Mathematics Achievement in Grades 8 and 9
Exhibit 1.2.1a presents the estimated growth in students’ mathematics achievement between the eighth and ninth grade for the three participating countries.¹ The numerical results tab displays each country’s average achievement at each grade, along with a growth estimate and its standard error (in parentheses). The graphical results tab shows the distribution of changes in achievement scores, including percentiles, and provides confidence intervals² for average growth.
On average, students in all countries showed growth in mathematics achievement between Grades 8 and 9. The interactive exhibit can be sorted by different criteria. When sorted by the magnitude of growth, the exhibit highlights Jordan as having the most substantial growth (+17 scale score points), followed by Sweden (+12 scale score points), and Korea (+8 scale score points).
Note that the estimates of average growth are provided with a margin of error, given in the form of a standard error for each country. For example, Jordan’s estimated growth of 17 points has a 95% confidence interval ranging from 11 to 23 points (17 plus and minus twice the standard error of 3.1, rounded). Besides the standard error, the percentiles of the change distribution are also informative.
It is helpful to relate the estimates of average growth to how progression from lower to higher achievement is described in TIMSS: the TIMSS International Benchmarks are located 75 points apart along the achievement scale (Advanced at 625, High at 550, Intermediate at 475, Low at 400), and the estimated average growth in Jordan is nearly one-fourth of a benchmark, or one-half of a benchmark when extrapolating this to two years of schooling. This magnitude of growth suggests that more students will meet the International Benchmarks over time as they continue to grow at this rate.
The graphical results tab of the exhibit provides a more comprehensive look at patterns in growth within and across countries. The variation in standard deviations between grades and countries, in interquartile ranges, and in the 5th–95th percentile difference in the growth distribution, all indicate that substantial variability in achievement growth exists both between and within countries. Thus, while one country’s average growth may exceed another’s, all three countries include students with varying growth trajectories between the two years. Overall fewer students showed a decline in achievement, while most students showed a gain, and some showed very little change. For instance, despite relatively lower overall growth in Sweden and Korea (+12 or 8 scale score points, respectively), some students in these countries demonstrated substantial growth in their mathematics scores and outpaced those who showed low or no growth, such as students in Jordan, where students showed higher growth on average. However, as can be inferred from the 95% confidence intervals shown in the graph, the average growth estimate in all three countries is statistically significantly³ different from zero at the 5% error level.
Exhibit 1.2.1b complements Exhibit 1.2.1a and presents the average mathematics achievement results for the three TIMSS 2023 Longitudinal countries in both assessment years: from Grade 8 (2023) to Grade 9 (2024). For each country and grade, the numerical results tab reports the average scale score, accompanied by its standard error in parentheses, the 95% confidence interval for the average achievement, and the standard deviation of student scores, along with its standard error. As noted above, all countries show gains in average mathematics achievement between the two years. However, higher average achievement in Grade 8 did not translate into larger growth in achievement between the two assessment years. Korea had the highest average mathematics achievement at both grades (596 in Grade 8 and 604 in Grade 9) and showed the least average growth. In contrast, Jordan had the lowest average achievement at both grades (388 in Grade 8 and 405 in Grade 9) and showed the largest average growth among the three countries.
The exhibit also provides information about within-country score variability. It shows that standard deviations increased somewhat from Grade 8 to Grade 9 in some countries— as can be seen with Sweden (an increase from 83 to 92) and Korea (an increase from 98 to 101). This suggests that achievement distributions within some countries widen over time.
¹See the TIMSS 2023 International Results for more information about the mathematics assessment. ²One can think of a confidence interval as a “net” we cast to catch the true average of a whole population. A 95% confidence interval means that if we were to repeat our study 100 times, the nets casted from those 100 studies would catch the true average about 95 times. It doesn’t mean there’s a 95% chance our specific net caught the true value—it either did or it didn’t. Any specific 95% confidence interval is one such application of a method that works 95% of the time. ³ Statistical significance means nothing more than that the difference found is big enough that we only expect to see it by random chance less than 5% of the time if there was truly no difference. It’s surprising enough for us to look closer but does not imply practical significance. Also, in very large studies, such as TIMSS where many students take the test, there is reason to be cautious. One can occasionally find very small differences that are technically statistically significant but are so small they don’t actually matter much in terms of real world effects (e.g., Berkson, J. (1938)).
