Mathematics Achievement in Grades 4 and 5
Exhibit 1.1.1a presents the estimated growth in students’ mathematics achievement between the fourth and fifth grade for the nine 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 associated with average growth.
On average, students in all countries showed growth in mathematics achievement between Grades 4 and 5. The interactive exhibit can be sorted according to different criteria. When sorted by magnitude of growth, the exhibit highlights Slovenia (growth of +42 scale score points), Korea (+40 scale score points), and Italy (+38 scale score points) as having the most substantial average achievement gains between the two years.
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, the 95% confidence interval for Korea’s estimated average growth of 40 points ranges from about 37 to 43 points (40 plus and minus twice the standard error of 1.6, rounded). Besides the standard error, the percentiles of the change distribution are also informative. Across countries, the distribution of change scores widens as the average growth decreases, meaning that countries with higher average growth tend to have, on average, smaller differences among students in terms of how much they learn. In countries with, on average, smaller growth, there are some students who show a much higher test score in 2024 compared to 2023, while some other students show much lower test scores in 2024 compared to 2023.
It is helpful to relate the estimates of average growth to how progressions from lower to higher achievement are 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 the four countries with highest growth between Grade 4 and 5 equates to an average student advancing more than half a benchmark, which is a substantial amount. See the TIMSS 2023 International Results for further details about the benchmarks.
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 nine countries include students with varying growth trajectories between the two years— overall fewer students showed a decline in observed achievement, most students showed a gain in achievement, and some showed very little change in achievement. For instance, while Jordan and North Macedonia showed the lowest average growth in mathematics achievement (+12 or 15 scale score points, respectively), some students within these two countries showed substantial growth in their mathematics scores and likely outpaced students who showed low or no growth in, on average, higher-growth nations.
Exhibit 1.1.1b complements Exhibit 1.1.1a and presents average mathematics achievement results for the nine TIMSS 2023 Longitudinal countries in both assessment years: from Grade 4 (2023) to Grade 5 (2024). For each country and grade, the numerical results tab shows the average scale score, accompanied by its standard error in parentheses, the 95% confidence interval for average mathematics achievement, and the standard deviation of student scores with its standard error. As noted above, all countries show gains in average mathematics achievement between the two years. The 95% confidence intervals for average achievement in each year do not overlap in eight of nine countries (the exception is Jordan), indicating statistical significance³ at the 5% level for the growth in these eight countries.
The exhibit also provides information about within-country score variability and shows that standard deviations generally increased from Grade 4 to Grade 5 — sometimes only 2 points or less, for example in Korea, Slovenia, and Sweden, while larger increases can be seen with North Macedonia (an increase from 86 to 94) and Kosovo (an increase from 79 to 87). This suggests that the achievement distributions within some countries widens considerably 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. ³Statistical 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)).
