hr. 1. Educarional Developmew, Vol. 11, No. 1. pp. 31-39. 1991 Printed in Great Britain

n73&ll593/91 $3.00+ .txl Pergamon Press plc

SOCIO-PERSONAL CORRELATES OF MATHEMATICS ACHIEVEMENT AMONG SECONDARY SCHOOL PUPILS IN

BOPHUTHATSWANA

MUHAMMAD MAQSUD* and CHAUDHRY M. KHALIQUE

University of Bophuthatswana

Abstract-This exploratory study investigated the relationships of mathematics achievements of Bophuthatswana secondary school pupils to some of their socio-personal variables (socio- economic background, school affiliation, sex, self-concept and attitude toward mathematics). Significant sex differences in favour of boys were found in mathematics achievement and attitude toward mathematics. Moderate correlations were found between mathematics attitude and mathematics performance for both sexes. Alienation from school moderately negatively correlated with attitude toward mathematics for boys, but it did not significantly correlate for girls. A significant positive correlation between self-concept and mathematics attitude was observed for girls but not for boys. Socio-economic background significantly negatively correlated with self- concept for boys, but it did not significantly correlate for girls.

INTRODUCTION

Educators and researchers are now paying increasing attention to cultural variations in schoolchildren’s performances in mathematics. It has recently been reported, for instance, that students from Asian countries (China, Japan, Taiwan) perform significantly higher in tests of mathematics and science than their American counterparts (Hess et al., 1987). Though knowledge of the factors responsible for such national differences is still incomplete, these discrepancies are generally attributed to divergencies in national educational systems, different mathematics curricula, time spent on learning mathematics, different pedagogical approaches and culturally transmitted values, beliefs and behaviours. Apart from national differences, importance is also being attached to gender variations in mathematics perfor- mance. Several studies (Aiken, 1976; Benbow and Stanley, 1980; Hanna, 1989) have shown that high school and college male students are significantly superior to their female counter- parts in both their mathematical performance and attitude toward mathematics. Hanna

*Correspondence to: Muhammad Maqsud, Professor of Educational Psychology, School of Education, University of Bophuthatswana, Mmabatho 8681, Southern Africa.

(1989), however, found that differences among countries were greater than sex differences.

Recent studies have identified mathematics anxiety (Battista, 1986; Balmahn and Young, 1982; Bush, 1989; Kelly and Tomhave, 1985; McLeod, 1988; Widmer and Chavez, 1982; Wigfield and Meece, 1988), attitude toward mathematics (Aiken, 1976; Kulm, 1980), self-confidence in learning mathematics (Kloosterman, 1988) and mathematics self- efficacy (Hackett and Betz, 1989) as forceful factors in the learning and teaching of mathematics. Feelings of tension and anxiety interfere with the processes of solving mathe- matical problems while positive attitudes towards mathematics facilitate the manipu- lation of numbers. Some researchers (Hackett and Betz, 1989) have stressed the importance of application of Bandura’s theory of self-efficacy (Bandura, 1982) while others (Meyer and Fennema, 1986; Reyes, 1984) emphasised the positive association between self-confidence and ability to learn mathematics.

Burns (1977) explained the construct of self- concept as the collection of attitudes and beliefs we hold about ourselves and that their development in school children is influenced by school and non-school environments. Sex differences in the development of self-concept had been reported. Olowu (1985), for instance, found that Nigerian boys had significantly more

31

32 MUHAMMAD MAQSUD and CHAUDHRY M. KHALIOUE

Table 1. Matric. mathematics results of 19X7, 1988 and 1Y8Y in Bophuthatswana

Year Candidates P3SS Fail -

1987 4495 1230 (27.4%) 3265 (72.6%)

1988 4985 Ii68 (27.4%) 3hl7 (77.6Q) - I

19x9 3Y73 12X8 (25.0%‘) 36% (74.1’5)

positive self-concept than girls. There is quite a body of research (Coopersmith, 1959, 1967; Maqsud, 1983; Obanya, 1976; Piers and Harris, 1964; Purkey, 1970; Wylie, 1979) suggesting a positive relationship between self-concept and educational attainment. These researchers believed that the child’s positive self-concept is perhaps the basis for educational progress. There are, however, some studies (Hart, 198.5; Thomas, 1973) which found no significant association between general self-concept and academic achievement.

mathematics, the aims of the present small- scale study were: (a) to investigate relationships of mathematics achievement of Bophuthats- wana secondary school pupils to some of their socio-personal variables (so~io-economic back- ground, school affiliation, sex, self-concept and mathematics attitude); and (b) to examine interrelationships among these variables.

Affiliation to or attitude toward school is one of the determinants of differences in self- concepts of school children (Beverly and Metcalfe, 1981: f’erri, 1971). Cohen (1974) explained alienation from school as powerless- ness, meaninglessness and social est~ngen~ent experienced by schoolchildren in their school environments. In a study conducted in a Yorkshire (England) comprehensive school, Cohen (1976) found that school alienation was significantly negatively correlated with measures of self-concept and self-esteem.

METHOD

Subjects

A significant body of research conducted in western countries established a close positive association between educational attainment and socio-economic background (Hyman, 1953; Kahl, 1960; Mizruchi, 1964). It was explained that students from higher socio- economic strata tend to have more favourable attitudes toward school and teachers (Glick, 1970).

One hundred and nine subjects (65 girls: 44 boys) of this study were students at a senior secondary school in Mmabatho (capital of Bophuthatswana). The school from which the subjects were taken was large enough to enrol more than 900 students. All students who participated in the investigation were studying mathematics as one of their academic subjects at standard (Std) 9 level: their ages ranged between 17 and 19 yr.

Instruments

The authors of this article analysed the matric. results of secondary schools in Bophut- hatswana (in the Southern African region) for the past three years (1957, 1988, and 1989); details are given in Table 1. it was found that the failure rate in mathematics was alarmingly higher (75%) than in other subjects. In our preliminary exploratory attempt to look into reasons for such a high failure rate in

Socio-economic background. A brief socio- economic background questionnaire (SBQ). requiring the subjects to give informati~~n on their parents’ educational and occupational background as well as on some economic facilities available at home. was constructed by the researchers. Educational backgrounds of the subjects’ mothers and fathers were catcgor- ized into six levels of formal education: no formal schooling, primary school. middle school, secondary school, college. and univcr- sity. These levels of education were quantified by using a six-point scale (l-6) for each parent. Parental occupations were classified into six categories: unskilled, semi-skilled. skilled.

MATHS ACHIEVEMENT IN SECONDARY SCHOOL PUPILS

Table 2. Means and standard deviations of socio-economic, school alienation, self-concept, maths attitude and maths achievement scores for boys and girls

33

Variable

Boys (N = 44) Girls (N = 65)

Mean SD Mean SD I

Socio-economic 8.93 3.41 8.48 3.02 0.64

School alienation 16.10 4.61 15.55 4.74 0.14

Self-concept 6.45 4.10 7.66 3.87 1.55

Maths attitude 70.34 10.15 63.83 12.54 2.99*

Maths achievement 144.77 52.28 123.03 46.14 2.231

*p <O.Ol.

tp <0.05.

clerical, administrative, and managerial/profes- sional. A six-point scale was used to quantify occupational information for each parent. The two researchers independently categorized occupational information and the inter-rater reliability was 0.87. The discrepancies between the two raters were resolved by seeking the opinion of a school counsellor. The SBQ also contained three items requiring the subjects to provide information as to whether or not their parents own a car, a television, or a video cassette recorder. A positive response to each of these three items carried a numerical score of one. The minimum and maximum scores on the SBQ could be 4 and 27, respectively.

Self-concept. The Bhatnager (1969) self- concept scale (BSCS), based on 15 multiple- choice items, was employed to take measures of the perceived self. Scores on the BSCS could range between + 15 and - 15. Respondents had to tick one of the three responses (true, false, not sure) against the items, such as ‘I am good at classwork’. Bhatnager (1969) reported a coefficient of reproductibility of 0.78 for his self-concept scale.

Alienation from school. Cohen (1974) con- structed a Likert-type school opinion question- naire (SOQ) and used it as a measure of pupils’ alienation in British secondary schools. The nine items of the questionnaire are concerned with the three dimensions of powerlessness, meaninglessness and social estrangement, three items for each dimension. One item of the questionnaire is given here for illustration purposes: ‘I cannot make much sense out of what happens at this school’. The maximum and minimum scores on the SOQ could be 45 and 9,

respectively. A high score on the SOQ indicates more alienation from school.

Attitudes toward mathematics. The Aiken (1979) scale of attitudes toward mathematics (ASATM) was used to measure the strength of attitude toward mathematics of the subjects of this study. The scale is based on 24 Likert-type items, such as ‘Mathematics is enjoyable and stimulating to me’. The scores on the ASATM could range between 0 and 96.

Mathematics achievement. Mathematics achievement scores of 109 subjects in their annual promotional examinations from Std 9 to Std 10 were taken from the school records. They sat for three mathematics papers, each paper carrying a maximum mark of 100, making a maximum mark of 300 for mathematics exmaminations. So, subjects’ mathematics achievement scores could range from 0 to 300.

Procedure

The 109 subjects were divided into two groups (of 55 and 54) and they were seated in two separate classrooms, as no classroom in the school was large enough to accommodate all 109 subjects at a time. The four instruments (SBQ, BSCS, SOQ and ASATM) were administered to all subjects at an arranged time with the principal of the school. The subjects took about 45 min to complete the four scales. Their mathematics achievement scores were obtained from the school records.

RESULTS

Sex differences

Table 2 gives the mean scores and standard

MUHAMMAD MAQSUD and CHAUDHRY M. KHALIQUE

Table 3. Pearson intercorrelations and f tests for significance for males (M, N = 44) and females (F, N = 65)

Variable 1

Socio-economic

3 4 5

M

F

School alienation

-0.10 -0.29* 0.13

0.10 -0.16 0.04

M -0.37t -0.40*

F -0.10 0.01

Self-concept

M

F

Maths attitude

0.01

0.39*

M

F

Maths achievement

*p <0.05.

tp <O.Ol.

deviations of five variables (socio-economic background, school alienation, self-concept, mathematics attitude, and mathematics achieve- ment) for male and female subjects. Compari- sons of mean scores by a t test showed that boys’ mean scores for mathematics achievement, t(107) = 2.23, p < 0.05, and attitude toward mathematics, t(107) = 2.99, p ~0.01, were significantly higher than those for girls.

Relationships of mathematics achievement to the otherfour variables

In order to explore relationships of mathe- matics achievement to other four variables (socio-economic background, school aliena- tion, self-concept and mathematics attitude), Pearson product-moment correlations were computed for male and female subjects separately. Table 3 provides the coefficients of correlation. It was found that there was a significant positive relationship between mathe- matics achievement and mathematics attitude (r = 0.49 for girls; r = 0.31 for boys). Mathematics achievement did not significantly correlate with the remaining three variables. For further analyses, male and female subjects were separately divided into three groups (high,

0.09

0.02

0.09

0.12

0.18

0.08

0.31*

0.491

middle, low) on the basis of the measures of mathematics attitude and a one-way analysis of variance (ANOVA) was performed on their mathematics achievement scores. Table 4 shows the means and standard deviations of mathematics achievement scores for the six groups together with F values. The mean differences between high and low groups for both sexes were found significant, t(27) = 2.36, p <0.05 for males, and t(41) = 3.54,~ co.01 for females.

Interrelationships A significant negative association between

self-concept and socio-economic background for the male group (r = -0.29) was found, but the coefficient of correlation for the female group (r = -0.16) did not reach a level of significance. ‘The measures of self-concept significantly negatively correlated with school alienation for the male group (r = -0.37) but the coefficient of correlation for the female group (r = -0.10) was not found to be significant. There was a significant positive relationship between self- concept and attitude towards mathematics (r = 0.39) for the female group, but no significant correlation between these variables for the male

MATHS ACHIEVEMENT IN SECONDARY SCHOOL PUPILS

Table 4. Means and standard deviations of mathematics achievement scores for high, middle and low groups

35

Variable Sex

Male

Group N

High (x = 81.02) 14

Middle (x = 71.03) 15

Low (X = 59.05) 15

Mathematics achievement F

B SD

175.14 61.01

135.86 36.07 4.21*

123.25 41.57

Maths attitude

High (x = 76.71) 22 133.86 49.18

Female Middle (J? = 64.84) 22 143.63 39.52 5.35t

Low (x = 49.85) 21 91.47 31.89

*p <0.05.

tp <O.Ol.

group (I = 0.01) was found. The data which yielded significant inter-

correlations were subjected to further analyses by use of a one-way analysis of variance (ANOVA) with subsequent comparisons be- tween groups by t tests. The male subjects (n = 44) were divided into three groups (high, middle, low) first on the basis of their socio- economic scores and then on the basis of school alienation measures. Similarly, the female subjects (n = 65) were divided into three groups on the basis of their self-concept scores. The measures of dependent variables (self-concept and mathematics attitudes for males, and mathematics attitude for females) for these groups were subjected to ANOVA and then comparisons were made between the means of high and low groups. Table 5 gives the means and standard deviations of the dependent variables together with F and t values. The t values in Table 5, based on comparisons between the means of high and low groups, substantiate the intercorrelations given in Table 3.

DISCUSSION

The results of this study confirmed the findings of earlier studies (Aiken, 1976; Backman, 1972; Mullis, 1975; Walden and Walkerdine, 1985) which reported that second- ary school-aged boys are significantly more positive than girls in both their attitudes towards mathematics and mathematics perfor-

mance. Burton (1978) explained sex differences in mathematics performance in terms of (i) biological reasons; (ii) strength of cultural pressures; and (iii) process of sex role identification. An explanation of these gender differences in terms of biological variations seems too simple. There is now evidence (Hanna. 1989) to indicate that sex differences in mathematics performance vary from country to country; in some countries girls out- perform boys in certain mathematical tasks. Some researchers (Burton, 1986; Fennema, 1985; Leder, 1985; Sells, 1980; Walden and Walkerdine, 1985) attributed gender-related differences in, mathematics as a filter into various career options, affective factors (lack of confidence and fear of success) and other psychosocial processes. In a longitudinal study, Marshall and Smith (1987) analysed the mathematics performances of their male and female subjects in various types of mathe- matical tasks and concluded that their sixth grade girls performed poorly in solving problems compared with boys, due to lack of skills in application of their computational abilities. Fox (1977) explained that the greater social interests of teenage girls, compared with their male counterparts, affect the concentrated effort required in mathematics. In Bophuthats- wana, a general fear of, and lack of confidence in, mathematics prevail. Bophuthatswana secondary school girls are perhaps more vulnerable to mathematics phobia than boys.

The variable of attitude toward mathematics

36 MUHAMMAD MAQSUD and CHAUDHRY M. KHALIQUE

Table 5. Means and standard deviations of dependent variables for high. middle and low groups

Sex Independent variable Dependent variable

Socio-economic N

Male

High (x = 13.02) 13

Middle (x = X.26) IS

Low (X = 5.61) 1.5

School alienation

Male

High (x= 21.19) I4

Middle (x = 16.11) I5

Low (X = 11.03) 15

School alienation

Self-concept

x

5.3X

6.21

7.71

SD

2.16

I .67

2.17

Self-concept

4.Y.i

5.87

x.53

Maths attitude

3.56

4.09

2.7s

F t*

3.YYf 2.53

3.44t 2.7%

Male

High (x= 21.19) I4 64.34

Middle(X= 16.11) IS 70.2x

Low (X = 1 I .03) IS 76.43

Self-concert Math attitude

x.3x

9.51

x.2’,

6.5X$ 3.36i

Female

High (x = 11.33) 22 6Y.Y2 13.36

Middle (x = 7.96) 22 63.59 13.22

Low (X = 3.66) 21 57.96 X.34

5.3s;t 3.04$

*Comparisons between high and low groups.

tp <o.os. $p 41.01.

significantly positively correlated with mathe- matics achievement of both male and female subjects of this investigation. Allport (193.5, p. 810) explained that ‘an attitude is a mental and neural state of readiness, organized through experience, exerting a directive or dynamic influence upon the individual’s response to all objects and situations with which it is related’. If we apply Allport’s definition to attitudes towards mathematics, ‘objects and situations’ might be ‘mathematics or solving mathematical problems’. Romberg and Wilson (1969, p. IS) described attitudes in these words: ‘If an individual has a set of predispositions toward an object in the environment (e.g. mathematics, self, school, teacher, etc.), it is reasonable to expect that such predispositions would interact with the perceptions of the object in such a way as to affect the individual’s response to that object’. This definition suggests that favourable predispositions of students toward mathematics are expected to favourably influence their mathematics performance. The ASATM gives measures of enjoyment of mathematics,

motivation in mathematics, importance of mathematics, and freedom from fear of mathematics. So as common sense suggests. students holding the characteristics of Aiken’s four dimensions would perform better in mathematical tasks than those who lack in them. The results of this study support the findings of Cheung (1988) who reported a positive correlation between secondary school students’ attitudes toward mathematics and their achievement in mathematics.

Data from this study revealed that the measures of self-concept of girls significantly positively correlated with their scores of atti- tude toward mathematics whereas self-concept scores of boys indicated no such relationship. Howcvcr, self-concept measures of both boys and girls did not reveal any significant association with their mathematics achievement. The finding of no relationship between general self-concept and academic achievement tends to substanti- ate the results of some other studies (Hansford and Hattie, 1982: Hart. 1985: Pottcbaum er 01.. 1986) which demonstrated no significant

MATHS ACHIEVEMENT IN SECONDARY SCHOOL PUPILS 37

association between general self-concept and school achievement. In a review on general self- concept and academic self-concept, Byrne (1984) concluded that self-concept is a multi- dimensional construct containing a general factor and several specific facets including academic self-concept. So, a different pattern is expected to emerge in studies examining relationships between academic attainment and academic self-concept. A significant positive relationship between self-concept and mathe- matics attitude for girls and no such relationship for boys in this study indicates a different sex interaction between self-concept and mafhe- matics attitude, but no adequate psychological explanation at this stage can be put forward for these types of gender differences,

Contrary to our expectations, socio-eco- nomic background measures consistently negatively correlated with self-concept scores. Coopersmith (1967) and Rosenberg (1965) suggested that the amount and quality of parental attention as well as interaction with significant others is one of the important social factors in shaping the self-concept of the child. The British Psychological Society (1986, p. 124) recently suggested that ‘material circumstances and class position seem less important than what may be referred to as family ‘climate’, which includes parents’ aspirations and atti- tudes and the support and encouragement for their child’s schooling’. A negative relationship between socio-economic background and self- concept for the subjects of this study may be explained in terms of two hypotheses: (a) affluent parents were satisfied with their economic status and thus they perhaps did not sense a need for encouraging their children in school activities; and (b) parents of higher socio-economic status did not have enough time to provide their children with qualitative parental attention and encouragement whereas children from lower socio-economic homes might not have sufficient material comforts but they received adequate parental attention and encouragement.

In this study, school alienation scores significantly negatively correlated with meas- ures of self-concept and attitudes toward mathematics for boys but no such relationship was found for female subjects. This finding is in congruence with the results reported by Cohen (1976) and Heaven and Bester (1986). More alienated students experience social estrange-

ment, isolation and powerlessness and such experiences tend to adversely affect their self- esteem. Richmond (1985) suggested that feminine attitudes are more in tune with the school ethos. Hence, there were no adverse effects on the development of girls’ self- concepts, though they may have the same level of alienation from schools.

Results of this investigation tend to invite the attention of mathematics educators and school administrators to four variables: attitude toward mathematics achievement, school alien- ation and self-concept. Although the causal relationship between mathematics attitude and mathematics performance is not yet clear, there is evidence that attitudes influence behaviour (Calder and Ross, 1973) and in the case of mathematics, either direction of causation can be supported (Kulm, 1980). Attempts in reducing children’s alienation from school may have a favourable impact on their self-concepts and attitudes toward mathematics.

REFERENCES

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

Aiken, L. R. (1979) Attitudes toward mathematics and science in Iranian middle schools. School Science and Mathematics 3, 229-234.

Allport, G. W. (1935) Attitudes. In A Handbook ofSociaf Psychology (Edited by Murchison. C). Clark University Press, Worcester, MA.

Backman, M. E. (1972) Patterns of mental abilities: ethnic, socioeconomic and sex differences. Americas Edzrca- tionaf Research Journal 9, 1-12.

Balmahn, B. J. and Young, D. M. (1982) On the transmission of mathematics anxiety. Arithmefic Teacher 30,55-56.

Bandura, A. (1982) Self-efficacy mechanism in human agency. American Psychologist 37. 122-147.

Battista, M. T. (1986) The relationship of mathematics anxiety and mathematics knowledge to the learning of mathematical pedagogy by preservice elementary teachers. School Science and Mathematics 86. 10-19.

Benbow, C. P. and Stanley, J. C. (1980) Sex differences in mathematical ability: fact or artifact? Science 210, 1262- 1264.

Beverly, M. and Metcalfe, A. (1981) Self-concept and attitude to school. British Journal of Educational Psychology 51, 66-76.

Bhatnager, J. (1969) A study of adjustment of immigrant children in a London school. Ph.D. dissertation, University of London.

British Psychological Society (19X6) Achievement in the primary school: evidence to the Education, Science and Arts Committee of the House of Commons. Bulletin of the British Ps.ychofogieai Society 39. 121-125.

38 MUHAMMAD MAQSUD and CHAUDHRY M. KHALIQUE

Burns, R. B. (1977) The self-concept and its relevance to academic achievement. In Readings in Psychologyfor the Teacher (Edited by Child, D.). Holt, Rinehart and Winston, London.

Burton, G. M. (1978) Mathematics ability-is it a masculine trait? School Science and Mathematics 78.566 574.

Burton, L. (1986) Girls into Maths Can Go. Holt, Rinehart and Winston, London.

Bush, W. S. (1989) Mathematics anxiety in upper elementary school teachers. School Science and Mathe- matics 89, 499-509.

Byrne, B. M. (1984) The general/academic self-concept nomological network: a review of construct validation research. Review of Educational Research 54, 427456.

Calder, B. J. and Ross, M. (1973) Attitude and Behaviour. General Learning Press, Morristown, NJ.

Cheung, K. C. (1988) Outcome of schooling: mathematics achievement and attitudes towards mathematics learning in Hong Kong. Educational Studies in Mathematics 19. 209-219.

Cohen, L. (1974) Labelling and alienation in a British secondary school. Educational Review 26, 10@108.

Cohen, L. (1976) Educational Research in Classroom and Schools: a Manual of Materials and Methods. Harper and Row, London.

Coopersmith, S. (1959) A method of determining types of self esteem. Journal of A bnorrnal and Socird Psychology 59, 87-94.

Coopersmith, S. (1967) The Antecedents of Self-Esteem. Freeman, London.

Fennema, E. (1985) Explaining sex-related differences in mathematics: theoretical models. Educational Studies in Mathematics 16, 303-320.

Ferri, E. (1971) Streaming: Two Years Later. NFER. Slough.

Fox, L. H. (1977) The effects of sex role socialization on mathematics participation and achievement (National Institute of Education, Papers in Education and Work, No. 8, U.S. Department of Health, Education and Welfare). U.S. Government Printing Office. Washington, D.C.

Glick, 0. (1970) Sixth graders’ attitudes toward school and interpersonal conditions in the classroom. Journal of Experimental Education 38, 17-22.

Hackett, G. and Betz, N. E. (1989) An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education 20, 261-273.

Hanna, ‘G. (1989) Mathematics achievement of girls and boys in grade eight: results from twenty countries. Educational Studies in Mathematics 20, 225-232.

Hansford, B. C. and Hattie, J. A. (1982) The relation between self and achievement/performance measures. Review of Educational Research 52, 123-142.

Hart, J. G. (1985) LAWSEQ: its relations to other measures of self-esteem and academic ability. British Journal of Educational Psychology 55, 167-169.

Heaven, P. C. L. and Bester, C. L. (1986) Alienation and its psychological correlates. The Journal of Social Psy- chology 126, 593-598.

Hess, R. D., Mei, C. C. and McDevitt, T. M. (1987) Cultural variations in family beliefs about children’s performance in mathematics: comparisons among People’s Republic of China, Chinese-American, and Caucasian-American families. Journal of Educational

Psychology 79. 179-188. Hyman, H. H. (1953) The value system of different classes:

a social psychological contribution to the analysis of stratification. In Class, Status and Power (Edited by Bendix, R. and Lipset, S. M.), pp. 42G442. Free Press. NY.

Kahl, J. A. (1960) The Americun Class Structure. Holt, Rinehart and Winston, NY.

Kelly, W. P. and Tomhave, W. K. (1985) A study of maths anxiety/maths performance in preservice elementary teachers. Arithmefic Teacher 32, 51-53.

Kulm, G. (1980) Research in mathematics attitude. In Research in Mathematics Education (Edited by Shumway, R. R.). pp. 356387. National Council of Teachers of Mathematics, Reston, VA.

Kloosterman, P. (1988) Self-confidence and motivation in mathematics. Journal of Educational Psychology 80. 345-351.

Leder, G. C. (1985) Sex-related differences in mathematics. Educational Studies in Mathematics 16, 304309.

Maqsud, M. (1983) Relationships of locus of control to self- esteem, academic achievement, and prediction of performance among Nigerian secondary school pupils. British Journal of Educational Psychology 53, 215-221.

Marshall, S. P. and Smith, J. D. (1987) Sex differences in learning mathematics: a longitudinal study with item and error analyses. Journal of Educational P.sychology 79. 3722383.

McLeod, D. B. (1988) Affective issues in mathematical problem solving: some theoretical considerations. Journal for Research in Mathematics Education 19. 134 141.

Meyer, M. R. and Fennema, E. (1986) Gender differences in the relationships between effective variables and mathematics achievement. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.

Mizruchi, A. A. (1964) Success and Opportunity. Free Press, NY

Mullis, I. V. S. (1975) Educational Achievement and Se.u Discrimination, National Assessment of Education Progress. Denver, CO.

Obanya, P. (1976) Relationship between self-concept and performance in achievement tests of French. West African Journal of Educational and Vocational Measurement 3, 39-43.

Olowu, A. A. (1985) Sex differences in the self-concept of English and Nigerian adolescents. Journal of Social Psychology 125, 129-130.

Piers, E. and Harris, P. (1964) Age and other correlates of self-concept in children. Journal of Educational Psy- chology 55,91-95.

Pottebaum, S. M., Keith, T. Z. and Ehly, S. W. (1986) Is there a causal relation between self-concept and academic achievement? Journal of Educational Research 79, 140-144.

Purkey, W. W. (1970) Self-Concept and School Achieve- ment. Prentice-Hall, NJ.

Reyes, L. H. (1984) Affective variables and mathematics education. Elementary School Journal 84, 558-581.

Richmond, P. G. (1985) The relationship of grade, sex. ability and socioeconomic status to parent, peer and school affiliation. British Journal of Educational Psychology 55, 233-239.

Romberg, T. A. and Wilson, J. W. (1969) The development of tests, NLSMA Report No. 7. Vroman, Pasadena, CA.

MATHS ACHIEVEMENT IN SECONDARY SCHOOL PUPILS 39

Rosenberg, M. J. (1965) Society and the Adolescent Self- Institute of Education, University of London. Image. Princeton University Press, Princeton, NJ. Widmer, C. C. and Chavez, A. (1982) Maths anxiety in

Sells, L. (1980) The mathematics filter and the education of elementary school teachers. Education 102, 272-276. women and minorities. In Women and the Mathematical Wigfield, A. and Meece, J. L. (1988) Maths anxiety in Mystique (Edited by Fox, L., Brody, L. and Tobin, D.). elementary and secondary school students. Journal of Johns Hopkins University Press, Baltimore, MD. Educational Psychology 80,21&216.

Thomas, J. B. (1973) Self-Concept in Psychology and Wylie, R. (1979) The Self-Concept: Theory and Research on Education: a Review of the Research. NFER, Slough. Selected Topics. University of Nebraska Press, Lincoln,

Walden, R. and Walkerdine, V. (1985) Girls and NE. Mathematics: From Primary to Secondary Schooling.