita says. "Destruction is destruction. But to better warnof tornadoes we must learn more about them."