Average Mathematics Achievement and Scale Score Distributions
The TIMSS 2023 fourth-grade mathematics assessment was delivered fully digitally and was based on a comprehensive assessment framework developed collaboratively with the participating countries to reflect their curricular goals. The fourth-grade mathematics assessment included three content areas—number, together with introductory algebraic concepts (50%); measurement and geometry (30%); and data (20%). The framework prescribed that the mathematics items assessed fourth-grade students in the three cognitive domains knowing, applying, and reasoning. To cover the framework at the fourth grade, the assessment comprised 187 items distributed across 14 item blocks with an average of 13 items per block.
The 2023 cycle marked the full transition to a computer-based assessment system, incorporating an adaptive booklet rotation to balance the proportion of more and less difficult booklets for countries with very high or very low expected average achievement. The 2023 assessment was carefully designed using a balanced incomplete block design, adhering to industry standards, and analyzed with state-of-the-art psychometric models. Consequently, the TIMSS 2023 mathematics achievement results for all 58 countries and 5 benchmarking participants are reported on the same TIMSS fourth-grade mathematics scale. The TIMSS fourth-grade mathematics achievement scale was established in TIMSS 1995, based on the combined distribution of achievement data across all participating countries, treating each country equally. A centerpoint of 500 was set to correspond to the mean of overall achievement in 1995, with 100 points set to correspond to the standard deviation. Students’ achievement is placed on the scale with each subsequent TIMSS cycle, most recently for TIMSS 2023.
Exhibit 1.1.1 reports the average mathematics achievement estimates at the fourth grade for each of the 58 TIMSS 2023 participating countries and the 5 benchmarking entities. The exhibit also presents the corresponding confidence intervals, and standard deviations for each country, together with the associated standard errors for these estimates (given in parentheses). Additionally, it includes a visualization of the score distribution, illustrating percentiles of the distribution and the confidence interval of the average achievement. The exhibit includes an international average estimate of the mean and confidence interval based on the 58 countries that participated in TIMSS 2023, with each country contributing equally. The standard error of this estimate reflects the variance of this international average based on these countries.
The exhibit is interactive and can be sorted by different criteria, with average achievement used as the default. Sorted by average achievement, the exhibit shows that the countries with the highest estimated average achievement are Singapore, Chinese Taipei, Korea, Hong Kong SAR, and Japan. That is, among the highest-ranking countries are participating countries from East Asia – as in previous TIMSS cycles. For example, the estimated average achievement in Korea is 594 and the 95% confidence interval ranges from 589 to 600. The confidence interval provides a score range around the estimated mean that illustrates the uncertainty in this estimate, which is based on a sample of students in a selection or subset of classrooms within a sample of schools in each country. Intervals constructed in this way around the estimated average have a 95% chance to include the true average of the country’s achievement.
Notably, there is considerable variability in achievement not only across participants, but also within each country, as indicated by the standard deviation, the interquartile range, and the difference between the 10th and 90th percentiles of the achievement distribution shown in the table. Therefore, it would be incorrect to assume that (all) students in any country achieve higher scores than students in another country. While the average achievement of one country may be considerably higher than the average achievement in another country, each country has some lower-achieving students and some higher-achieving students.
While examining the average achievement across countries can provide an initial summative impression of achievement in participating countries, the data collected by TIMSS 2023 and reported here is much more comprehensive. TIMSS also provides results about the range of achievement observed in each country, and in later sections about associations with contextual factors, which provide a deeper understanding of student performance relative to student background.
