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Anxiety, Cognitive Style, andMathematics AchievementTrevor E. Sewell a , Frank H. Farley a & Fay B. Sewella

a Temple University, University of Wisconsin-Madison,and Montgomery Community College , USAPublished online: 06 Jul 2010.

To cite this article: Trevor E. Sewell , Frank H. Farley & Fay B. Sewell (1983) Anxiety,Cognitive Style, and Mathematics Achievement, The Journal of General Psychology,109:1, 59-66, DOI: 10.1080/00221309.1983.9711509

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The Journal of General Psychology, 1983, 109,59-66.

ANXIETY, COGNITIVE STYLE, AND MATHEMATICS ACHIEVEMENT*

Temple University, University of Wisconsin-Mudison, and Montgomery Community College

TREVOR E. SEWELL, FRANK H. FARLEY, AND FAY B. SEWELL

SUMMARY This study examined the relationships among state and trait anxiety,

cognitive style, and mathematics achievement. The Ss were 50 junior col- lege students enrolled in a mathematics course. The results confirmed the hypothesis that high state anxiety would be associated with poor mathemat- ics achievement; trait anxiety showed no significant relationship to achieve- ment. The need to develop learning aids and strategies to counteract the possible debilitating effects of state anxiety in learning and mathematics assessment was discussed.

A. INTRODUCTION Although conceptual differences in the theoretical analysis of the con-

struct of anxiety are pervasive (l), the increasing empirical evidence that has emerged using different operational definitions and methodologies indicates that high levels of anxiety generally have a negative impact on academic achievement (17). Despite a need for further conceptual clarification of the meaning of anxiety, Spielberger (20) has highlighted state and trait anxiety as “fundamental constructs” in anxiety theory.

With remarkable consistency, research points to state anxiety (A-State), which is reflected in a feeling of apprehension and heightened autonomic nervous system activity, as being more highly related to achievement, learn- ing, and problem-solving performance than is trait anxiety ( A-Trait), which refers to consistent individual differences in anxiety proneness (19). For example, for concept learning tasks Meyers and Martin (8) found the perfor- mance of high A-State Ss to be significantly inferior to that of low A-State Ss

*Received in the Editorial Office, Provincetown, Massachusetts, on November 15, 1982. Copyright, 1983, by The Journal Press.

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in contrast to no difference in performance between high and low A-Trait Ss. Suggesting that high A-State individuals “tended to use less focusing strategies,” Gross and Mastenbrook (5, p. 605) reported that high A-State Ss solved fewer problems than did middle and low state anxious Ss.

Although the evidence supports the position that a high A-State adversely affects academic problem-solving skills, it should be noted that the intensity of the anxiety and the difficulty level of the tasks may produce an interaction between anxiety and performance. When an intermediate level of anxiety is achieved for difficult tasks, anxiety facilitates problem-solving behavior (13), and, conversely, at an intense level, the effects are likely to be debilitat- ing ( 2 ) . Consistent with this position, O’Neil, Spielberger, and Hansen (10) reported that the magnitude of the errors on a computer-assisted learning task was highly related to task difficulty and to A-State scores. In line with prediction, high A-State students, in contrast to low A-State students, made relatively more errors on difficult tasks and fewer errors on easy tasks.

The theoretical framework from which much of the earlier empirical investigation of anxiety and learning has been generated has often been some variant of drive theory which holds that highly anxious students are inferior to less anxious students on complex or difficult tasks in which competing responses are a factor (18). Another, more recent model, applied particularly to test anxiety, is that of information processing (e.g., 1, 9, 22) . This general model “. . . explains the performance deficit of high test-anxious students in terms of problems in encoding and organizing information and in retrieval of this information in a test situation” (1, p. 816).

One area of academic achievement and test performance in which the role of anxiety has recently received considerable attention is mathematics. It has been argued by some writers that girls shows greater “math anxiety” than boys do ( i f 3 ) . Such math anxiety is conceived of as a content-specific form of anxiety. Also of interest is the question whether the more pervasive distinc- tions of A-State and A-Trait anxiety contribute to mathematics achieve- ment. This question is the focus of the present report. On the basis of the literature cited above, it would be hypothesized that mathematics achieve- ment as reflected in mathematics tests would be impaired by high A-State anxiety (when intellectual ability is equated). Anxiety is a major personality dimension, characterized by Wiggins (24) as one of the “big two” in the measured personality domain. Cognitive styles are major individual differ- ence dimensions that have been shown to be importantly involved in many areas of academic achievement (7). Probably the most central cognitive style

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for academic achievement is that of field dependence-field independence (25). In light of the consistent findings that mathematics achievement relates differentially to field dependence 2rs field independence (14, 23), it would seem desirable, in the present study, to consider the relationship of anxiety to mathematics achievement within each of these cognitive styles.

B. METHOD 1 . Subjects

The Ss were 50 junior college students (20 males, 30 females) in a large eastern U.S. city enrolled in a required mathematics course during the Fall semester. The Ss were in two sections of the identical course with the same instructor. Ninety-four percent of the students were Anglo-American. Ss volunteered to participate in the research project. Although no one refused, missing data attributable to absences during the testing sessions resulted in the loss of six Ss. Sufficient data were obtained on 50 Ss on which the analyses are based.

2 . Instruments and Procedure 1. The State-Trait Anxiety Inventory (2 1) was administered following

standard instructions. The scale was administered after mid-term examina- tions when an impending examination was of no immediate concern to the students. Separate scores were obtained for State Anxiety (A-State) and Trait Anxiety (A-Trait).

2 . The Group Embedded Figures Test (GEFT), a measure of cognitive style, was administered according to standard procedures (26). The test consists of 18 complex figures. Performance on this test allowed for assess- ment of field-dependent and field-independent cognitive styles. Ss who scored at or above the median were classified as field-independent (N = 26); those whose scores were below, were classified as field-dependent ( N = 24).

3. Intellectual ability was estimated by the Standard Progressive Matrices (12). The Standard Progressive Matrices (Sets A, B, C, D, and E) consists of 60 problems divided into five sets of 12. It provides nonverbal (spatial) graded difficulty assessment of a person’s intellectual ability.

4. Achievement in mathematics was determined by averaging Ss’ perfor- mance on three major tests during the semester. All examinations in the two sections were administered on the same day.

Data collection was completed on all measures, with the exception of mathematics achievement, within a two-week period.

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TABLE 1 MEAN SCORES ON ANXIETY AND PERFORMANCE MKASURES

Female (n = 30) Total (n = 50) Variables M SD M SD M SD

Male (n = 20)

Ravens 49.37 10.03 51.92 3.88 49.73 8.40 A-State 44.10 8.94 43.5 12.61 44.0i 11.37 A-Trait 44.2 1 12.76 43.69 9.26 42.91 10.28 Cognitive style 8.25 5.06 9.24 4.40 8.78 6.30 Math achievement 60.1 25.14 68.83 15.43 6S.06 20.30

C. Results

The means and standard deviations of all variables for the total sample, and for males and females separately, are presented in Table 1. Despite apparent sex differences in the means of all variables, none was significant in t-test comparisons for each variable, with Dunn’s (6) procedure being em- ployed because of the lack of independence of the comparisons.

Table 2 presents the intercorrelation of all variables for the total sample. Worthy of note is the striking contrast between State and Trait Anxiety in their relationship to mathematics achievement and the measure of intellectu- al ability (Ravens). Further analysis of the correlation for the dichotomized groups of field-dependent and field-independent groups, respectively, was undertaken to determine whether cognitive style was moderating the anxi- ety/math performance relationship. No moderating effect was found. The two groups were constructed with the use of a median split on the cognitive style score distribution, with unequal ns resulting due to the number of

TABLE 2 PEARSON CORRELATIONS AMONG INTELLECTUAL. ANXIETY, COGNITIVE STYLE, AND

MATH VARIABLES ~

Variables 1 2 3 4 5

1. Ravens matrices - 2 . State anxiety - .25 3. Trait anxiety .40** .2 9* - 4. Cognitive style - .49** .20 - .39** - 5 . Math achievement .33** - .49*** .11 -.13 - Note: N = 50.

-

* p < .05. ** p < .01.

*** p < ,001.

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scores at the median. For field-dependent Ss the relevant comparisons, with as, were as follows: A-Statelmatch, r = - 3 3 , n = 21, p < .01; A-Trait/ math r = .13, n = 21, NS. For field-independent Ss the relevant compari- sons, with ns, were as follows: A-Statelmath, r = -.41, n = 24, p < .05; A-Trait/math, r = - .03, = 24, NS. Comparison of the A-State correla- tions between the two cognitive style groups with the use of z transforma- tions, and a comparable comparison for the A-Trait correlations, yielded no significant differences and thus no evidence of a moderating influence (15) of cognitive style.

A 2 X 2 (sex X A-State) analysis of covariance with mathematics score as the dependent variable, and Ravens as the covariate, was performed. A significant main effect for A-State was found [F(1, 44) = 12.04, p < .001]. The analysis did not yield a significant main effect for sex, nor was the interaction significant. Similar analyses for Trait Anxiety and Cognitive Style did not yield significant main effects of interactions.

D . DISCUSSION One of the most striking findings with respect to mathematics achieve-

ment is its strong negative relationship to A-State anxiety. Since A-Trait was negligibly related to mathematics scores, it seems reasonable to infer that individuals whose behavior might not reflect a proneness to anxiety might still be very vulnerable to A-State anxiety in mathematics activities. It is of interest to contrast the present findings of a - .49 correlation between A-State anxiety and math achievement, and the findings of Sepie and Keeling (1 6) who correlated three measures of anxiety with math achieve- ment on a standardized test. For test anxiety and general anxiety, no significant correlations were obtained. For a measure of mathematics- specific anxiety, correlations of - .30 (p < .01) and - .28 (p < .01) for girls and boys, respectively, were obtained. The present results suggest that A- State, rather than the other conceptions of anxiety, might be particularly worth pursuing vis d vis mathematics achievement,

The effect of anxiety on both intellectual ability and cognitive style is unclear. A-State did not correlate significantly with intelligence, thus not supporting Phillips, Martin, and Meyers (1 l), nor with cognitive style. It should be noted that the significant negative relationship of A-trait to cognitive style is exactly opposite to the significant positive relationship between A-Trait and intelligence. Although the meaning of these relation- ships is unclear, the recognition of a possible “personality” dimension in cognitive style allows for the speculation that the proneness or predisposition

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to anxiety as assessed by A-Trait might be interacting with the personality dimensions thus resulting in the negative relationship. An examination of the pattern of correlations for A-State/A-Trait anxiety and both intellectual ability and mathematics achievement variables in which personality factors are not highlighted further supports the above assumption. Whereas the A- State results (nonsignificant) “suggested” impaired performance on both tasks, the opposite was true of A-Trait.

To further explicate the relationship between anxiety and mathematics achievement, the separate correlations for field dependentlindependent Ss were examined. It is of interest to note that evidence indicates that field- dependent in contrast to field-independent students are unlikely to do well in mathematics and the sciences generally (25). On the basis of this evidence, it seems entirely reasonable to assume that if a weakness in mathematics problem-solving skills exists for field-dependent students, A-State would have a more debilitating effect for such students than for field-independent students. The finding in the present study supports this assumption. State anxiety accounted for slightly more than twice the variance in mathematics achievement in field-dependent students (33.6%) compared to field- independent students (1 6.8%)-although the nonsignificant moderator re- sults should be noted. For the field-dependent students A-State was also negatively related to intelligence at a significant level ( Y - .39, n = 20, p C .05), but not in field-independent Ss ( Y - .14, n = 20, NS). One might, therefore, argue that anxiety may have a more deleterious effect on students of lower aptitude. This finding is consistent with that of Feldhusen and Klausmeier (4) who reported negative correlations for low and average ZQ groups between anxiety, intelligence, and achievement, but not for the superior group of children.

The result of the present study with respect to the relationship of A-State and mathematics achievement is relatively clear and straightforward, being supportive of previous research indicating performance decrement associ- ated with high A-State (8, 10). Given the evidence that math-specific anxiety correlated negatively with achievement in mathematics (16), the significant improvement in the problem-solving ability of high A-State Ss resulting from memory aids, along with the present results, an important educational implication of these various results is the need to develop learning aids and strategies to counteract the possible debilitating effects of anxiety in learning and testing situations. This view is in agreement with the recent recom- mendations of Benjamin et al. (1).

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Department of School Psychology Temple University College of Education Philadelphia, Pennsylvania 19122

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