METHOD Participants

The participants were 230,229 Grade-8 students (50.3% girls, 49.2% boys, and 5% missing) from 47 countries participating in the TIMSS study of 2003.

Indicators

Five kinds of indicators (including 11 items) were taken from the database.

(1) Math achievements included students achievement results for measurement and algebra (TIMSS-variables bsmmea01 and bsmalg01).

(2) Gender (girls = 0; boys =1; TIMSS-variable itsex).

(3) Affective factors included students’ confidence in learning math, e.g.,

‘I usually do well in math’ (TIMSS derived-variable bsdmscl) and students’ academic aspiration as to how far in school they expect to go (TIMSS-variable bsbghfsg).

(4) Cognitive factors referred to closed and open teaching strategies or learning experiences. Closed learning experiences included working on problems on their own and reviewing their homework in class (TIMSS-variable bsbmhwpo and bsbmhroh). Open learning experiences consisted of working in small groups and relating math to daily lives in class (TIMSS-variable bsbmhwsg and bsbmhmdl).

(5) Social factors comprised parents’ highest education levels (TIMSS derived-variable bsdgedup) and extra lessons or tutoring in math that is not part of regular class (TIMSS-variable bsbmexto).

The achievement scores were obtained based on students’ answers to a set of math problems in the content domains of measurement and algebra.

The scores on the other indicators were derived from students’

self-reports on a questionnaire. A higher score on all the indicators, except for gender, represented a higher achievement, degree, or frequency in the present study.

Statistical analysis

The major analysis method used here is linear regression. As suggested by the TIMSS 2003 user guide, student weights had to be used in all analyses in order to generate results representing the populations and SENWGT was used in the present study as it treated each country equally by setting a sample size of 500 for each country. Missing data were dealt with by pairwise exclusion in regression analyses.

RESULTS

Correlations between factors

The results of correlation analyses revealed that there were low correlations between all the items (below .331), except for a high correlation between measurement and algebra achievements (.873) (Table 1). The low correlations indicate a low degree of the problem of multicollinearity in regression analyses. No regression analysis was performed between the measurement and algebra achievements.

Factors in reducing gender differences in measurement achievements The relation between gender and measurement achievements, or the regression coefficient for the effect of gender on measurement achievements, was small but significant (.022), as can be seen in Table 1 and in Model 1 (M01) in Table 2. The results mean that the .048%

variance in measurement achievements could be explained by gender differences and that the positive value could indicate that boys are favored in solving measurement problems.

M A 1 2 3 4 5 6 7 8

Measurement achievement (M)

Algebra achievement (A) .873

1. Gender .022 -.045

2. Confidence in math .198 .201 .066 3. Academic aspiration .226 .265 -.069 .207 4. Working on problems alone .144 .139 .020 .133 .094 5. Reviewing homework -.069 -.045 -.029 .075 .050 .140 6. Working in groups -.260 -.255 .042 .029 -.026 .048 .117 7. Relating math to daily lives -.160 -.153 .051 .126 .031 .095 .201 .280 8. Parental education levels .330 .327 .017 .106 .240 .130 .005 -.146 -.071 9. Extra math tutoring -.169 -.138 .054 -.003 -.018 -.016 .050 .168 .114 -.073

Table 1: Pearson correlations between the 11 indicators. The correlations underlined are not significant at the .05 level.

The sub-factors that could reduce the regression coefficients for the effect of gender on measurement achievements included confidence (.022 in M01 Æ .009 in M02), working on problems alone (.022 Æ .019 in M04), reviewing homework (.022 Æ .020 in M05), and parental education levels (.022 Æ .017 in M08). The other sub-factors showed an increase in gender differences in measurement (M03, M06, M07, and M09). In addition, confidence alone could successfully reduce gender differences from significant (M01) to non-significant (M02). The two most effective sub-factors were confidence and parental education levels, which together could reduce the effect of gender differences from .022 to .006 (non-significant) (M10), and the three most effective sub-factors (i.e., confidence, parental education levels, and reviewing homework) all together could reduce gender differences from .022 to .005 (non-significant).

Factors in reducing gender differences in algebra achievements

The regression coefficient for the effect of gender on algebra achievement was -.045, which meant that .203% of the variance in algebra achievements could be explained by gender differences and the negative value revealed that girls were favored in solving algebra problems (M12 in Table 3). The effect of gender differences on algebra achievements was around four times (4.23 = .203% / .048%) larger than that on measurement achievements.

The sub-factors that could reduce the regression coefficient for the effect of gender on algebra achievements were academic aspiration (-.045 in M12 Æ -.023 in M14), working in groups (-.045 Æ -.030 in M17), relating math to daily lives (-.045 Æ -.033 in M18), and extra math tutoring (-.045 Æ -.033 in M20). None of these sub-factors could successfully reduce the significant gender effect to a non-significant one, perhaps partly because of the large effect of gender on algebra achievements. The two strongest sub-factors (i.e., aspiration and working in groups) together could reduce the regression coefficient for the effect of gender on algebra from -.045 to -.017 (M21), which, however, was still statistically significant. The two strongest sub-factors (i.e., aspiration and working in groups) with extra math tutoring all together could reduce the regression effect of gender on algebra from -.045 to -.013 (M22), which was non-significant. A point to note is that the two open learning experiences, working in groups and relating math to daily lives, and extra math tutoring were negatively related to algebra achievements but that these interventions and investments could effectively reduce gender differences.

Models Factors

M01 M02 M03 M04 M05 M06 M07 M08 M09 M10 M11 1. Gender .022 .009 .038 .019 .020 .033 .030 .017 .031 .006 .005 Affective factors

2. Confidence in math .197 .164 .154

3. Academic aspiration .229

Cognitive factors (Math in class)

4. Working on problems alone .144 .048

5. Reviewing homework -.068

6. Working in groups -.261

7. Relating math to daily lives -.162

Social factors

8. Parental education levels .329 .312 .302

9. Extra math tutoring -.170

Table 2: Beta estimates obtained by regression analyses for the sub-factors in predicting measurement achievements. The estimates

underlined are not significant at the .05 level.

Models Factors

M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 1. Gender -.045 -.054 -.023 -.048 -.047 -.030 -.033 -.046 -.033 -.017 -.013 Affective factors

2. Confidence in math .201

3. Academic aspiration .261 .257 .256

Cognitive factors (Math in class)

4. Working on problems alone .140

5. Reviewing homework -.047

6. Working in groups -.253 -.247 -.232

7. Relating math to daily lives -.150

Social factors

8. Parental education levels .329

9. Extra math tutoring -.138 -.094

Table 3: Beta estimates obtained by regression analyses for the sub-factors in predicting algebra achievements. The estimates underlined

are not significant at the .05 level.

DISCUSSION

The above findings indicate that affective, cognitive, and social factors can be effective in reducing gender differences in math achievements, but that there exist qualitative differences between the sub-factors in reducing gender differences in measurement and those in reducing gender differences in algebra. Gender differences in measurement achievements can be reduced by sub-factors such as confidence (inductive affects), parental education levels (social backgrounds), working on problems alone, and reviewing homework in class (cognitively closed learning experiences), in a descending sequence. On the other hand, gender differences in algebra achievements can be reduced by sub-factors such as academic aspiration (deductive affects), working in groups, relating math to lives (cognitively open learning experiences), and receiving extra math tutoring (social resources), also in a descending sequence. In addition, affective factors are the strongest factors in reducing both the weakness of girls in measurement and weakness of boys in algebra. The second strongest factor, however, is social factors for girls and cognitive factors for boys. This qualitative difference is further depicted in Figure 2.

Figure 2: Differential affective, cognitive, and social sub-factors in reducing gender differences in measurement and algebra

The findings are consistent with the results of related studies that indicate that girls’ weakness in math problem-solving is at least partly related to their weakness in affective factors, especially girls’ low confidence in math (Gallagher & de Lisi, 1994). Academic aspiration is likely to be an important affective factor for boys. Closed and open teaching strategies or learning experiences were found to be related to gender differences in achievements in different math content domains. Past research on social factors in education typically focuses on SES. The recognition of the effect of social resources, which are provided to students in an active way, is a manifestation of the benefit that social investment can bring in improving students’ math achievements.

The researcher took an integrated, domain-specific, and context-dependent approach to researching multiple factors in the relationships between gender and math achievements. In other words, it is argued that there is an integrated relationship between gender, math content domains, and cultural tools. Future research can further identify other effective sub-factors in affective, cognitive, and social aspects that may reduce gender differences in math achievements. For example, the frequent use of computers in learning math may be of benefit to boys and an interest-induced teaching program of benefit to girls.

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