predicting mathematics grades of high school girls and boys: a further study

CONTEMPORARY EDUCATIONAL PSYCHOLOGY 5, 2499255 (1980)

Predicting Mathematics Grades of High School Girls and Boys: A Further Study

JULIA A. SHERMAN WRI of’ Wisconsin. Inc.

Eighth grade scores for 140 females and 115 males for three cognitive tests (SRA Math Concepts, CAT Vocabulary, and Space Relations Test of the Differential Aptitude Tests) and the eight FennemaaSherman Mathematics Attitudes Scales were used to predict mathematics grades l-3 years later using multiple regression. Multiple correlation coefftcients were significant (8 of 9). In addition to math achievement, significant relationships were confirmed for Spatial Visualization and Confidence in Learning Mathematics. Implications for Research, curriculum development, and teaching are discussed.

Achievement in mathematics has been increasingly recognized as a critical factor in girls’ career development (Astin, 1968; Astin & Myint, 1971; Carnegie Commission, 1973; Fox, Fennema, & Sherman, 1977; Goldman & Hewitt, 1976; Wise, Note 1). Variables important to girls’ mathematics achievement are generally the same as for boys. In the cognitive domain they include level of mathematical knowledge, verbal and spatial skill, and in the affective domain, they especially include confidence in learning mathematics. Relationships have been demonstrated with other affective variables, but these findings have been less robust. Relationships with affective variables have sometimes been higher for females, particularly for measures related to sex role expectations regarding the study of mathematics. (See Aiken, 1971, 1972, 1973, 1974, 1976; Dwyer, 1974; Fennema & Sherman, 1976, 1977, 1978; Schildkamp- Ktindiger, 1974; Burnett, Lane, & Dratt, Note 2; Connor, Serbin, & Nosofsky, Note 3).

Large scale data collections in 1975 and 1976 (Fennema & Sherman, 1977, 1978) have provided the opportunity to follow up students to see how they later performed and how well earlier data could predict later performance. Subsequent mathematics grades were obtained for 305 students tested in the ninth grade. Using multiple regression techniques, cognitive and affective variables significantly predicted geometry grade for females, males, and both sexes combined and algebra-trig and precalculus grades for both sexes combined (Sherman, 1979). Important pre- dictors of geometry grade were mathematics achievement, verbal skill as

Requests for reprints should be sent to: Julia A. Sherman, WRI of Wisconsin, Inc., 3917 Plymouth Circle, Madison, WI 53705.

This research was supported in part by a grant from the National Institute of Education. The opinions herein do not necessarily reflect the position or policy of the National Institute of Education and no official endorsement should be inferred.

249 0361-476X/80/030249-07$02.00/0 Copyright 0 1980 by Academic Press, Inc. All rights of reproduction in any form reserved.

250 JULIA A. SHERMAN

measured by vocabulary, spatial visualization, and confidence in learning mathematics. For grades in the following year of theoretical mathematics, the highest standardized regression coefficient was not for a cognitive variable, but for an affective variable measuring effectance motivation in mathematics (joy in problem solving). The most noteworthy aspects of these results were that spatial visualization did relate to mathematics performance contrary to the opinion of Very (1967) and affective variables were demonstrated to have some power in predicting mathematics performance (Aiken, 1976).

The study to be reported here used data obtained from subjects in the eighth grade in 1976 to predict their grades in theoretical (college track) math courses in Grades 9- 11.

METHODOLOGY Greater detail regardingthe population, variables, and data collection procedure is avail-

able in Fennema and Sherman (1977, 1978), and only a summary will be given here. In 1976, data were collected from eighth grade students in all four public high school districts in a medium-sized midwestern city of diverse socioeconomic range. Nearly all the subjects were white. Subjects were representatively selected by mathematics class and tested in their own classrooms by trained male and female testers. Data to be reported here include scores of the Mathematics Concepts test (Naslund, Thorpe, & Lefever, 1971); the vocabulary test of the Cognitive Abilities Test: Verbal Battery (Thorndike & Hagen, 1971); spatial visualization as measured by the Space Relations Test of the Differential Aptitude Test (Bennett, Seashore, & Wesman, 1973), and a simplified version of the 5-point Likert, Fennema-Sherman Math- ematics Attitudes Scales (Fenneman & Sherman, 1976). These scales were the same as the original ones except that vocabulary and wording were simplified. This was done in order to make them more suitable for use with a younger population. Each of these scales correlated >.90 with the corresponding original scale in a sample of 38, 10th graders. The scales are Confidence in Learning Mathematics, perceived Usefulness of Mathematics, perceived attitudes of Mother, Father, and Teacher toward one as a learner of mathematics, Attitude toward Success in Mathematics, Mathematics as a Male Domain (ranging from low score, male, to high score, sex-neutral), and Effectance Motivation in Mathematics, a sort ofjoy in problem solving. Low scores represent less favorable attitudes (except possibly for Math as a Male Domain for males).

Of the 483 students tested in 1976, 139 were not found; 9 refused to participate in the study; 19 did not take algebra; 1 was eliminated, leaving 315. Algebra grades for 60 were not available since they took albegra in 8th (50) or 1 lth grade (4) or received an incomplete (6). Thus the number of subjects for the analysis predicting algebra grade was 140 females and 115 males. Subjects for the geometry analysis consisted of that portion of the sample who took algebra who continued to geometry. The subjects for the 11th year math analysis likewise consisted of that portion of the sample who continued to a third year of theoretical math. For the third year of theoretical math most students took an algebra-trig course, some took a more advanced algebra course, and a few took precalculus. Means of the cognitive variables for the final sample (n = 255) were similar to the original pool, indicating that no important bias was introduced by subject attrition. (Interested readers may compare means in Fennema & Sherman, 1978, with those in Table 1.) Data from 1976 were merged with follow-up data. Using multiple regression techniques, grade in mathematics was predicted entering all 1 I variables (3 cognitive, 8 affective).

PREDICTING MATHEMATICS GRADES 251

RESULTS

The n’s, means, and standard deviations for each variable for the analyses predicting grades in algebra, geometry, and a third year of theoretical math (designated algebra-trig) are presented in Table 1. Ex- cept for the dependent variables, values given are as they were assessed in the eighth grade. Scores of subjects generally became higher (more favorable) as the groups became more select.

The raw score correlations between the dependent variables and each of the independent variables are presented in Table 2. Significant correlations were found between math achievement and spatial visualization and grades in five of six instances while significant correlations were found for Confidence in Learning Mathematics and the Teacher Scale in four of six instances. Verbal skill, as measured by vocabulary, yielded only three significant correlations as did Effectance Motivation in Math. There were

TABLE 1 MEANS, STANDARD DEVIATIONS, AND ns FOR ALL. VARIABLES FOR ALL ANALYSES

Algebra Geometry Algebra-Trig Possible

range Female Male Female Male Female Male

Math achievement

Vocabulary

Spatial visualization

Confidence in learning math

Mother

Father

Attitude toward success in math

Teacher

Math as a male domain

Usefulness of mathematics

Effectance motivation in math

Grades

n

O-40 M SD

O-25 M SD

O-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

12-60 M SD

O-4 M SD

28.78 27.49 30.74 29.79 31.82 30.81 5.56 6.67 5.21 6.13 4.74 5.79

16.59 16.22 17.69 17.26 17.98 17.61 3.45 3.86 3.24 3.41 3.43 3.04

31.08 30.70 33.08 33.34 34.24 34.10 9.96 10.02 9.34 11.04 9.24 11.61

44.25 46.67 46.39 49.11 48.07 50.46 8.72 7.47 8.00 6.69 6.91 5.99

42.86 43.38 43.94 44.32 44.26 44.86 5.83 5.80 5.84 5.74 5.72 5.57

44.36 44.48 45.42 45.92 45.67 46.04 6.93 7.05 6.84 6.31 6.56 6.25

45.88 46.55 46.36 47.06 47.58 47.09 5.57 5.66 5.86 5.44 5.71 5.67

42.73 42.59 44.26 44.10 45.33 44.92 6.74 6.60 6.59 6.72 5.84 6.58

53.16 47.72 54.21 48.80 54.83 48.77 4.71 7.06 4.46 6.72 4.18 6.58

46.09 46.76 47.41 47.94 48.79 48.49 7.89 8.22 7.55 8.17 7.19 7.58

38.25 37.44 39.96 38.66 41.38 39.42 8.07 8.02 7.84 8.24 7.47 7.58 2.66 2.58 2.77 2.85 2.89 2.75 1.04 1.10 1.05 .9l 1.02 .93 140 115 140 106 84 77


TABLE 2 CORRELATIONS BETWEEN GRADES AND INDEPENDENT VARIABLES

Algebra Geometry

Female Male Female Male

Algebra-Trig

Female Male

Math achievement Vocabulary Spatial visualization Confidence in learning

math Mother Father Attitude toward

success in math Teacher Math as a male domain Usefulness of mathe-

matics Effectance motivation

in math n

.41** .43** .42** .37** .33** .20

.14 .27** .24** .12 .25* .I2

.27** .I6 .28** .27** .23* .27*

.35** .22* .23** .41** .I9 .18

.ll -.14 .03 .13 .24* .I3

.I1 -.09 .09 .15 .lO - .03

.07 -.I3 -.07 .06 -.06 .Ol

.27** -.04 .30** .21* .26* .06

.I5 -.04 .11 .04 -.04 -.19

.17* -.02 .I5 .20* .18 -.05

.21** .ckl .18* .20*

140 115 140 106 84 77

.I3 .07

*p < .05. **p i .Ol.

no significant differences between the sexes in the correlations, but while 17 of 33 correlations were significant for females, only 10 correlations were significant for males. Eighth grade data were particularly poor in relating to algebra-trig grades for males, spatial visualization being the only significant correlate.

The results of multiple regression analyses predicting algebra, geometry, and algebra-trig grades for females, males, and both sexes combined are presented in Table 3. All multiple regression coefftcients significantly predicted mathematics grades l-3 years later (except algebra- trig grades for males). The size of the multiple correlation coefftcients dropped sur- prisingly little over the years. By the 11th grade, for the algebra-trig regression, the predictive value of math achievement dropped while the value increased for cognitive measures less dependent on direct instruction, vocabulary, and particularly spatial visualization. Among the affective variables, Confidence in Learning Math declined in importance as a predictor while perceived attitude of Mother toward one as a learner of mathematics showed more predictive power. Generally speaking then, for the first 2 years (algebra, geometry) math achievement and Confidence in Learning Mathematics had the highest standardized regression coefti- cients. For the third year (algebra-trig), spatial visualization and the Mother Scale were most important.

TABL

E 3

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varia

bles

Fe

mal

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Alge

bra

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Both

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mal

es

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Both

Alge

bra-

Trig

Fem

ales

M

ales

Bo

th

Mat

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hiev

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t Vo

cabu

lary

Sp

atia

l vi

sual

izat

ion

Con

fiden

ce

in

lear

ning

m

ath

Mot

her

Fath

er

Attit

ude

tow

ard

succ

ess

in m

ath

Teac

her

Mat

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a m

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dom

ain

Use

fuln

ess

of

mat

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ance

m

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mat

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n

*p

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-.@3

-.04

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-.12

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-.04

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140

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255

140

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246

84

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161


CONCLUSIONS AND IMPLICATIONS

The data confirm the importance for mathematics achievement of spatial visualization and affective variables, particularly confidence in learning mathematics. However, little direct information was gained about the special problems of women achieving in mathematics except that scores for females have often been less favorable for these two variables (Fen- nema & Sherman, 1977, 1978; Maccoby & Jacklin, 1974; Sherman, 1978). Hence presumably efforts to improve spatial visualization and/or confidence in learning mathematics would be helpful to females’ learning of mathematics. Neither factor has received much explicit attention in the educational curriculum provided either for students or teachers. Methods of teaching spatial visualization and/or providing relevant experiences for its development need further exploration in terms of techniques, feasibil- ity, timing, and usefulness. Further research is also needed regarding the development of confidence in learning mathematics. What contributions can teachers make to a good mathematics self-concept? There is a philosophy of mathematics instruction which believes that mathematics is a rigorous discipline and it is the teacher’s job to see which students can master it. There is another philosophy which believes it is the teacher’s job to enable the students to master as much mathematics as desired. It seems likely that all but the most accomplished students will develop more self-confidence under teachers with the latter philosophy. Questions such as this could serve as a useful basis for further research.

REFERENCES AIKEN, L. R. Verbal factors in mathematics learning: A review of research. Journnljiv

Reseurch in Mathemutics Education, 1971, 2, 304-313. AIKEN, L. R. Research on attitudes toward mathematics. Arithmetic Teachrr. 1972, 19,

229-234. AIKEN, L. R. Ability and creativity in mathematics. Rrrsiw, ofEducationn/ Reseurch. 1973,

43, 405-432. AIKEN, L. R. Two scales of attitude toward mathematics. Journcrlfiv Rrsrurch in Muthe-

matics Education. 1974, 5, 67-71. AIKEN, L. R. Update on attitudes and other affective variables in learning mathematics.

Review. ofEducutiona1 Rrsrurch. 1976, 46, 293-311. ASTIN, H. S. Career development of girls during the high school years. Journal ofCounsr/-

ing Psychology, 1968, 15, 536-540. ASTIN, H. S., & MYINT, T. Career development and stability of young women during the

post high school years. Journul of Counseling Psychology, 1971, 19, 369-394. BENNETT, G. K., SEASHORE, H. G., & WESMAN, A. G. Differential aptitude tests, fbrms S

und 7’. New York: Psychological Corp., 1973. 4th ed. Carnegie Commission on Higher Education. Opportunities fbr \t‘orncn in higher rducution.

New York: McGraw-Hill, 1973. DWYER, C. A. Influence of children’s sex role standards on reading and arithmetic achieve-

ment. Jortrnul of Educutionnl Psychology. 1974, 66, 81 l-816. FENNEMA, E., & SHERMAN, J. Fennema-Sherman Mathematics Attitudes Scales. JSAS

Cotolog o.f Srlwted Documents in Psychology, 1976, 6, 31 (Ms. No. 1225).

PREDICTING MATHEMATICS GRADES 255

FENNEMA, E., & SHERMAN, J. Sex-related differences in mathematics achievement, spatial visualization and affective factors. American Educational Research Journal, 1977, 14, 51-71.

FENNEMA, E. H., & SHERMAN, J. Sex-related differences in mathematics achievement and related factors: A further study. Journalfor Research in Mathematics Education, 1978, 9, 189-203.

Fox, L. H., FENNEMA, E., & SHERMAN, J. Women and mathemutics: Research perspec-

tives for change. Washington, D.C.: U.S. Government Printing Offrce, 1977. GOLDMAN, R. D., & HEWITT, B. N. The scholastic aptitude test “explains” why college

men major in science more often than college women. Joornal of Counseling Psychol-

ogy, 1976, 23, 50-54. MACCOBY, E. E., & JACKLIN, C. N. Psychology oj’sex dijferences. Palo Alto, Calif.: Stan-

ford Univ. Press, 1974. NASLUND, R. A., THORPE, L. P., & LEFEVER, D. W. Mathematics Concepts Test. Chicago:

Science Research Associates, 1971. SCHILDKAMP-K~NDIGER, E. Stadien zar lehrforschung: Frauenrolle and mathematik-

leistung. Dusseldorf: Schwann, 1974. SHERMAN, J. Predicting mathematics performance in high school girls and boys. Journal of

Edrrcational Psychology, 1979, 71, 242-249. SHERMAN, J. Sex-related cognitive dqferrnces: An essay on theory and evidence.

Springfield: Thomas, 1978. THORNDIKE, R. L., & HACEN, E. Cognitive Abilities Test. Form I (levels A-H). Boston:

Houghton-Mifflin, 1971. VERY, P. S. Differential factor structures in mathematical ability. Genetic Psychology

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REFERENCE NOTES 1. WISE, L. Role of mathematics in tcwmen’s career development. Paper presented at the

meeting of the American Psychological Association, Toronto, September, 1978. 2. BURNETT, S. A., LANE, D. M., & DRATT. L. Spatial visualization and sex differences

in qaantitative ability. Manuscript submitted for publication, 1978. 3. CONNOR, J., SERBIN, L., & NOSOFSKY, R. Visual-spatial skills and mathematics

achievement. Paper to be presented at the meeting of the American Psychological Association, New York, September, 1979.