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Change in differences between the sexes in mathematics achievement at the lower secondary school level in Australia: Over time

Tilahun Mengesha Afrassa
Department of Education, Training and Employment
tilahun@ssabsa.sa.gov.au

John P Keeves
Flinders University School of Education
john.keeves@flinders.edu.au

Abstract

In this paper an investigation is reported on whether changes have occurred in the differences between the sexes in mathematics achievement at the lower secondary school level over the 30 year period from 1964 to 1994. In order to make meaningful comparisons the mathematics test scores from the three studies conducted in Australia under the auspices of the International Association for Evaluation of Educational Achievement were brought to a common interval scale using Rasch measurement procedures. The scale scores are used to examine differences between boys and girls in mathematics achievement on the three occasions as well as the changes that have occurred between occasions. No significant sex differences in mathematics achievement are found on each of the occasions. However, a significant decline in mathematics achievement is recorded for boys between 1964 and 1994, but not for girls. The decline in mathematics achievement over this 30 year period for boys is equivalent to nearly one year of mathematics learning, while the drop for girls is only approximately equivalent to half a year of mathematics learning.

Gender differences, mathematical achievement, Rasch modelling

Abstract

Introduction

Analytical Procedures Employed in the Study

Comparison of Sex Difference in FIMS, SIMS and TIMS

Sex Differences in Decline of Achievement over Time

Discussion and Conclusion

References

 
Introduction

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During the past 30 years the issue of differences between the sexes in mathematics achievement in Australian schools has attracted considerable research, discussion and recommendations for change in policy and practice. Major reviews of research conducted in Australia by Leder and Forgasz (1992) and Barnes and Horne (1996) in gender and mathematics learning refer to "gender" rather than "sex" differences. However, Megarry (1984) has argued for the use of "sex" to refer to the biological category to which a person belongs, and for the use of "gender" to denote "the set of meanings, expectations and roles that a particular society ascribes to sex". In this paper interest is primarily focused on estimated differences in mathematics achievement between male and female students, without the examination of gender related influences. As a consequence the differences considered are commonly referred to here as "sex differences".

Leder (1992) has also reviewed changing perspectives in the area of gender differences in mathematics learning from an international viewpoint. However, this review does not examine factors that account for differences either across countries or over time. Articles by Keeves (1973) and Baker and Jones (1993) examine some of the data sets that are considered in this paper from a cross national perspective. Their investigations address particular relationships associated with such differences and provide evidence that the estimated differences between the sexes in mathematics achievement are at least in part, societally based. From these findings there is clear evidence that gender based effects have an influence on the learning of mathematics. However, it is necessary to clarify whether significant differences in mathematics achievement between male and female students can be detected in Australia and at what year and age levels these are found as well as whether levels of achievement have changed over time.

Unfortunately much of the research into differences in mathematics achievement between the sexes in Australia has suffered from several serious shortcomings: (a) selection bias, since comparisons are made using groups that are not representative of a target population which is complete and has not suffered from self selection; (b) the sampling procedures employed are inadequate because, while large numbers of students are tested, they are drawn from too few schools; and (c) the estimation of error for significance testing fails to take into consideration the use of a cluster sample design. If sound comparisons are to be made for the detection of differences between the sexes in mathematics achievement, then large representative and random samples of students must be tested and significance tests with appropriate estimates of error must be employed. Unless, the research findings reported are free from these problems, any discussion of these findings and the recommendations developed from such findings are likely to be highly misleading.

The problems associated with the inappropriate use of significance tests in situations where schools are selected as the primary sampling unit and students are selected from within schools have been recognised for over 30 years. Sometimes very crude estimates of error have been calculated which sought to make allowance for the use of a cluster sample design (for example, Keeves, 1968). In general, the problem has been ignored, because appropriate computer programs have not been available for the accurate estimation of sampling and measurement errors. In the past few years computer programs have become available, for example WesVarPC (Brick et al. 1997) and HLM (Bryk, Raudenbush and Congdon 1992), that can be readily used to estimate errors that would permit the testing of such data for statistical significance. Under these circumstances, in order to examine differences between boys and girls in mathematics achievement, it would seem necessary for analyses to be undertaken with data sets that involve large random samples, with the nested structure of students within schools clearly identified, so that appropriate estimates of error can be calculated prior to testing for statistical significance.

The aim of this paper is to examine whether differences can be detected between the sexes in mathematics achievement in Australia at the lower secondary school level. Furthermore, this paper considers whether changes have occurred over time in levels of mathematics achievement as might be expected from the programs that have been introduced in Australia over the period under survey.

Several questions must be addressed before the analyses can be undertaken.

  1. The samples selected must not be confounded by the effects of selection bias. This requires that the samples are drawn from schools across Australia, at a stage of schooling where the study of mathematics is compulsory and prior to the period either where some students have dropped out from school or where the study of mathematics is optional.
  2. It is necessary to establish that the instruments employed to measure mathematics achievement are assessing one dimension and that the examination of a single mathematics score is meaningful, rather than separate dimensions for the different branches of mathematics at the lower secondary school level - as arithmetic, algebra and geometry.
  3. Furthermore, in order to make meaningful comparisons over time, it is necessary to bring the different measures of mathematics achievement on the different occasions to a common scale. This can be done through the use of the Rasch scaling of the scores using concurrent equating procedures, provided the items and the persons satisfy the requirement of unidimensionality, and there are common items in the tests used across the different occasions.

Sampling Procedure

In the First International Mathematics Study (FIMS), (Keeves, 1968) conducted in 1964, two groups of students participated, 13-year-old students in Years 7, 8 and 9 and students in Year 8 of schooling. In total 2275 male and 2044 female students participated in this study. In FIMS only government schools in New South Wales (NSW), Victoria (VIC), Queensland (QLD), Western Australia (WA) and Tasmania (TAS) participated. In the Second International Mathematics Study (SIMS), (Rosier, 1980) which was administered in 1978, nongovernment schools and the Australian Capital Territory (ACT) and South Australia (SA) were also involved as well as those states that participated in FIMS. Subsequently, in the Third International Mathematics Study (TIMS), (Lokan, Ford and Greenwood, 1996) which was conducted in 1994, government and nongovernment school students in all states and territories including the Northern Territory were involved. In the TIMS study 6089 male and 6761 female students were tested at the lower secondary school level.

In 1964 and 1978 the samples were age samples and included students from Years 7, 8 and 9 in all participating states and territories, although in FIMS a Year 8 sample was also tested. In TIMS the samples were grade samples drawn from Years 7 and 8 or Years 8 and 9. In ACT, NSW, VIC and TAS Years 7 and 8 students were selected while in QLD, SA, WA and NT samples were drawn from Years 8 and 9, enabling a Year 8 Australia wide sample to be derived for purposes of comparison with the 1964 data.

Therefore, to make the most meaningful possible comparison of mathematics achievement of boys and girls over time by using the 1964, 1978 and 1994 data sets, the following steps were taken.

The 1964 students were divided into two groups 13-year-old students in one group (FIMSA) and all Year 8 students including 13-year-old students at that year level as the second group (FIMSB) since in addition to an age sample, a grade sample had also been drawn. It is important to observe that 13-year-old students in Year 8 were considered as members of both groups. In the first group, students were chosen for their age and in the second group for their year level. The 1978 students were chosen as an age sample and included students from both government and nongovernment schools. In order to make meaningful comparisons between the 1978 sample and the 1964 sample, the 1978 government school students were divided into two groups. The first group included all government school students who participated in the study (SIMSG), and the second group included all government school students in the five states excluding students from SA and ACT (SIMSR).

Meanwhile, in TIMS the students were chosen as a grade sample. The common sample for all states and territories was Year 8 students. In order to make the TIMS samples comparable with the other samples, only Year 8 government school students in the five states that participated in FIMS and SIMS are considered as the TIMSR data set in this study.

Analytical Procedures Employed in the Study

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In this study the procedures employed to compare the achievement differences between male and female students on the three occasions involved the use of the Rasch model to scale students' responses to the mathematics test items. The Rasch model has been shown to be the most robust of the item response models (Sontag, 1984), and was used in this study primarily to equate students' performance in mathematics on a common scale for the Australian investigations conducted in FIMS, SIMS and TIMS.

Unidimensionality

In order to employ the Rasch model for calibrating the items in the mathematics tests it was necessary to examine whether or not the items satisfied the requirement of unidimensionality (Hambleton and Cook, 1977). If the items were found not to satisfy the condition of unidimensionality, it would not be possible to employ the Rasch procedures for the calibration of the tests. Furthermore, it would not be meaningful to compare differences between the sexes with respect to mathematics achievement since a total score would be meaningless.

Consequently, confirmatory factor analysis procedures were employed to test the unidimensionality of the mathematics test items using the LISREL computer program (Jöreskog and Sörbom, 1992).. Confirmatory factor analysis is a statistical procedure employed for investigating relations between a set of observed variables and the underlying latent variables (Byrne, 1989; Spearritt,, 1997). The results of the confirmatory factor analyses of FIMS and SIMS data sets revealed that a nested model in which the mathematics items were assigned to three specific correlated first-order factors of Arithmetic, Algebra and Geometry as well as a general higher order factor, which was labelled as Mathematics provided the best fitting model. In addition, in the confirmatory factor analyses undertaken, no evidence was found to reject the assumption of the existence of one general factor involved in the mathematics tests, in so far as in the nested model the Mathematics factor extracted more of the total variance than did the specific first-order factors taken together. Therefore, the mathematics test items in the FIMS and SIMS studies are considered to satisfy the requirement of unidimensionality. The item cluster-based design procedure employed in the construction of the TIMS data sets would seem to preclude the use of confirmatory factor analysis to test the unidimensionality of the TIMS data set. and confirmation of unidimensionality must be provided by the introductory steps in the Rasch analysis.

Effect of mathematics learning in one year

It is possible since the TIMS project tested at two adjacent grades to estimate the gain between the lower grade and the upper grade for the Australian sample and thus to interpret the calibrated effect size in terms of years of mathematics learning at the lower secondary school level. The difference between the lower and the upper grade levels show the growth on mathematics achievement over one year in Australian lower secondary schools. Thus to examine the growth between grade levels, the estimated mean scores difference between the lower and the upper level students was compared using the WesVarPC 2.11 computer program (Brick et al. 1997). The results of the comparisons are presented in Table 1.

The estimated mean score for the lower level was 520 centilogits, while for the upper level students, it was 557 centilogits. The difference was 37 centilogits in favour of the upper level students. Hence, the growth in achievement per year in mathematics performance in Australian lower secondary schools was 37 centilogits. The effect size and t-value were 0.30 and 3.96 respectively. Thus, the mean difference between the lower and the upper grade levels, namely 37 centilogits is equivalent to an effect size of 0.30. Keeves (1992) reported that 38 centilogits was found to be equivalent to a year of science learning between the 10 and 14 year-old levels in the Second IEA Science Study in Australia. Therefore, this information allows the differences between the achievement level of the different groups to be interpreted in terms of practical significance as well as statistical significance. Thus, the mean difference between the lower and the upper grade levels in Australian lower secondary schools in 1994 was practically and statistically (at the 0.01 level) significant. Hence it is estimated their learning in one year between Year 7 and Year 8 is 37 centilogits and

  • 1 centilogit = 1 week of mathematics learning,
  • 4 centilogits = 1 month of mathematics learning.

Table 1. Comparisons between the Lower and Upper group Levels in TIMS

Effect size

In this paper both the standardized effect size and the magnitude of effect on the calibrated scales are used to examine the level of practical significance of the differences between FIMS, SIMS and TIMS in mathematics achievements over time. The following formula was employed to calculate an effect size value.

Where
= estimated mean score for group one;
= estimated mean score for group two;
= standard deviation of group one; and
= standard deviation of group two.

In this study effect size values less than 0.20 are considered as trivial, while values between 0.20 and 0.50 are considered as small. Furthermore, effect size values between 0.50 and 0.80 are taken as moderate and values above 0.80 are treated as large (Cohen, 1992).

The t -test

In order to determine the level of statistical significance between the mean scores on FIMS, SIMS and TIMS in mathematics achievement a t-statistic was calculated, which took into account errors from three sources: (a) sampling error, (b) errors of calibration, and (c) equating error. Since the samples all involved a cluster sample design with schools sampled with a probability proportional to size at the first stage and students sampled from within schools at the second stage, it was necessary to use the WesVarPC (Brick et al. 1997) computer program to test the data for statistical significance, taking into account both the stratification and cluster sample design employed in all three studies.

Developing a common mathematics scale

The calibration of the mathematics data permitted a scale to be constructed that extended across the three groups, namely FIMS, SIMS and TIMS students on the mathematics scale. The fixed point of the scale was set at 500 with one logit, the natural metric of the scale, being set at 100 units. The fixed point of the scale, namely 500 was taken as the mean of the difficulty level of the calibrated items in the FIMS test administered in 1964.

Rasch Analysis

Three groups of students namely FIMS (4320), SIMS (5120) and TIMS (12850) were employed in the calibration and scoring analyses. The necessary requirement for calibration in Rasch scaling is that the items and persons must fit the Rasch scale. In order to examine whether or not the items and persons fitted the scale, it was important to evaluate both the item fit statistics and the person fit statistics. The results of these analyses are presented below.

Item Fit statistics

One of the key item fit statistics is the infit mean square (INFIT MNSQ). The infit mean square measures the consistency of fit of the students to the item characteristic curve for each item with weighted consideration given to those persons close to the 0.5 probability level. The acceptable range of the infit mean square statistic for each item in this study was taken to be from 0.77 to 1.30 (Adams and Khoo, 1993). In calibration, items that do not fit the Rasch model and which are outside of the acceptable range must be deleted from the calibration analyses (Wright and Stone, 1979). Hence, in FIMS two items (Items 13 and 29), in SIMS two items (Items 21 and 29) and in TIMS one item [(Item T1b no 148) with one item (no. 94) having been excluded from the international TIMSS analysis] were removed from the calibration analyses due to the misfitting of these items to the Rasch model.

Case Estimates

A second way of investigating the fit of the Rasch scale to the data is to examine the estimates for each case. The case estimates give the performance level of each student on the total scale. In order to identify whether the cases fit the scale or not, it is important to examine the case OUTFIT mean square statistic (OUTFIT MNSQ) which measures the consistency of the fit of the persons to the student characteristic curve for each student, with special consideration given to extreme items. In this study, the general guideline used for interpreting t as a sign of misfit is if t> 5 (Wright and Stone, 1979, p. 169). Thus, if the OUTFIT MNSQ value for a person has a |t &endash; value| greater than 5, that person does not fit the scale and is deleted from the analysis. In this analysis no person was deleted, because the |t &endash; value| for all cases was less than 5. However, students with a zero score or with a perfect score were automatically excluded from the calibration procedure, since they would not provide useful information for the purposes of scale calibration, although such students were necessarily included in the scoring of the data.

Comparison of Sex Difference in FIMS, SIMS and TIMS

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In Table 2 the mathematics achievement levels of boys and girls in FIMSA, FIMSB, SIMS and TIMS are compared (see Table 2). The paper compares differences in mathematics achievement between the two sexes on the three occasions. These comparisons for Australia in 1964 and 1978, differ from those carried out in previous studies (Keeves, 1968; Moss, 1982) in that proper account can now be taken for the complex design of the samples employed in testing for statistical significance.

However, in testing for significant differences, while multiple comparisons are involved no use is made of the Bonferroni Adjustment (Finn, 1997), because the thrust of the comparisons is more toward the detection of no differences, than towards the detection of highly significant ones.

The first comparison to be discussed is between FIMS Students.

Table 2. Descriptive statistics for mathematics achievement of all students for the three occasions by sex


Restricted =Those groups of students in SIMS which are comparable with FIMSA, and students in TIMS which are comparable with FIMSB

Comparisons of Sex Differences between 1964 Australian Students

Table 2 and Figures 1 and 2 show the three comparisons which are considered in FIMS. The estimated mean score differences for the three comparisons are seemingly in favour of boys. This suggests that boys achieved at a higher level than girls. However, the effect size is trivial and t-values are non-significant. Thus, in all the comparisons the differences are neither practically nor statistically significant. It should be noted that Keeves (1968) using a very crude approximation for the design effect of the complex sample reported a significant difference. However, the procedures employed currently in significance testing, make proper provision for the complex sample design using the jackknife routine in WesVarPC (Brick et al. 1997).


Figure 1. t-values for differences between boys and girls in Mathematics test score for FIMS, SIMS and TIMS

Comparisons of Sex Differences between 1978 Australian Students

In the SIMS data set four comparisons are undertaken and presented in Table 1 and Figures 1 and 2. The comparisons are between boys and girls in government schools, nongovernment schools, in all schools, and the restricted sample of schools.

The mean score differences between the two sexes in government schools (both Government and Restricted) indicated that girls achieved at a higher level than boys. However, the differences were neither practically nor statistically significant since the effect size and t-values were too small to be considered significant.

Furthermore, the estimated mean score difference between male and female nongovernment school students in SIMS is seemingly in favour of the boys, although the effect size (0.22) is small and the t-value (1.35) is non-significant. Thus, the difference is not statistically significant. Nevertheless, the achievement level of the boys is higher than that of the girls by approximately two-thirds of a year of mathematics learning in Australian schools (as estimated in the mid 1990s), although this result may be influenced by the particular schools selected in the analysis and the result is not significant statistically.

The last comparison in SIMS is between boys and girls in all schools. The mean score difference is apparently in favour of boys. However, the effect size (0.05) and t-value (0.72) are very small. Hence, the difference between boys and girls in 1978 is not practically or statistically significant across Australian schools. Out of the four comparisons, only in government schools is the achievement of the girls slightly higher than that of the boys. In the remaining comparisons boys appear to perform better than girls. These findings appear dissimilar to the findings in FIMS. In the 1964 data set all the differences are in favour of boys. This might indicate that over the 14-year period there was a small shift in achievement level differences between boys and girls. However, the differences are not statistically or practically significant.

Comparisons of Sex Differences between 1994 Australian Students

The estimated mean score differences between the two sexes in government schools (both Government and Restricted) are in favour of girls (see Table 1 and Figures 1 and 2). However, the effect size and t-values are very small and the mean differences are neither practically nor statistically significant.

The other comparison is between the two sexes in nongovernment schools. Unlike the government school students the difference is seemingly in favour of boys. However, the difference is not statistically or practically significant since the effect size is trivial (0.12) and the t-value is very small, because the design effects are large.


Figure 2. Effect size values for differences between boys and girls in Mathematics test score for FIMS, SIMS and TIMS

The last comparison in TIMS considers all students (government and nongovernment together). The mean score difference is apparently in favour of girls. However, the effect size (-0.04) and t-value (-0.52) are too small to be considered significant. Consequently the mean difference is neither practically nor statistically significant.

Three of the four different comparisons in TIMS between boys and girls in mathematics achievement reveal that the mathematics achievement levels of the girls are slightly greater than that of the boys. When the findings in TIMS are compared with the findings in FIMS and SIMS, the direction of the difference between the sexes has apparently changed, but the changes are not significant. In Figures 1 and 2 these results for the differences in the t-values employed for significance testing and in effect size are presented graphically in order to summarize the results.

In 1964 the differences are in favour of the boys, while in 1978 the difference is in favour of the girls only in government schools. However, in 1994 the differences, except in nongovernment schools, are in favour of the girls. Nevertheless none of the differences are found to be statistically significant. These nonsignificant differences might seem to suggest that some differences between the sexes in mathematics achievement are starting to emerge in the 1990s in favour of girls and in contrast to the findings of Keeves (1973), Carss (1980), Moss (1982), Leder and Forgasz (1992). These researchers would appear to contend that a difference between the sexes in mathematics achievement in Australian schools starts to emerge at the junior secondary school stage in favour of boys. The apparent change in direction in the 1990s could then be argued to have been a result of the implementation of different government policies to increase the participation and the mathematics achievement level of girls by the State and Federal Governments. Alternatively, it could be argued that the level of performance of the boys has declined more than that of the girls over time, as can be seen from Table 1 there is a general decline in achievement of all Australian students over the 30-year period. The possibility of a significant decline in the level of achievement in mathematics of boys, rather than a noticeable gain in the achievement of girls would be of some concern for Australian education.

 

Table 3. Descriptive statistics for mathematics achievement of male and female students for the three occasions

Sex Differences in Decline of Achievement over Time

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While this paper has so far reported no significant differences between the sexes on the three occasions, the possibility exists that there has been a significant decline in the standard of achievement of the boys over time, and no significant decline in the achievement of girls.

Table 3 and Figure 3 present the results of the analyses that test the differences in achievement in mathematics for boys and girls separately between occasions.

When the 1964 13-year-old male students (FIMSA) mean score is compared with the mean score of the 1978 13-year-old male students (SIMS), the mean score of the FIMSA students is higher than that of the SIMS students. The difference is 22 centilogits (see Table 3 and Figure 3). The difference is practically and statistically significant at 0.05 level. This significant difference shows that the mathematics achievement of male students declined over time by more than half a year of mathematics learning.


Scaled mean scores recorded with standard errors of mean.

Figure 3. The Mathematics test scale of government school students, FIMSA, FIMSB, SIMS and TIMS

The mean difference between FIMSA and SIMS female students is 14 centilogits (see Table 3 and Figure 3). This difference is not practically or statistically significant. This indicates that there is no significant difference between 1964 and 1978 female students mathematics achievement.

The mathematics achievement mean difference between 1964 Year 8 (FIMSB) and 1994 Year 8 (TIMS) male students is 33 centilogits (see Table 3and Figure 3). This difference is practically and statistically significant significant at the 0.05 level. This significant difference indicates that the mathematics achievement level of male Year 8 students declined from 1964 to 1994, by approximately one year of mathematics learning.

The mean difference between FIMSB and TIMS female students is 17 centilogits (see Table 3 and Figure 3). However, this difference is not practically or statistically significant. This indicates that there is no significant difference between 1964 and 1994 female students’ mathematics achievement.

Hence, these four analyses show that the mathematics achievement of male students has declined significantly over the last 30 years, while there is not a significant decline for female students over time.

The reasons for the decline in achievement have not been examined. However, Tilahun and Keeves (1999) have shown that the Australian states differ in the extent of the decline recorded with one state out of the five showing a slight but not statistically significant gain in achievement. Nevertheless, it can be argued that any relative change in the performance in mathematics of girls with respect to boys is not a consequence of the improved performance of girls, but rather the significant drop in the performance of boys.

Discussion and Conclusion

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In 1964 the differences are in favour of the boys, while in 1978 the difference is in favour of the girls only in government schools. However, in 1964 the differences, except in nongovernment schools are in favour of the girls. Nevertheless none of the differences are found to be statistically significant. These nonsignificant differences might seem to suggest that a difference between the sexes on mathematics achievement is starting to emerge in the 1990s in favour of girls and in contrast to the findings of previous studies. These researchers would appear to argue that a difference between the sexes in mathematics achievement in Australian schools starts to emerge at the junior secondary school stage in favour of boys. The apparent change in direction reported above might then be argued to have been a result of the implementation of government policies to increase the participation and the mathematics achievement level of girls by the State and Federal Governments. The evidence presented in this paper suggests that other forces are operating, that have resulted in a decline in performance of both male and female students of some practical significance when assessed in terms of a year of mathematics learning as well as being of a small but recognizable size for boys when assessed in terms of an effect size and statistical significance.

Until, there is clear evidence of statistically significant differences between the sexes in mathematics achievement and of sufficient magnitude to warrant resources being diverted to addressing the problem, there would appear to be more pressing problems to be considered in Australian education than the nature and origin of differences between the sexes in mathematics achievement at the lower secondary school level (see, for example, Rowe, 1998; Marsh and Rowe, 1996, particularly since both studies have ignored the multilevel nature of the data in their analysis). Moreover, such programs as have been undertaken in Victoria of establishing separate classes for boys and girls in mathematics at the lower secondary school stage would seem to be a misdirection of effort and resources until it can be shown that a substantial problem exists. Futher (1995) has already questioned the existence of such a problem.

However, this comment should not be taken to divert attention from the problem of the lower participation of girls in advanced mathematics classes at the senior secondary school level.

The failure to detect significant differences between the sexes in mathematics achievement in this study which uses the largest and most carefully designed samples available in Australia over a period of more than 30 years has several important implications for educational research in this field. There is a need to :

  • employ large well designed random samples and to attain high response rates in order to test relationships that are widely assumed to exist;
  • use appropriate statistical procedures to test for the statistical significance of differences that allow for the multilevel or nested nature of the data;
  • report and discuss the magnitudes of effect sizes and the pattern of results, as well as use appropriate procedures to test for statistical significance;
  • conduct research into the problems encountered by both boys and girls in learning mathematics as they pass through the lower and middle secondary stage;
  • monitor in a systematic way changes in mathematics achievement over time, as well as changes in the performance of clearly identified subgroups of students; and
  • maintain the view that all students can learn mathematics successfully irrespective of sex at all stages of schooling and in particular at the lower and middle secondary school levels.

Acknowledgment

The first author was sponsored by a Flinders University of South Australia Overseas Postgraduate Research Scholarship and the Flinders University Research Scholarship, while undertaking these analyses.

The authors would like to thank the several unknown reviewers of this paper for their helpful comments, which have been taken into consideration in the revisions of the paper.

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 Afrassa, T.M. and Keeves, J.P. (2001) Change in differences between the sexes in mathematics achievement at the lower secondary school level in Australia: Over time International Education Journal, 2 (2), 96-108 [Online] http://iej.cjb.net


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