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The authors have declared that no competing interests exist.

Analyzed the data: GS DCG. Wrote the paper: GS DCG.

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations’ gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits.

In recent decades, women’s participation in the workforce and pursuit of higher education has increased substantially, but there continue to be striking sex differences in college majors and career choices. Sex differences are particularly notable at the highest levels of scientific achievement; for example, under 3% of Nobel laureates in science are women, and no women have so far received one of the top three awards in mathematics (the Fields Medal, the Abel Prize, and the Wolf Prize).

A much publicized study showing that boys greatly outperform girls at the highest ranges of mathematics ability

The causes of the sex difference in mathematics performance, in general, have been extensively discussed over the ensuing years. A number of biological

A number of scholars have argued that the international variation in the sex difference in mathematics performance is correlated with country’s implementation of gender-equality measures

In the current paper, we focus on two related issues in regard to the sex differences in mathematics and reading performance: 1) We explore further the paradoxical relation between sex differences in mathematics and sex differences in reading performance. 2) We explore further whether sex differences in reading and mathematics are related to national indicators of gender equality.

We analyzed the sex differences in all four available assessments (carried out in 2000, 2003, 2006, and 2009) of the Programme for International Student Assessment (PISA), funded by the Organisation for Economic Co-Operation and Development (OECD,

Another strength of these data is that PISA scores are strongly correlated with the prosperity of nations, which indicates that the competencies measured have real-life validity

This inverse relation between the sex differences in mathematics and reading achievement poses a critical challenge for educators and policy makers who might wish to eliminate such differences. After all, as we demonstrate, it means that that there are currently no countries that have successfully eliminated

Before detailing the relation between the sex differences in mathematics and reading, we examine each separately.

For all analyses, we express sex differences in PISA score points. These scores are not “raw” scores, but result from a statistical analysis that normalizes student scores (see

Across nations, the mean overall sex difference in mathematics was small but remained relatively stable over the ten years at 10 to 11 points (

Top: For each PISA assessment, the sex differences in mathematics (boys’ performance – girls’ performance) is displayed for the 5th, 50th, and 95th percentile of the performance distribution. Bottom: Similar for sex differences in reading (girls’ performance – boys’ performance).

Another common way of expressing the sex difference is the ratio of boys to girls at different points along the performance distribution (

Achievement Percentile | 2000 | 2003 | 2006 | 2009 |

1^{st} |
1.1 | 1.3 | 1.1 | 1.0 |

5^{th} |
1.0 | 1.1 | 1.0 | 1.0 |

95^{th} |
1.8 | 1.9 | 1.7 | 1.7 |

99^{th} |
2.7 | 2.3 | 2.3 | 2.3 |

In contrast to the sex difference in mathematics, the difference in reading, favoring girls, receives relatively little attention, despite the fact that the average sex difference in reading was three times larger than the sex difference in mathematics (

Achievement Percentile | 2000 | 2003 | 2006 | 2009 |

1^{st} |
3.1 | 4.1 | 4.8 | 5.9 |

5^{th} |
2.5 | 2.8 | 2.9 | 3.2 |

95^{th} |
0.6 | 0.6 | 0.5 | 0.5 |

99^{th} |
0.5 | 0.5 | 0.4 | 0.4 |

Further, the very poor performance of boys at the low end of reading achievement drove, in large part, the overall sex difference and the increase in it (

At the first percentile of reading performance, the ratio of boys to girls ranged from 3.1∶1 in 2000 to 5.9∶1 in 2009, and at the fifth percentile from 2.5∶1 to 3.2∶1 (

Previously, the relation between the sex differences in reading and mathematics were noted by Marks

We found that the across-nation inverse correlations between the sex differences in reading and mathematics were consistent and strong in all four assessments (Pearson’s

Each data point indicates the sex differences of one country. Positive values indicate a larger disadvantage, negative values an advantage. Red points indicate nations in which girls’ mathematics achievement is significantly higher than that of boys; blue points indicate nations in which boys’ mathematics achievement is significantly higher than that of girls; and, black points indicate nations in which there is no statistically significant difference in mathematics achievement. The advantage of girls in reading achievement is statistically significant in all nations, except for 2 in 2000 (Israel, Peru) and one in 2003 (Liechtenstein).

The two curves represent the magnitude of sex difference in mathematics (black) favoring boys and the sex difference in reading (green) favoring girls in all 33 countries that participated in all four PISA assessments (2000,2003,2006 and 2009). Grey shading indicates ±1 SEM. Within these countries boys at the 50th percentile of the distribution of boys’ scores have a 10 point advantage in mathematics over girls at the 50th percentile of the distribution of girls’ scores. There is no gap for the lowest performing students and a doubling of the average gap for the highest performing students. For students at the 50th percentile, girls reading advantage is about 37 points and increases for lower performing students and decreases for higher performing students. The relation between the two gaps within these countries is the same as found between countries (

Multiple research teams have studied the relation between sex differences in mathematics on the one hand and national gender equality, economic, and human development indicators on the other hand

Sex difference in mathematics | Sex difference in reading | |||||||

2000 | 2003 | 2006 | 2009 | 2000 | 2003 | 2006 | 2009 | |

HDI | 0.36* | 0.01 | 0.24 | 0.24 | 0.02 | 0.25 | −0.04 | 0.09 |

GII | −0.22 | 0.01 | −0.16 | −0.12 | −0.27 | −0.28 | 0.06 | −0.14 |

GDI | 0.34* | −0.01 | 0.23 | 0.21 | 0.05 | 0.26 | −0.03 | 0.13 |

GEM | 0.11 | −0.21 | 0.03 | 0.24 | 0.31 | 0.33 | 0.09 | −0.03 |

GGGI | −0.10 | −0.42** | 0.04 | 0.12 | 0.38* | 0.50 ** | −0.01 | 0.05 |

Gini | 0.17 | 0.05 | 0.18 | 0.25 | −0.39* | −0.16 | −0.20 | −0.49*** |

If anything, economically developed countries with strong gender-equality and human development scores tended to have a larger sex difference in mathematics than less economically developed countries (e.g., for non-OECD countries the sex difference in mathematics was 5.4 vs 10.5 points for OECD countries,

The mathematics scores have been averaged for the four assessments, which means that some countries’ scores are based on four assessments (e.g., Germany and 32 other countries/regions which participated in all four assessments), and some countries’ scores on only one assessment (e.g., Malta and 15 other countries). Sex difference in mathematics equals boys’ mean score - girls’ mean score. The OECD countries not only have higher overall scores, their mathematics gap, favoring boys, is more tightly clustered between −5.5 and 17.5 points (

Percentage of countries in which boys score higher than girls in mathematics. | ||

Of countries with average mathematics score of > = 500 | Of countries with average mathematics score <500 | |

2000 | 88.9% | 70.8% |

2003 | 95.2% | 95% |

2006 | 90.9% | 85.3% |

2009 | 95.0% | 72.2% |

We found that the paradoxical relation between the sex differences in mathematics and reading across different nations occurred in each of the four PISA assessments carried out over 10 years. That is, countries with a smaller sex difference in mathematics tended to have a larger sex difference in reading. This inverse relation between the sex differences in mathematics and reading is not merely an effect that emerged between countries, it also occurred across the performance distributions within countries. The sex difference in mathematics was non-existent at the lower end of the performance distribution, but the sex difference in reading at the lower end was at its peak. As with the between-country findings, the larger the sex differences in mathematics within countries, the smaller the sex differences in reading.

This finding has important implications for the way we think about the nature of sex differences in mathematics and reading. Previously, Guiso and colleagues hypothesized that the negative correlation of mathematics and reading scores between countries might simply reflect that girls in countries with good resources will reap the benefits in both mathematics (improving in comparison to boys and thus reducing the sex difference) and in reading (improving in comparison to boys, and thus increasing the already existing sex difference)

The finding that the sex differences in mathematics achievement were larger at the high end of the continuum is important for understanding the underrepresentation of women in STEM fields. Whereas some have argued that the average sex difference in mathematics in the second PISA assessment is negligibly small

In any case, the inverse relation between the sex differences in reading and mathematics, especially at the extreme ends of the achievement distributions, poses unique challenges for those who wish to resolve these sex differences. First of all, the previously held assumption that countries’ positive equality policies are

The finding that countries with higher living standards showed larger sex differences in mathematics is similar to that found for spatial cognition and matches the conclusion of Fryer and Levitt’s study

What do these findings mean for policy makers or educators who wish to reduce the sex differences in mathematics performance, in particular the underrepresentation of women in fields such as mathematics? Given our finding that nations’ rankings on equality policies are not consistently predictive of sex differences in mathematics achievement, educators and policy makers might reconsider the extent to which the current underrepresentation is related to equality issues. In regard to this point, Ceci and Williams

The implications for policy makers or educators who wish to reduce the sex differences in reading performance are different. Whereas sex differences in mathematics may be related to the male advantage in spatial abilities

Further, it is important to distinguish between the benefits of national prosperity on scholastic achievement of girls on the one hand and the sex differences in scholastic achievement on the other hand. These are two separate issues that are easy to conflate. Although it is true that women’s achievement is higher in economically developed countries than in less economically developed countries (

Related to this latter problem is that the increased participation of women in higher education might actually obscure the continuing underrepresentation of women choosing a career in STEM. This is because the number of women attending college has increased much faster than that of men; for example, in the U.S. the percentage of women enrolling in college increased from 42% in 1970 to 56% in 2000

In summary, there are two distinct sex differences in scholastic performance that affect very different segments of the population. On the one hand, boys score lower in reading, in particular at the low end of the reading performance continuum. On the other hand, girls score lower in mathematics at the high end of the mathematics performance continuum. It is important to realize that the latter phenomenon continues to exist, despite the educational gains of women in economically developed countries, and the increased participation of women in higher education in general can easily give the false impression that we are getting closer to the end of the sex difference in mathematics. Our data show that it is important to consider the two types of sex differences separately. On the one hand, if policy makers and educators wish to reduce these sex differences in performance, they need to focus on the higher-achieving girls, and they need to look beyond traditional equality issues and invest in research in how other factors, such as interest differences contribute to the sex differences in performance. Further, the relatively ignored situation for reading and boys seems entirely different. Sex differences in reading are not only persistent and growing, they are particularly large for the most vulnerable boys at the bottom of the reading performance continuum. Addressing this situation will likely require a very different approach than that needed to reduce sex differences in mathematics performance.

The Programme for International Student Assessment (PISA) conducted four separate assessments (in 2000, 2003, 2006, and 2009). All PISA data, guidance for data analysis, and reports are freely available from

The number of countries contributing to the PISA data sets include both OECD and OECD-partner countries. The number of participating countries/regions (e.g., Hong Kong) has increased to 74 in 2009 (

PISA selects a representative sample of schools and students from each participating country. Each student’s scores in the different domains (mathematics, reading, science) are scaled such that the average of students in OECD countries is 500 points and the standard deviation is 100 points. The exact details of how average country scores are calculated is not relevant for understanding the current analyses. We would like to point out that PISA gives detailed guidance on how to perform data analyses

Sex differences in mathematics performance are calculated by subtracting the boys’ and girls’ scores (

In order to calculate whether or not a sex difference within a country is statistically significant (

We downloaded the human development and equality indicators (

Most of these variables are not normally distributed; only the GEM and GGGI are not significantly different from the normal distribution (as tested with the Shapiro Wilks test of normality). For correlational analyses (

We used the PSPP (

The curves in

(TIFF)

Total scores and sex differences in mathematics and reading by country and assessment year. For each country and each assessment, the average scores of boys and girls are listed (Total). For sex differences (abbreviated as “Diff”) in mathematics, a negative number indicates girls outperformed boys. For sex differences in reading, all numbers are positive (i.e., girls always outperformed boys). If a difference is in

(DOC)

Sex difference in mathematics in all participating countries. The first set of scores compares boys and girls at the same points on the gender-specific achievement distributions. Comparing the bottom 5% of boys (relative to all other boys) to the bottom 5% of girls (relative to all other girls), the difference in mathematics achievement ranges from a 1.1 point advantage for girls (2003) to a 1.1 point advantage for boys (2006). The second set of scores is the ratio of boys to girls at various percentiles of overall (including both genders) achievement.

(DOC)

Sex difference in reading in all participating countries. The first set of scores compares boys and girls at the same points on the gender-specific achievement distributions. Comparing the bottom 5% of boys (relative to all other boys) to the bottom 5% of girls (relative to all other girls), the advantage of girls ranges from 40.8 points (2000) to 50.3 points (2009). The second set of scores is the ratio of boys to girls at various percentiles of overall (including both genders) achievement.

(DOC)

Correlations between mathematics (top) and reading scores (bottom) and human development and equality indicators. HDI: Human Development Index. GII = Gender Inequality Index. GDI = Gender Development Index. GEM = Gender Empowerment Measure. GGGI = Global Gender sex difference Index. Gini = Gini coeffient. Stars indicate significance level: *

(DOC)

Sample sizes for participating countries and economic regions.

(DOC)

Human development and gender equality scores. HDI: Human Development Index. GII = Gender Inequality Index. GDI = Gender Development Index. GEM = Gender Empowerment Measure. GGGI = Global Gender Gap Index. Gini = Gini coeffient. We correlated the magnitude of the sex differences in mathematics and reading for each year with each of these variables to determine if a consistent pattern of correlation emerged (i.e., the sex differences in mathematics in each PISA assessment correlates with the variable). No such pattern was found (

(DOC)

This work was undertaken using the Advanced Research Computing facilities at The University of Leeds. We thank Dr. Stephen Westerman and the anonymous reviewers for comments on an earlier draft.