PsychologicalReports, 1990, 67,619-623.
O Psychological Reports 1990
ATHLETIC SELF-CONCEPT AND MATHEMATICS ACHIEVEMENT IN GIRLS '** TOM M. RANDALL Rhode Island College Summary.-Several researchers have suggested that girls' mathematics performance may be mediated by an assertive sex role or "masculine interest." The present study made the assumption that girls' athletic self-confidence reflects "masculine interest" so girls' test scores for perceived athletic competence would be related to their mathematics achievement scores. A total of 207 boys and girls in Grades 4, 5, and 6 were tested for their perceived athletic ability using the Athletic Competence subscale of Hatter's 1985 Self-perception Profile, and these scores were correlated with their mathematics achievement as measured on the Metropolitan Achievement Test and term grades. A low but significant correlation with Athletic Competence scores was found for girls on both measures of mathematics achievement. Although boys scored higher on the Athletic Competence subscale, there were no sex differences on either measure of mathematics achievement. Results are discussed in terms of both sex-role theory and cognitive development.
The issue of sex differences in cognitive abilities has been a perennial favorite among psychologists (e.g., Maccoby & Jacklin, 1974) and with the popular press as well (Begley, 1988). This Newsweek April 11, 1988 article was based largely on Benbow and Stanley's (1983) work concerning SAT scores and mathematical giftedness and tended to favor biological/genetic interpretations of sex differences on mathematical achievements. Indeed, there has been considerable research on biological factors in both mathematics and spatial abilities (see Crockett & Peterson, 1984). Hypotheses regarding the biological influence on sex differences in mathematics achievement have been supported by studies linking sex differences in maturation and age of puberty to sex differences in spatial ability (Waber, 1977; Sanders & Soares, 1986). O n the environmental side, there have been numerous articles concerned with social and developmental factors that may produce sex differences in mathematics achievement. Two such factors are differential parental encouragement and expectations for boys to excel in mathematics (Entwisle & Baker, 1983; Raymond & Benbow, 1986), and/or teachers' expectancies of sex differences in mathematics abhty, and differential classroom behaviors that contribute to observed sex differences in cognitive achievements (Stallings, 1985). 'Portions of this paper were presented at the annual meetings of the Eastern Psychological Association, Buffalo, NY, April 22, 1988. Address correspondence to T. M. Randall, Department of Psychology, Rhode Island College, Providence, RI 02908. The author ex resses appreciation to Principal Ed Mara, the teachers, and staff of the Wm. C. Callahan ~ c h o o f Harrisville, , Rhode Island for their support in collecting these data.
T.M. RANDALL These expectations of parents and teachers are thought to contribute to children's internalized expectancies regarding their mathematical performance. The resultant sex-typing of mathematics ability most often favors boys, but as Fennema (1985) suggested, girls who adopt a more active instrumental and assertive orientation to gender-role (i.e., "masculine interest") may also show greater mathematics ability. In the years since the Maccoby and Jacklin (1974) article appeared, girls have received greater encouragement to develop a more active, instrumental gender-role orientation, including increased encouragement to participate in athletic programs (Butcher, 1986). Although research has confirmed that "masculine-interest" girls who apparently have adopted assertive, instrumental traits and values performed significantly better at mathematics than did girls with traditional "feminine values" (Mills, 1980), very few studies have been reported on the influence of girls' sports activities and mathematics achevement. One study (Newcombe, Bandura, & Taylor, 1983) examined the role of gender-typed spatial activities on spatial ability in college-aged adults, but this still leaves virtually no information on the possible relationship of girls' sports interest and mathematics achievement. In the present study a girl's self-concept of sports abihty rather than actual sports performance was chosen for analysis, because studies reported previously most often refer to the sex-role identification process, i.e., an internalized self-evaluation process. It was hypothesized that there would be a positive relationship between girls' self-perception of athletic competence and mathematics achievement.
The subjects were 207 elementary school children from a rural New England public school (Grade 4, n = 55; Grade 5 , n = 86; Grade 6, n = 66). They represented roughly 60% of the school's population (i.e., those pupils whose parents consented to testing). The school contains these three grades only and represents a township-wide consolidation of the district, which is in transition from rural to distant suburban demography. All subjects were w h t e and from working and middle-class backgrounds.
Perceived Athletic Competence The Harter Self-perception Profile (1985) contains a subscale (Athletic Competence) of 6 items, each of which is scored on a 4-point scale (maximum score = 24). For each item the child chooses which one of two alternative statements is "sort of true" or "really true" of himself, e.g., "Some kids are good at sports." But "Other kids have a hard time at sports." Reliability estimates provided by Harter (1985) for four samples av-
GIRLS: SELF-CONCEPT AND MATHEMATICS
62 1
eraged .83 for the subscale of Athletic Competence, and for the present study the reliabihty was .77; all five studies used Cronbach alpha.
Mathematics Achievement Mathematics achievement was measured using both report card grades and standardized achievement testing. The mathematics subtest of the Metropolitan Achievement Test (1978) is one often-used standard measure of mathematics achievement. To simplify analysis, term letter grades for mathematics were converted to a standard numerical scale (e.g., A = 93, B + = 87, etc.), and then the grades were averaged from the fall and the spring grade reports to provide a more stable estimate of classroom mathematics achievement. Procedure The Harter Self-perception Profile was administered to small classroom groups of children as teachers' schedules permitted. The examiner read each item aloud as the students read their copies of the scale. The items were presented at a measured pace to assure an orderly and formal assessment. During the summer of the same year, data from the Metropolitan Achievement Test scores (assessed prior to the Harter scale assessments) and report-card grades were retrieved from the students' folders. RESULTS Mathematics achievement test scores averaged 67.2 (SD = 11.7) for girls and averaged 67.0 (SD = 10.3) for boys, and numerical term grades in mathematics averaged 82.8 (SD = 7.7) for girls and averaged 82.0 (SD = 7.3) for boys. Mean total scores for Athletic Competence of the Harter Selfperception Profile were 15.8 (SD = 4.5) for girls and 17.3 (SD = 3.7) for boys. As there are six items on the Athletic Competence subscale, the average subscale scores were 3.22 for boys and 2.63 for girls, and these average scores for the Athletic Competence subscale were essentially the same as those of Harter's (1985) samples. Grade-level by sex-of-student analyses indicated no over-all sex differences in students' mathematics achievement test scores (F,,,,, = 0.03) or in their mathematics grades (F,,,,, = 1.5), but boys had higher scores on self-concept of athletic ability than did girls (F,,,,, = 33.4, p < ,001). There were no effects for term grade and no interactions for these variables. A significant positive Pearson correlation was obtained between girls' Metropolitan Achievement Test mathematics scores and perceived athletic ability (r = 0.23, p < .01) and also for term grades (r = 0.21, p < .02). These correlations were highest for the older girls in Grade 6, with correlations of 0.38 (14% of variance) between girls' athletic self-confidence scores and their achievement test scores and 0.48 (23% of variance) for term grades in mathematics.
T. M. RANDALL
The data did support the hypothesis that girls' perceptions of their athletic ability would be correlated with their mathematics achievement. Although Harter (1985) made no mention of Athletic Competence in girls reflecting "masculine interest," the fact that boys consistently scored higher on this subscale, both in Harter's own research (Harter, 1985) and in the present study, bolsters the notion that self-perception of sports ability of girls may well reflect "mascdne interest." To the extent that high scores on athletic competence are associated with an assertive, instrumental sex-role definition, the present results are consistent with prior work (e.g., Paulsen & Johnson, 1983; Raymond & Benbow, 1986). Beyond the assumption of sports involvement for girls being merely a manifestation of sex-role orientation or "masculine interest" lies the intriguing possibility of a more direct role for athletics in the development of high mathematics achievement in girls. The hypothesis of a direct effect for the visual motor practice on spatial abihties has been presented previously (see Harris, 1981) but generally has received little serious attention. From the cognitive developmental viewpoint, however, this sort of hypothesis is not only quite reasonable but expected. The cognitive-developmental (i.e., Piagetian) explanation would anticipate a causal link between the amount of spatial and quantitative judgement experiences girls had, by virtue of being encouraged to become physically active and well-coordinated, and later cognitive achievements. The present results are provocative, but they leave several important questions unanswered. First, can one be sure that the girls in Grade 6 who have high self-perception scores on Athletic Competence are in fact good at athletics? Second, is there in fact a special relationship between athletic ability and mathematics, or could the observed relationships be attributed more parsimoniously to other factors, i.e., parental encouragement of both sports and cognitive s k d s ? These are empirical questions which need to be addressed. Such research should include objective assessment of girls' actual athletic a b h t y in addition to perceived athletic ability. I n addition, information should be included pertinent to the question of gender-role identification, using parents' interviews and other assessments, e.g., the children's version of the Personal Attributes Questionnaire (Hall & Halberstadt, 1980), along with measures of mathematics interest and other affective variables (see Femema & Sherman, 1977). While it is tempting for psychologists to search for some single factor which seems to produce sex differences in mathematics achievement, the eventual conclusion on this puzzle may well have to involve an interactionist model of effects (e.g., Linn, 1986). To use the present research as an example, it is quite plausible to assume that young girls' early-recognized physical
GIRLS: SELF-CONCEPT AND MATHEMATICS
623
coordination (biological predisposition) would affect the feedback and encouragement by parents and lead to increased parental expectations about sports abilities. These parental influences may very well encourage girls to be physically skillful; these girls then become increasingly independent-minded and assertive ("masculine-interest" sex-role expectancy). These biological and social/environmental variables most likely have a mutually synergistic effect on the observed cognitive achievements of girls. REFERENCES BEGLEY,S. (1988) Closing the gender gap. Newsweek, April 11, 73. BENBOW, C. P., & STANLEY, J. C. (1983) Sex differences in mathematical reasoning ability: more facts. Science, 222, 1029-1031. BUTCI-IER, J. (1986) Longitudinal analysis of adolescent girls' aspirations at school and perceptions of popularity. Adolescence, 21, 133-143. CROCKETT,L., & PETERSEN, A. C. (1984) Biology: its role in gender-related educational experiences. In E. Fennema & J. Ayer (Eds.), Equity of eqlrality: women and education. Chicago, IL: NSSE & McCutchan. EN-IWISLE, D. R., & BAKER,D. P. (1983) Gender and young children's expectations for performance in arithmetic. Developmental Psychology, 19, 200-209. FENNEMA, E. (1985) Explaining sex-related differences in mathematics: theoretical models. Educational Studies in Mathematics, 16, 303-320. FENNEMA, E., & SHERMAN, J. (1977) Sex-related differences in mathematical achievement, spatial visualization and affective factors. American Educational Research Journal, 14, 51-71. A. G . (1980) Masculinity and femininity in children: developHALL, J. A,, & HALBERSTADT, ment of the children's personal attributes questionnaire. Developmental Psychology, 16, 270-280 HARRIS,L. J. (1981) Sex differences in spatial skill. In L. S. Liben, A. H. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the lifespan: theory and application. New York: Academic Press. Pp. 83-125. HARTER,S. (1985) Manual for the Self-perception Profile for Children. Denver, CO: Univer. of Denver. LINN,M. C. (1986) Meta-analysis of studies of ender differences: implications and future directions. In J. S. Hyde & M. C. Linn ( E ~ S . )The , psychology of gender: advances through me&-analysis. Baltimore, MD: Johns Hopkins Univer. Press. Pp. 210-231. MACCOBY, E. E., & JACKLIN,C. N. (1974) Psychology of sex differences. Palo Alto, CA: Stanford Univer. Press. k s , C. J. (1980) Sex roles, personality and intellectual abilities in adolescents. Journal of Youth and Adolescence, 10, 85- 111. NEWCOMBE, N., B A N D ~ RM. A , M., & TAYLOR, D. G . (1983) Sex differences in spatial ability and spatial activities. Sex Roles, 9, 377-386. PAULSEN, K., &JOHNSON, M. (1983) Sex role attitudes and mathematical ability in 4th.. 8th-, and 11th-grade students from a high socioeconomic area. Developmental psycho lo^, 19, 210-214. RAYMOND, C. L., & BENBOW,C. P. (1986) Gender differences in mathematics: a function of parental support and student sex typing? Developmental Psychology, 22, 808-819. SANDERS, B., & SOARES,M. P. (1986) Sexual maturation and spatial ability in college students. Developmental Psychology, 22, 199-203. STALLINGS, X. X. (1985) WABER,D. l? (1977) Sex differences in mental abilities, hemispheric lateralization, and rate of physical growth at adolescence. Developmental Psychology, 13, 29-38.
Accepted September 10, 1990.
O Psychological Reports 1990
ATHLETIC SELF-CONCEPT AND MATHEMATICS ACHIEVEMENT IN GIRLS '** TOM M. RANDALL Rhode Island College Summary.-Several researchers have suggested that girls' mathematics performance may be mediated by an assertive sex role or "masculine interest." The present study made the assumption that girls' athletic self-confidence reflects "masculine interest" so girls' test scores for perceived athletic competence would be related to their mathematics achievement scores. A total of 207 boys and girls in Grades 4, 5, and 6 were tested for their perceived athletic ability using the Athletic Competence subscale of Hatter's 1985 Self-perception Profile, and these scores were correlated with their mathematics achievement as measured on the Metropolitan Achievement Test and term grades. A low but significant correlation with Athletic Competence scores was found for girls on both measures of mathematics achievement. Although boys scored higher on the Athletic Competence subscale, there were no sex differences on either measure of mathematics achievement. Results are discussed in terms of both sex-role theory and cognitive development.
The issue of sex differences in cognitive abilities has been a perennial favorite among psychologists (e.g., Maccoby & Jacklin, 1974) and with the popular press as well (Begley, 1988). This Newsweek April 11, 1988 article was based largely on Benbow and Stanley's (1983) work concerning SAT scores and mathematical giftedness and tended to favor biological/genetic interpretations of sex differences on mathematical achievements. Indeed, there has been considerable research on biological factors in both mathematics and spatial abilities (see Crockett & Peterson, 1984). Hypotheses regarding the biological influence on sex differences in mathematics achievement have been supported by studies linking sex differences in maturation and age of puberty to sex differences in spatial ability (Waber, 1977; Sanders & Soares, 1986). O n the environmental side, there have been numerous articles concerned with social and developmental factors that may produce sex differences in mathematics achievement. Two such factors are differential parental encouragement and expectations for boys to excel in mathematics (Entwisle & Baker, 1983; Raymond & Benbow, 1986), and/or teachers' expectancies of sex differences in mathematics abhty, and differential classroom behaviors that contribute to observed sex differences in cognitive achievements (Stallings, 1985). 'Portions of this paper were presented at the annual meetings of the Eastern Psychological Association, Buffalo, NY, April 22, 1988. Address correspondence to T. M. Randall, Department of Psychology, Rhode Island College, Providence, RI 02908. The author ex resses appreciation to Principal Ed Mara, the teachers, and staff of the Wm. C. Callahan ~ c h o o f Harrisville, , Rhode Island for their support in collecting these data.
T.M. RANDALL These expectations of parents and teachers are thought to contribute to children's internalized expectancies regarding their mathematical performance. The resultant sex-typing of mathematics ability most often favors boys, but as Fennema (1985) suggested, girls who adopt a more active instrumental and assertive orientation to gender-role (i.e., "masculine interest") may also show greater mathematics ability. In the years since the Maccoby and Jacklin (1974) article appeared, girls have received greater encouragement to develop a more active, instrumental gender-role orientation, including increased encouragement to participate in athletic programs (Butcher, 1986). Although research has confirmed that "masculine-interest" girls who apparently have adopted assertive, instrumental traits and values performed significantly better at mathematics than did girls with traditional "feminine values" (Mills, 1980), very few studies have been reported on the influence of girls' sports activities and mathematics achevement. One study (Newcombe, Bandura, & Taylor, 1983) examined the role of gender-typed spatial activities on spatial ability in college-aged adults, but this still leaves virtually no information on the possible relationship of girls' sports interest and mathematics achievement. In the present study a girl's self-concept of sports abihty rather than actual sports performance was chosen for analysis, because studies reported previously most often refer to the sex-role identification process, i.e., an internalized self-evaluation process. It was hypothesized that there would be a positive relationship between girls' self-perception of athletic competence and mathematics achievement.
The subjects were 207 elementary school children from a rural New England public school (Grade 4, n = 55; Grade 5 , n = 86; Grade 6, n = 66). They represented roughly 60% of the school's population (i.e., those pupils whose parents consented to testing). The school contains these three grades only and represents a township-wide consolidation of the district, which is in transition from rural to distant suburban demography. All subjects were w h t e and from working and middle-class backgrounds.
Perceived Athletic Competence The Harter Self-perception Profile (1985) contains a subscale (Athletic Competence) of 6 items, each of which is scored on a 4-point scale (maximum score = 24). For each item the child chooses which one of two alternative statements is "sort of true" or "really true" of himself, e.g., "Some kids are good at sports." But "Other kids have a hard time at sports." Reliability estimates provided by Harter (1985) for four samples av-
GIRLS: SELF-CONCEPT AND MATHEMATICS
62 1
eraged .83 for the subscale of Athletic Competence, and for the present study the reliabihty was .77; all five studies used Cronbach alpha.
Mathematics Achievement Mathematics achievement was measured using both report card grades and standardized achievement testing. The mathematics subtest of the Metropolitan Achievement Test (1978) is one often-used standard measure of mathematics achievement. To simplify analysis, term letter grades for mathematics were converted to a standard numerical scale (e.g., A = 93, B + = 87, etc.), and then the grades were averaged from the fall and the spring grade reports to provide a more stable estimate of classroom mathematics achievement. Procedure The Harter Self-perception Profile was administered to small classroom groups of children as teachers' schedules permitted. The examiner read each item aloud as the students read their copies of the scale. The items were presented at a measured pace to assure an orderly and formal assessment. During the summer of the same year, data from the Metropolitan Achievement Test scores (assessed prior to the Harter scale assessments) and report-card grades were retrieved from the students' folders. RESULTS Mathematics achievement test scores averaged 67.2 (SD = 11.7) for girls and averaged 67.0 (SD = 10.3) for boys, and numerical term grades in mathematics averaged 82.8 (SD = 7.7) for girls and averaged 82.0 (SD = 7.3) for boys. Mean total scores for Athletic Competence of the Harter Selfperception Profile were 15.8 (SD = 4.5) for girls and 17.3 (SD = 3.7) for boys. As there are six items on the Athletic Competence subscale, the average subscale scores were 3.22 for boys and 2.63 for girls, and these average scores for the Athletic Competence subscale were essentially the same as those of Harter's (1985) samples. Grade-level by sex-of-student analyses indicated no over-all sex differences in students' mathematics achievement test scores (F,,,,, = 0.03) or in their mathematics grades (F,,,,, = 1.5), but boys had higher scores on self-concept of athletic ability than did girls (F,,,,, = 33.4, p < ,001). There were no effects for term grade and no interactions for these variables. A significant positive Pearson correlation was obtained between girls' Metropolitan Achievement Test mathematics scores and perceived athletic ability (r = 0.23, p < .01) and also for term grades (r = 0.21, p < .02). These correlations were highest for the older girls in Grade 6, with correlations of 0.38 (14% of variance) between girls' athletic self-confidence scores and their achievement test scores and 0.48 (23% of variance) for term grades in mathematics.
T. M. RANDALL
The data did support the hypothesis that girls' perceptions of their athletic ability would be correlated with their mathematics achievement. Although Harter (1985) made no mention of Athletic Competence in girls reflecting "masculine interest," the fact that boys consistently scored higher on this subscale, both in Harter's own research (Harter, 1985) and in the present study, bolsters the notion that self-perception of sports ability of girls may well reflect "mascdne interest." To the extent that high scores on athletic competence are associated with an assertive, instrumental sex-role definition, the present results are consistent with prior work (e.g., Paulsen & Johnson, 1983; Raymond & Benbow, 1986). Beyond the assumption of sports involvement for girls being merely a manifestation of sex-role orientation or "masculine interest" lies the intriguing possibility of a more direct role for athletics in the development of high mathematics achievement in girls. The hypothesis of a direct effect for the visual motor practice on spatial abihties has been presented previously (see Harris, 1981) but generally has received little serious attention. From the cognitive developmental viewpoint, however, this sort of hypothesis is not only quite reasonable but expected. The cognitive-developmental (i.e., Piagetian) explanation would anticipate a causal link between the amount of spatial and quantitative judgement experiences girls had, by virtue of being encouraged to become physically active and well-coordinated, and later cognitive achievements. The present results are provocative, but they leave several important questions unanswered. First, can one be sure that the girls in Grade 6 who have high self-perception scores on Athletic Competence are in fact good at athletics? Second, is there in fact a special relationship between athletic ability and mathematics, or could the observed relationships be attributed more parsimoniously to other factors, i.e., parental encouragement of both sports and cognitive s k d s ? These are empirical questions which need to be addressed. Such research should include objective assessment of girls' actual athletic a b h t y in addition to perceived athletic ability. I n addition, information should be included pertinent to the question of gender-role identification, using parents' interviews and other assessments, e.g., the children's version of the Personal Attributes Questionnaire (Hall & Halberstadt, 1980), along with measures of mathematics interest and other affective variables (see Femema & Sherman, 1977). While it is tempting for psychologists to search for some single factor which seems to produce sex differences in mathematics achievement, the eventual conclusion on this puzzle may well have to involve an interactionist model of effects (e.g., Linn, 1986). To use the present research as an example, it is quite plausible to assume that young girls' early-recognized physical
GIRLS: SELF-CONCEPT AND MATHEMATICS
623
coordination (biological predisposition) would affect the feedback and encouragement by parents and lead to increased parental expectations about sports abilities. These parental influences may very well encourage girls to be physically skillful; these girls then become increasingly independent-minded and assertive ("masculine-interest" sex-role expectancy). These biological and social/environmental variables most likely have a mutually synergistic effect on the observed cognitive achievements of girls. REFERENCES BEGLEY,S. (1988) Closing the gender gap. Newsweek, April 11, 73. BENBOW, C. P., & STANLEY, J. C. (1983) Sex differences in mathematical reasoning ability: more facts. Science, 222, 1029-1031. BUTCI-IER, J. (1986) Longitudinal analysis of adolescent girls' aspirations at school and perceptions of popularity. Adolescence, 21, 133-143. CROCKETT,L., & PETERSEN, A. C. (1984) Biology: its role in gender-related educational experiences. In E. Fennema & J. Ayer (Eds.), Equity of eqlrality: women and education. Chicago, IL: NSSE & McCutchan. EN-IWISLE, D. R., & BAKER,D. P. (1983) Gender and young children's expectations for performance in arithmetic. Developmental Psychology, 19, 200-209. FENNEMA, E. (1985) Explaining sex-related differences in mathematics: theoretical models. Educational Studies in Mathematics, 16, 303-320. FENNEMA, E., & SHERMAN, J. (1977) Sex-related differences in mathematical achievement, spatial visualization and affective factors. American Educational Research Journal, 14, 51-71. A. G . (1980) Masculinity and femininity in children: developHALL, J. A,, & HALBERSTADT, ment of the children's personal attributes questionnaire. Developmental Psychology, 16, 270-280 HARRIS,L. J. (1981) Sex differences in spatial skill. In L. S. Liben, A. H. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the lifespan: theory and application. New York: Academic Press. Pp. 83-125. HARTER,S. (1985) Manual for the Self-perception Profile for Children. Denver, CO: Univer. of Denver. LINN,M. C. (1986) Meta-analysis of studies of ender differences: implications and future directions. In J. S. Hyde & M. C. Linn ( E ~ S . )The , psychology of gender: advances through me&-analysis. Baltimore, MD: Johns Hopkins Univer. Press. Pp. 210-231. MACCOBY, E. E., & JACKLIN,C. N. (1974) Psychology of sex differences. Palo Alto, CA: Stanford Univer. Press. k s , C. J. (1980) Sex roles, personality and intellectual abilities in adolescents. Journal of Youth and Adolescence, 10, 85- 111. NEWCOMBE, N., B A N D ~ RM. A , M., & TAYLOR, D. G . (1983) Sex differences in spatial ability and spatial activities. Sex Roles, 9, 377-386. PAULSEN, K., &JOHNSON, M. (1983) Sex role attitudes and mathematical ability in 4th.. 8th-, and 11th-grade students from a high socioeconomic area. Developmental psycho lo^, 19, 210-214. RAYMOND, C. L., & BENBOW,C. P. (1986) Gender differences in mathematics: a function of parental support and student sex typing? Developmental Psychology, 22, 808-819. SANDERS, B., & SOARES,M. P. (1986) Sexual maturation and spatial ability in college students. Developmental Psychology, 22, 199-203. STALLINGS, X. X. (1985) WABER,D. l? (1977) Sex differences in mental abilities, hemispheric lateralization, and rate of physical growth at adolescence. Developmental Psychology, 13, 29-38.
Accepted September 10, 1990.
