To learn about TIMSS 2019 achievement results in mathematics and science at the fourth and eighth grades, navigate using the TIMSS 2019 International Results in Mathematics and Science menu, or click an image below.

### Mathematics Grade 4

#### Average Achievement and Scale Score Distributions

The TIMSS 2019 fourth grade mathematics assessment 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, which included prealgebra (50%); measurement and geometry (30%); and data (20%). In accordance with the framework, the majority of TIMSS 2019 mathematics items assessed fourth grade students’ applying and reasoning skills. To cover the framework at the fourth grade, the TIMSS 2019 mathematics assessment comprised 175 assessment items.

This cycle marked the beginning of the transition to a computer-based assessment system. More than half of the TIMSS 2019 countries administered the assessment in an “e” (electronic) format and almost half administered the assessment in a paper format, as in TIMSS 2015. The “e” countries also administered the trend items in the paper format to provide a bridge to the TIMSS 2015 and TIMSS 2019 paper-based assessments. At the fourth grade, the paper-based assessment also was available in a less difficult version, with some items being less difficult, and the rest of the items in common with the regular version. Some countries opted to administer the less difficult TIMSS mathematics assessment at fourth grade in order to better measure student achievement of their student populations. The assessment was carefully designed and analyzed, so that the TIMSS 2019 mathematics achievement results for all 58 countries are reported on the same TIMSS fourth grade mathematics scale.

Exhibit 1.1 presents the average achievement at the fourth grade for each participating country (from highest to lowest) together with the scale score distribution underlying the average scale score. Exhibit 1.2 shows whether relatively small differences in average achievement between one country and the next are statistically significant.

The five East Asian countries had the highest average achievement, with Singapore having higher average achievement than all of the other TIMSS 2019 countries. Singapore was followed by Hong Kong SAR, Korea, and Chinese Taipei, whose students had similar average achievement that was higher than all the rest of the countries except Singapore. Fourth grade students in Japan had higher achievement than students in all of the other countries except the other four East Asian countries. In turn, the Russian Federation and Northern Ireland, which performed similarly, had higher achievement than all of the other remaining countries. England and Ireland, and then Latvia, Norway (fifth grade), and Lithuania also performed very well. Essentially, Exhibit 1.2 shows clusters of several similarly performing countries, followed by the next highest achieving clusters of similarly performing countries, and so on.

A number of fourth grade TIMSS 2019 participating countries performed well. Thirty-six countries (including those discussed above) had higher average achievement than the centerpoint of 500 (Exhibit 1.1), which is a point of reference on the TIMSS fourth grade mathematics scale that remains constant from TIMSS assessment to TIMSS assessment. However, there was a considerable difference between the highest average achievement and the lowest. Also, the scale score distributions show that there is wide variation in achievement in every country. Every TIMSS 2019 country has some higher achieving and some lower achieving students.

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#### Trends in Average Achievement

Exhibit 1.3 graphs the differences in average mathematics achievement between assessment cycles for TIMSS 2019 countries that have comparable data from previous assessments, while Exhibit 1.4 provides more detail. The countries are presented in alphabetical order in both exhibits. The trends in mathematics achievement at the fourth grade signal more improvements than downturns across the assessment cycles internationally. However, since 1995, most countries have had some periods of increases and decreases in average achievement as well as periods of stability.

Most recently, for the 45 countries that participated in both TIMSS 2015 and 2019, 14 had increases in average achievement, and 8 had declines. The trends in average achievement between 2007 and 2019, as well as between 1995 and 2019, show considerably more progress than declines in average mathematics achievement at the fourth grade over the long term. In 2019, compared with 2007, the 21 countries in both assessments had 14 increases and no decreases. In 2019, compared with 1995, the 16 countries in both assessments had 13 increases and 1 decrease.

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#### Average Achievement by Gender

Exhibit 1.5 shows the differences in average mathematics achievement between girls and boys. In TIMSS 2019, fourth grade boys had higher average achievement than girls in close to half of the 58 participating countries. More specifically, girls had higher average achievement than boys in 4 countries, there was gender equity in average mathematics achievement in 27 countries, and boys had higher average achievement than girls in 27 countries (although the differences were small).

### Mathematics Grade 4

#### Trends in Average Achievement by Gender

For the TIMSS 2019 countries with comparable data from previous TIMSS assessments, Exhibit 1.6 contains graphs of average mathematics achievement across assessments by gender. The countries are presented in alphabetical order. The difference in average mathematics achievement between boys and girls has remained relatively stable in most countries, with any overall increases or decreases in achievement from assessment to assessment occurring similarly for both girls and boys. However, a number of countries with no gender gap in TIMSS 2015 had a gap favoring boys in TIMSS 2019, including Chile, Georgia, Germany, Hungary, Poland, the Russian Federation, Singapore, Sweden, and the United Arab Emirates. On a more positive note, the gender gap in average achievement favoring boys in TIMSS 2015 was closed in Chinese Taipei, England, and Hong Kong SAR, while the gap favoring girls was closed in Bahrain, Finland, and Kuwait.

### Mathematics Grade 4

#### TIMSS 2019 International Benchmarks

To provide an interpretation of the results on the TIMSS fourth grade mathematics achievement scale in relation to the students’ performance on the assessment items, TIMSS describes achievement at four points along the scale as International Benchmarks: Advanced International Benchmark (625), High International Benchmark (550), Intermediate International Benchmark (475), and Low International Benchmark (400). The descriptions of mathematics achievement at the International Benchmarks were updated from TIMSS 2015 based on an analysis of the items that students with average achievement at each of the benchmarks answered successfully in TIMSS 2019.

Exhibit 1.7 summarizes what fourth grade students who reached each of the TIMSS International Benchmarks in 2019 could do in mathematics. The progression in mathematics achievement is evident from benchmark to benchmark, from demonstrating basic mathematics knowledge at the Low International Benchmark to applying and justifying their mathematical understanding at the Advanced International Benchmark. As much as possible, each description references achievement in the three content areas covered in the assessment at the fourth grade: number, measurement and geometry, and data. The following tables show the target percentages for the content and cognitive domains.

The interactive map of the benchmark descriptions links to example items. It provides an overview of the mathematics understanding demonstrated by the fourth grade students who performed at the four different levels on the achievement scale. The following sections provide more information about students’ achievement in TIMSS 2019 at each International Benchmark as well as more detailed descriptions of each level together with example items.

+ Read MoreINTERNATIONAL BENCHMARKS | EXAMPLE ITEMS |

### Mathematics Grade 4

#### Percentages of Students Reaching International Benchmarks

Exhibit 1.8 presents the percentages of students reaching each TIMSS 2019 International Benchmark. The results are presented in descending order according to the percentage of students reaching the Advanced International Benchmark, which is indicated on the graph with black dots. Because students who reached the Advanced Benchmark also reached the other benchmarks, the percentages illustrated in the exhibit and shown in the columns to the right are cumulative. The five highest-performing East Asian countries had the highest percentages of students reaching the Advanced International Benchmark. More than half of the fourth grade students reached the Advanced International Benchmark in Singapore (54%), and one-third or more did so in Hong Kong SAR (38%), Korea (37%), Chinese Taipei (37%), and Japan (33%). Northern Ireland had about one-fourth (26%) of its students reaching the Advanced International Benchmark, and England and the Russian Federation had about one-fifth (21% and 20%, respectively).

Most countries had fewer than 10 percent of their fourth grade students performing at the Advanced level. As a point of reference, Exhibit 1.8 provides the international median percentage of students reaching each benchmark at the bottom of the four right-hand columns. By definition, half the countries have a percentage in that column above the median and half below the median. The median percentages of students reaching the International Benchmarks were as follows: Advanced—7 percent, High—34 percent, Intermediate—71 percent, and Low—92 percent. Many TIMSS 2019 countries had more than 90 percent of their fourth grade students reaching the Low Benchmark, which can be considered a level of minimum proficiency internationally. In 6 countries, essentially all the students reached this benchmark—100 percent in Hong Kong SAR and Chinese Taipei, and 99 percent in Singapore, Korea, Japan, and the Russian Federation.

Not only are the East Asian countries and the Russian Federation educating high percentages of their students to an advanced level, they are educating all of their students to a level of minimal proficiency.

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#### Trends in Percentages of Students Reaching International Benchmarks

Exhibit 1.9 shows the changes in percentages of students reaching the benchmarks for countries that have comparable data from previous assessments. The short-term trends show about the same numbers of increases and decreases, with a few more decreases in the midrange of the scale. Of the 45 countries that participated in both 2015 and 2019, 8 increased and 7 decreased at the Advanced International Benchmark, 9 increased and 9 decreased at the High Benchmark, 8 increased and 9 decreased at the Intermediate Benchmark, and 9 increased and 6 decreased at the Low Benchmark.

In contrast, the longer-term trends show considerable improvement across the percentages of students reaching all four of the benchmarks. Between 2007 and 2019, the 21 countries participating in those two assessments had 11 increases and no decreases at the Advanced level, 13 increases and no decreases at the High level, 14 increases and 2 decreases at the Intermediate level, and 12 increases and 1 decrease at the Low level. Between 1995 and 2019, the 16 countries participating in those two assessments had 12 increases and 2 decreases at the Advanced level, 12 increases and 1 decrease at the High level, and 11 increases with no decreases at both the Intermediate and Low levels.

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#### Low Benchmark: Full Description and Example Items

Exhibit 1.10 presents the description of fourth grade students’ achievement at the Low International Benchmark. Essentially, students demonstrated some basic understanding in each of the content domains: number, measurement and geometry, and data.

Exhibit 1.10.1 shows an example item from the data content domain. Students could read the numbers in the table and use the data to draw two bars on the graph. Nearly all the students in a number of countries completed this task successfully. The international average across countries was 81 percent.

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#### Intermediate Benchmark: Full Description and Example Items

Exhibit 1.11 provides the description of student achievement at the Intermediate International Benchmark. At this level, students could apply their mathematics understanding in a variety of simple situations.

Example 1.11.1 presents an item from the measurement and geometry domain. Students reaching the Intermediate level could complete the symmetrical figure. Ninety-seven percent of the Singaporean fourth grade students could do this task, and the international average was 70 percent.

Example 1.11.2 presents an item from the data domain. High percentages of fourth grade students in a number of countries were able to read data from the line graph. The international average was 68 percent.

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#### High Benchmark: Full Description and Example Items

Exhibit 1.12 presents the description of achievement at the High International Benchmark. Fourth grade students reaching this level demonstrated proficiency with a variety of topics in the framework.

Exhibit 1.12.1 provides an example from the number domain. Fifty-three percent of the fourth grade students, on average, were able to identify the expression that represented how to calculate the amount of water in the tank. With 79 percent correct, Japan and Singapore had the highest percentages of students answering this item correctly.

Exhibit 1.12.2 provides another example from the number domain. In this item, students were asked to solve a word problem involving fractions. Students in the five high-performing East Asian countries and students in Finland were the most successful—more than 75 percent correct. The international average was 47 percent.

Exhibit 1.12.3 shows an example from the data domain. Two-thirds or more of the fourth grade students in a number of countries were able to complete a pictograph, with 61 percent correct, on average.

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#### Advanced Benchmark: Full Description and Example Items

Exhibit 1.13 presents the description of fourth grade performance at the Advanced International Benchmark. Students reaching the Advanced level demonstrated a solid conceptual understanding of many of the topics in the framework.

Exhibit 1.13.1 shows a multi-part item from the number content domain that required reasoning with odd numbers and multiples. To receive full credit (2 points), students needed to provide two different correct answers. This item was very difficult, with an international average of 24 percent of students receiving full credit. More than half of the Singaporean fourth grade students (55%) received full credit.

Exhibit 1.13.2 shows a multi-part item from the measurement and geometry domain. Students were required to cover the area of a square with three different two-dimensional shapes to receive full credit (2 points). On average, only 21 percent of students received full credit. More than half the fourth grade students received full credit in Korea and Hong Kong SAR (53–54%).

Exhibit 1.13.3 shows another multi-part item from the measurement and geometry domain. Students were asked to visualize the number of faces making up three different three-dimensional shapes. On average, 27 percent of students received full credit.

The last example item illustrating the Advanced benchmark asked students to label the *y*-axis of a bar graph based on tabular data (Exhibit 1.13.4). Internationally, on average, about one-third of the fourth grade students (34%) were able to accomplish this task. Eighty percent or more answered correctly in Japan, Korea, and Hong Kong SAR.

### Mathematics Grade 4

#### TIMSS 2019 Mathematics Content and Cognitive Domains

TIMSS 2019 assessed three content areas in mathematics at the fourth grade: number, measurement and geometry, and data.

Fifty percent of the fourth grade assessment was devoted to the number content domain apportioned as follows: whole numbers (25%); expressions, simple equations, and relationships (15%); and fractions and decimals (10%). The predominant component of the number domain involved computation of whole numbers. The prealgebra concepts included the concept of variables (unknowns) in simple equations, and initial understandings of relationships between quantities. Students were asked to compare, add, and subtract familiar fractions and decimals to solve problems.

Thirty percent of the assessment was devoted to measurement and geometry (15% each). Measurement included using a ruler to measure length, calculating areas and perimeters of simple polygons, and using cubes to determine volumes as well as identifying the properties and characteristics of lines, angles, and a variety of two- and three-dimensional shapes. Geometry included describing and drawing a variety of geometric figures as well as using geometric relationships to solve problems.

The remaining 20 percent of the assessment was devoted to the data content domain, which consisted of two topic areas: reading, interpreting, and representing data (15%) and using data to solve problems (5%). Students were asked to read and recognize various forms of data displays; to collect, organize, and represent the data in graphs and charts to address a simple question; and to use data from one or more sources to solve problems.

Fourth grade students also needed to draw on a range of cognitive skills across the content domains described above. The cognitive skills were categorized into three broad domains—knowing, applying, and reasoning. Forty percent of the fourth grade assessment was devoted to the knowing cognitive domain, 40 percent to applying, and 20 percent to reasoning. The knowing domain covers the facts, concepts, and procedures students need to know, while the applying domain focuses on students’ ability to apply knowledge and conceptual understanding to solve problems or answer questions. The reasoning domain goes beyond the solution of familiar problems that may have been routinely practiced in mathematics lessons to encompass unfamiliar situations, complex contexts, and multistep problems.

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#### Average Achievement in Content Domains

Exhibit 1.14 shows countries’ average mathematics achievement in each of the three content domains relative to their overall average achievement (presented from highest to lowest overall average achievement). Based on countries’ relative strengths and weaknesses, the TIMSS 2019 countries appear to be placing relatively more instructional emphasis on the number content domain and much less on the data content domain. Of the 55 participating countries for which content domain scores were estimated, 27 had a relative strength in number and 17 had a relative weakness; 19 had a relative strength in measurement and geometry and 23 had a relative weakness, and 11 had a relative strength in data and 33 had a relative weakness. Almost all countries had at least one relative strength or relative weakness compared with their overall achievement, except Albania.

### Mathematics Grade 4

#### Trends in Average Achievement in Content Domains

Exhibit 1.15 presents trends in average achievement for the three mathematics content domains assessed by TIMSS 2019 at the fourth grade—number, measurement and geometry, and data. Of the 55 TIMSS 2019 countries with mathematics content domain scores, 42 also participated in TIMSS 2015 and have comparable data for the two assessment cycles. In each of the three content areas, about just over half the countries showed no or little change in average achievement. For the countries that did have changes, there were similar numbers of increases and decreases: in the number content area, 11 showed improvement and 7 declined; in measurement and geometry, 13 showed improvement and 9 declined; and in data, 10 showed improvement and 7 declined.

In comparison, the longer term trends showed many more improvements than declines. TIMSS began providing scaled results in the content domains in 2007, with 21 countries having trends between 2007 and 2019. Compared with 2007, these countries showed considerable improvement in TIMSS 2019 across the content domains—14 had higher average achievement in number, 12 in measurement and geometry, and 12 in data. One country had lower achievement in number compared with 2007, 3 countries had lower average achievement in measurement and geometry and 2 had lower achievement in data.

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#### Average Achievement in Content Domains by Gender

Exhibit 1.16 shows the differences in average achievement between boys and girls in the three mathematics content domains. The differences in average achievement between girls and boys in all three content areas largely reflected the overall TIMSS 2019 results, where boys had higher achievement than girls in close to half the countries (27 out of 55). In the number content domain, girls had higher average achievement than boys in 3 countries, and boys had higher average achievement in 25 countries. In measurement and geometry, girls had higher average achievement than boys in 3 countries, and boys had higher average achievement in 26 countries. In data, girls had higher average achievement than boys in 8 countries, and boys had higher average achievement in 11 countries.

### Mathematics Grade 4

#### Average Achievement in Cognitive Domains

Exhibit 1.17 shows countries’ average achievement in the knowing, applying, and reasoning cognitive domains relative to their overall average achievement (from highest to lowest overall average achievement). Interestingly, few countries had a relative strength in the knowing cognitive domain, especially compared with the applying domain. Nine countries had a relative strength in the knowing cognitive domain, and 25 had a relative weakness. Twenty-four countries had a relative strength in the applying cognitive domain, and 10 had a relative weakness. Seventeen countries had a relative strength in the reasoning cognitive domain, and 28 had a relative weakness. Hungary, Croatia, and Malta were the only countries with no relative strengths or weaknesses in the cognitive domains.

### Mathematics Grade 4

#### Trends in Average Achievement in Cognitive Domains

Exhibit 1.18 presents differences in average achievement for the three cognitive domains across four assessment cycles back to 2007, when TIMSS first began providing scaled results in the cognitive domains. Forty-three countries participated in both the TIMSS 2015 and TIMSS 2019 assessments and have comparable cognitive domain scores for the two assessment cycles. The recent trends in the knowing cognitive domain showed increases in 7 countries and decreases in 9 countries. In the applying domain, 12 countries showed increases and 10 decreases. In the reasoning domain, 6 showed increases and 8 decreases.

Between 2007 and 2019 there were more differences in average achievement in the cognitive domains than there were in short-term—almost all of them positive. In the knowing and applying domains, 14 countries had higher average achievement in 2019 than 2007 and 13 had higher average achievement in the reasoning domain. Two countries had lower average achievement in the knowing domain, only 1 country had lower average achievement in the applying domain, and none had lower average achievement in the reasoning domain.

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#### Average Achievement in Cognitive Domains by Gender

Exhibit 1.19 shows the differences between girls’ and boys’ average achievement in the cognitive domains of knowing, applying, and reasoning. Reflecting the higher average achievement overall for boys in 27 of the 56 TIMSS 2019 countries for which cognitive domain scores were estimated, boys also had higher average achievement than girls in many countries in the cognitive domains—31 countries in the knowing domain, 15 in the applying domain, and 28 in the reasoning domain. Girls had higher average achievement than boys in all three domains in the same 3 countries—Oman, the Philippines and South Africa (fifth grade).

### Science Grade 4

#### Average Achievement and Scale Score Distributions

The TIMSS 2019 fourth grade science assessment was based on a comprehensive assessment framework developed collaboratively with the participating countries to reflect their curricular goals. The fourth grade science assessment included three content areas—life science, physical science, and Earth science. In accordance with the framework, the majority of the TIMSS 2019 science items assessed students’ applying and reasoning skills. To cover the framework at the fourth grade, the TIMSS 2019 science assessment comprised 175 assessment items.

This cycle marked the beginning of the transition to a computer-based assessment system. More than half of the TIMSS 2019 countries administered the assessment in an “e” (electronic) format and almost half administered the assessment in a paper format, as in TIMSS 2015. The “e” countries also administered the trend items in the paper format to provide a bridge to the TIMSS 2015 and TIMSS 2019 paper-based assessments. The assessment was carefully designed and analyzed, so that the TIMSS 2019 science achievement results for all 58 countries are reported on the same TIMSS fourth grade science scale.

Exhibit 2.1 presents the average achievement at the fourth grade for each participating country (from highest to lowest) together with the scale score distribution underlying the scale score average. Exhibit 2.2 shows whether relatively small differences in average achievement between one country and the next are statistically significant.

Singapore and Korea performed similarly and had higher average achievement than all of the other countries, followed by the Russian Federation and Japan, whose students had similar achievement. However, the Russian Federation’s performance was higher than all the remaining countries, while Japan performed higher than all the remaining countries except Chinese Taipei. Next, fourth grade students in Chinese Taipei performed similarly to students in Japan and Finland and had higher achievement than students in all of the other countries except the four top performing countries and Finland. In turn, Finland performed similarly to Chinese Taipei and had higher achievement than all of the other remaining countries. Latvia, Norway (fifth grade), the United States, Lithuania, Sweden, and England also performed very well. Essentially, Exhibit 2.2 shows clusters of several similarly performing countries, followed by the next highest achieving clusters of similarly performing countries, and so on.

A number of fourth grade TIMSS 2019 participants performed well. Thirty-two countries (including those discussed above) had higher average achievement than the centerpoint of 500 (Exhibit 2.1), which is a point of reference on the TIMSS fourth grade science scale that remains constant from TIMSS assessment to TIMSS assessment. However, although there was little difference between countries from one to the next, there was a considerable difference between the highest average achievement and the lowest. Also, the scale score distributions show that there is wide variation in achievement in every country. Every country has some higher achieving and some lower achieving students.

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#### Trends in Average Achievement

Exhibit 2.3 graphs the differences in average science achievement between the assessments for TIMSS 2019 countries that have comparable data from previous assessments, while Exhibit 2.4 provides more detailed results. The countries are presented in alphabetical order in both exhibits. The trends in science achievement at the fourth grade signal more improvements than downturns across the assessment cycles internationally. However, since the inception of TIMSS in 1995, most countries have had some periods of increases and some of decreases in average achievement, as well as periods of stability.

Most recently, for the 44 countries that participated in both TIMSS 2015 and 2019, 10 had increases in average achievement and 10 had declines, but the majority stayed the same. As a midway point, 21 countries participated in both TIMSS 2007 and 2019, with 6 showing increases and 3 declines. For the 16 countries that participated in both 1995 and 2019, most showed improvement—11 with higher average achievement in 2019 and only 2 with lower average achievement.

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#### Average Achievement by Gender

Exhibit 2.5 shows the differences in average science achievement between girls and boys. In TIMSS 2019, fourth grade girls had higher average achievement than boys in 18 countries, there was gender equity in average science achievement in 33 countries, and boys had higher average achievement than girls in 7 countries.

### Science Grade 4

#### Trends in Achievement by Gender

For the TIMSS 2019 countries with comparable data from previous TIMSS assessments, Exhibit 2.6 contains graphs of average science achievement across assessments by gender. The countries are presented in alphabetical order. Most recently between 2015 and 2019, there were not a lot of changes, and the changes that did occur were varied. In Chinese Taipei, Hong Kong SAR, Portugal, Slovak Republic, and Spain, the gender gap favoring boys in 2015 closed in 2019. In Bulgaria, Finland, Sweden, and the United Arab Emirates, the gender gap favoring girls in 2015 closed in 2019. In Canada and Singapore, boys had higher average achievement than girls in 2019, whereas there was no gender gap in 2015. In Japan and Serbia, girls had higher achievement than boys in 2019, whereas that was not the situation in 2015.

### Science Grade 4

#### TIMSS 2019 International Benchmarks

To provide an interpretation of the results on the TIMSS fourth grade science achievement scale in relation to the students’ performance on the assessment items, TIMSS describes achievement at four points along the scale as International Benchmarks: Advanced International Benchmark (625), High International Benchmark (550), Intermediate International Benchmark (475), and Low International Benchmark (400). The descriptions of science achievement at the International Benchmarks were updated from TIMSS 2015 based on an analysis of the items that students with average achievement at each of the benchmarks answered successfully in TIMSS 2019.

Exhibit 2.7 summarizes what fourth grade students who reached each of the TIMSS International Benchmarks in 2019 could do in science. The progression in science achievement is evident from benchmark to benchmark, from showing limited knowledge of science facts at the Low International Benchmark to communicating their science understanding about a variety of topics in life science, physical science, and Earth science at the Advanced International Benchmark. As much as possible, each description references achievement in the three content areas covered in the assessment at the fourth grade, as well as science practices assessed by TIMSS. Science practices include skills from daily life and school studies that students use systematically to conduct scientific inquiry and investigation. The following tables show the target percentages for the content and cognitive domains.

The interactive map of the benchmark descriptions links to example items. It provides an overview of the science understanding demonstrated by the fourth grade students who performed at the four different levels on the achievement scale. The following sections provide more information about students’ achievement in TIMSS 2019 at each International Benchmark as well as more detailed descriptions of each level together with example items.

+ Read MoreINTERNATIONAL BENCHMARKS | EXAMPLE ITEMS |

### Science Grade 4

#### Percentages of Students Reaching International Benchmarks

Exhibit 2.8 presents the percentage of students reaching each TIMSS 2019 International Benchmark. The results are presented in descending order according to the percentage of students reaching the Advanced International Benchmark, which is indicated in the graph with black dots. Because students who reached the Advanced Benchmark also reached the other benchmarks, the percentages illustrated in the exhibit and shown in the columns to the right are cumulative. The two highest-performing countries had the highest percentages of students reaching the Advanced International Benchmark—38 percent in Singapore and 29 percent in Korea. The Russian Federation and Japan were next with 17–18 percent.

Most countries had fewer than 10 percent of their fourth grade students performing at the Advanced Benchmark. In general, more countries are having success in educating their fourth grade students to a minimal level of proficiency in science than to an advanced level. As a point of reference, Exhibit 2.8 provides the international median percentage of students reaching each benchmark at the bottom of the four right-hand columns. By definition, half the countries have a percentage in that column above the median and half below the median. The median percentages of students reaching the International Benchmarks were as follows: Advanced—6 percent, High—32 percent, Intermediate—71 percent, and Low—92 percent. Many TIMSS 2019 countries had more than 90 percent of their fourth grade students reaching the Low Benchmark, and in three countries—Korea, the Russian Federation, and Chinese Taipei—essentially all the students (99%) reached this benchmark.

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#### Trends in Percentages of Students Reaching International Benchmarks

Exhibit 2.9 shows the changes in percentages of students reaching the benchmarks for countries that have comparable data from previous assessments. Most recently, there were about as many decreases as increases at each level across the distribution. Of the 44 countries participating in both 2015 and 2019, 5 increased and 5 decreased at the Advanced International Benchmark, 8 increased and 7 decreased at the High Benchmark, 7 increased and 9 decreased at the Intermediate Benchmark, and 9 increased and 6 decreased at the Low Benchmark.

The recent trends from 2015 differ from previous assessments, when the countries made progress at all but the Advanced Benchmark. The pattern across the benchmarks between 2007 and 2019 shows decreases at the Advanced Benchmark but increases at the other three levels. Of the 21 countries that also participated in TIMSS 2007, 4 increased and 8 decreased at the Advanced International Benchmark, 7 increased and 4 decreased at the High Benchmark, 9 increased and 3 decreased at the Intermediate Benchmark, and 6 increased and only 1 decreased at the Low Benchmark. For the 16 countries with data for 1995 and 2019, although the Advanced International Benchmark had 7 increases and 5 decreases, there were substantial gains at the other three levels—High International Benchmark with 9 increases and 2 decreases, Intermediate International Benchmark with 11 increases and 2 decreases, and Low International Benchmark with 10 increases and 1 decrease.

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#### Low Benchmark: Full Description and Example Items

Exhibit 2.10 provides the description of fourth grade students’ achievement at the Low International Benchmark. Students demonstrated limited understanding of scientific concepts and limited knowledge of foundational science facts in life science, physical science, and Earth science.

Exhibit 2.10.1 shows an example item from the life science domain. On average, 74 percent of the students were able to recognize that the frog was the animal with a backbone. The top performing students on this item were in Hungary and Latvia with 88–89 percent correct.

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#### Intermediate Benchmark: Full Description and Example Items

Exhibit 2.11 provides the description of student achievement at the Intermediate International Benchmark. At this level, students showed knowledge and understanding of some aspects of science across the three content domains.

Exhibit 2.11.1 presents an item from the life science domain. It illustrates that students reaching the Intermediate Benchmark understood why plastic objects in the ocean are dangerous for sea animals. Sweden, Finland, and Norway (fifth grade) had best achievement on this item, 85–86 percent correct. The international average was 57 percent.

Exhibit 2.11.2 shows an item from the physical science domain. On average, internationally, 66 percent of fourth grade students recognized why wheels on a wagon make it easier to pull. Finland and Korea had the highest percentage correct—87–88 percent.

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#### High Benchmark: Full Description and Example Items

Exhibit 2.12 presents the description of achievement at the High International Benchmark. Fourth grade students reaching this level could communicate and apply knowledge about various topics in life science, physical science, and Earth science.

Exhibit 2.12.1 provides an example from the life science domain. When shown a picture of a desert, 45 percent of students, on average, identified two living things and two non-living things. Eighty-four percent of the Singaporean fourth grade students successfully completed this task.

Exhibit 2.12.2 shows an example from the physical science domain. On average, internationally, 64 percent of the fourth grade students recognized that a flashlight changed electrical energy into light energy. The highest achievement was posted by Chinese Taipei, Korea, and Hong Kong SAR—80–82 percent.

Exhibit 2.12.3 shows an example from the Earth science domain. Sixty-one percent of Finnish students could explain that the shape of the Moon changes during the month. The average across countries was 37 percent.

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#### Advanced Benchmark: Full Description and Example Items

Exhibit 2.13 presents the description of fourth grade performance at the Advanced International Benchmark. Students reaching the Advanced level could communicate their understanding of science concepts in the three content areas and demonstrate familiarity with the process of scientific inquiry.

Exhibit 2.13.1 shows an item from the life science domain that asks students to identify two competitors in a food web. Bulgaria was by far the highest achieving country, with 69 percent correct. The international average was 30 percent.

Exhibits 2.13.2 and 2.13.3 present a two-part item from the physical science domain about an experiment involving dissolving sugar in water. Part A asked students to recognize three situations that would dissolve the sugar faster—higher water temperature, stirring the water, and smaller sugar cubes. Latvia had the highest percentage correct—74 percent. The international average was 37 percent. Part B asked why the amount of water in each beaker had to be same. The international average was only 21 percent. However, 66 percent of the Singaporean fourth grade students provided the correct explanation.

Exhibit 2.13.4 shows the example from the Earth science domain. Students at the Advanced level demonstrated they understood that Earth’s seasons are related to the tilt of its axis and its orbit around the Sun. Chinese Taipei had the highest percentage correct (59%), and the international average was 36 percent.

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#### TIMSS 2019 Science Content and Cognitive Domains

TIMSS 2019 assessed three content areas in science at the fourth grade: life science, physical science, and Earth science.

Forty-five percent of the fourth grade science assessment was devoted to life science topics, including characteristics and life processes of organisms; life cycles, reproduction, and heredity; organisms, environment, and their interactions; ecosystems; and human health. Students were expected to have some knowledge about general characteristics of organisms, how they function, and how they interact with other organisms and with their environment, as well as to be familiar with fundamental science concepts related to life cycles, heredity, and human health.

The topic areas for the physical science content domain made up 35 percent of the assessment, including classification and properties of matter and changes in matter; forms of energy and energy transfer; and forces and motion. Students were asked about physical states of matter (solid, liquid, and gas), as well as common changes in the state and form of matter; common forms and sources of energy and their practical uses; and basic concepts about light, sound, electricity, and magnetism, as well as forces and motion.

The Earth science domain (20% of the assessment) included three topic areas: Earth’s physical characteristics, resources, and history; Earth’s weather and climates; and Earth in the Solar System. Students were asked about the structure and physical characteristics of Earth’s surface and about the use of Earth’s most important resources, and were asked to describe some of Earth’s processes in terms of observable changes and recognize the time frame over which such changes have occurred. They also were asked about Earth’s place in the Solar System based on observations of patterns of change on Earth and in the sky.

Fourth grade students also needed to draw on a range of cognitive skills across the content domains described above. The cognitive skills were categorized into three broad domains—knowing, applying, and reasoning. Forty percent of the fourth grade assessment was devoted to the knowing domain, 40 percent to applying, and 20 percent to reasoning. The knowing domain covers the facts, concepts, and procedures students need to know, while the applying domain focuses on students’ ability to apply knowledge and conceptual understanding to solve practical problems or answer questions. The reasoning domain goes beyond the solution of familiar problems to encompass unfamiliar situations, complex contexts, and multistep problems. Also, five science practices fundamental to scientific inquiry were assessed within the content areas and cognitive domains.

+ Read More### Science Grade 4

#### Average Achievement in Content Domains

Exhibit 2.14 shows countries’ average science achievement in each of the three content domains relative to their overall average achievement (presented from highest to lowest overall average achievement). Based on countries’ relative strengths and weaknesses, the TIMSS 2019 countries appear to be placing relatively less instructional emphasis on the Earth science content domain than the other two science content domains. Of the 53 participating countries with scores in the science content domains, 21 had a relative strength in life science and 13 had a relative weakness; 17 had a relative strength in physical science and 21 had a relative weakness, and 10 had a relative strength in Earth science, and 26 had a relative weakness. All countries except Austria had at least one relative strength or relative weakness compared with their overall achievement.

### Science Grade 4

#### Trends in Average Achievement in Content Domains

Exhibit 2.15 presents trends in average achievement for the three science content domains assessed by TIMSS 2019—life science, physical science, and Earth science. Of the 53 TIMSS 2019 countries for which science content domain scores were estimated, 42 had comparable data from TIMSS 2015, with each of three content areas showing no recent changes in average achievement for about half the countries. However, in the life science content area, 6 showed improvement and 12 declined; in physical science, 12 showed improvement and 9 declined; and in Earth science, 9 showed improvement and 6 declined.

TIMSS began providing scaled results in the content domains in 2007, with 21 countries having trends between 2007 and 2019. Compared with 2007, in TIMSS 2019 across the content domains in these countries, 7 had higher average achievement in life science and 6 had lower average achievement, 11 had higher average achievement in physical science and 2 had lower average achievement, and in Earth science, 7 had higher average achievement and 7 had lower average achievement.

+ Read More### Science Grade 4

#### Average Achievement in Content Domains by Gender

Exhibit 2.16 shows differences in average achievement between girls and boys in the three science content domains. The differences in average achievement between girls and boys are very different from content domain to content domain across the TIMSS 2019 countries, with girls having higher achievement in life science than boys in many countries, and boys having higher achievement in physical and Earth science. In the life science content domain, girls had higher average achievement than boys in 26 countries, and boys did not have higher average achievement in any country. In physical science, girls had higher average achievement than boys in 4 countries, and boys had higher average achievement in 13 countries. In Earth science, girls had higher average achievement than boys in 4 countries, and boys had higher average achievement in 16 countries.

### Science Grade 4

#### Average Achievement in Cognitive Domains

Exhibit 2.17 shows countries’ average achievement in the knowing, applying, and reasoning cognitive domains relative to their overall average achievement (from highest to lowest overall average achievement). Eighteen countries had a relative strength in the knowing cognitive domain and 11 had a relative weakness, only 9 countries had a relative strength in the applying cognitive domain and 22 had a relative weakness, and 17 had a relative strength in the reasoning cognitive domain, and 15 had a relative weakness. Five countries had no relative strengths or weaknesses in the cognitive domains: Croatia, Germany, Portugal, Malta, and Montenegro.

### Science Grade 4

#### Trends in Average Achievement in Cognitive Domains

Exhibit 2.18 presents differences in average achievement for the three cognitive domains across four assessment cycles back to 2007, when TIMSS first began providing scaled results in the cognitive domains. Forty-one countries for which cognitive domain scores were estimated participated in both the TIMSS 2015 and TIMSS 2019 assessments. The recent trends compared with 2015 in the knowing cognitive domain showed increases in 12 countries and decreases in 9 countries. In the applying domain, 8 countries showed increases and 12 showed decreases. In the reasoning domain, 9 showed increases, and 9 showed decreases. These recent increases in average achievement in the knowing cognitive domain together with the decreases in the applying domain may have contributed to more countries having a relative strength in knowing compared with applying in 2019.

Between 2007 and 2019, 6 countries had higher average achievement and 5 had lower average achievement in knowing; 6 had higher average achievement and 4 had lower average achievement in applying; and 7 had higher average achievement and 3 had lower average achievement in reasoning.

+ Read More### Science Grade 4

#### Average Achievement in Cognitive Domains by Gender

Exhibit 2.19 shows the differences between girls’ and boys’ average achievement in the cognitive domains of knowing, applying, and reasoning. Interestingly, boys had higher average achievement in more countries than girls in the knowing cognitive domain, but the situation was reversed in the applying and reasoning domains. In the knowing domain, girls had higher average achievement than boys in 3 countries, and boys had higher average achievement than girls in 16 countries. However, in the applying domain, girls had higher average achievement than boys in 12 countries compared with only 3 countries where boys had higher achievement than girls, and in the reasoning domain, girls had higher average achievement than boys in 16 countries compared with no countries with higher average achievement for boys.

### Mathematics Grade 8

#### Average Achievement and Scale Score Distributions

The TIMSS 2019 eighth grade mathematics assessment was based on a comprehensive assessment framework developed collaboratively with the participating countries to reflect their curricular goals. The eighth grade mathematics assessment included four content areas—number (30%), algebra (30%), geometry (20%), and data and probability (20%). In accordance with the framework, the majority of TIMSS 2019 mathematics items assess students’ applying and reasoning skills. To cover the framework at the eighth grade, the TIMSS 2019 mathematics assessment comprised 211 assessment items.

This cycle marked the beginning of the transition to a computer-based assessment system. More than half of the TIMSS 2019 countries administered the assessment in an “e” (electronic) format and almost half administered the assessment in a paper format, as in TIMSS 2015. The “e” countries also administered the trend items in the paper format to provide a bridge to the TIMSS 2015 and TIMSS 2019 paper-based assessments. The assessment was carefully designed and analyzed, so that the TIMSS 2019 mathematics achievement results for all 39 countries are reported on the same TIMSS eighth grade mathematics scale.

Exhibit 3.1 presents the average achievement at the eighth grade for each participating country from highest to lowest together with the scale score distribution. Exhibit 3.2 shows whether relatively small differences in average achievement between one country and the next are statistically significant.

The five East Asian countries had the highest average achievement, with Singapore, Chinese Taipei, and Korea performing similarly and having higher average achievement than all of the other TIMSS 2019 countries. These three countries were followed by Japan, whose eighth grade students had higher average achievement than students in all of the other countries except those three countries, and then by Hong Kong SAR, whose students had higher average achievement than students in all of the other countries except those four countries. In turn, the Russian Federation had higher achievement than all of the other remaining countries. Next, Ireland, Lithuania, Israel, Australia, Hungary, the United States, and England also performed well. Essentially, Exhibit 3.2 shows clusters of several similarly performing countries, followed by the next highest achieving clusters of similarly performing countries, and so on.

A number of eighth grade TIMSS 2019 participants performed well. Fourteen countries (including those discussed above) had higher average achievement than the centerpoint of 500 (Exhibit 3.1), which is a point of reference on the TIMSS eighth grade mathematics scale that remains constant from TIMSS assessment to TIMSS assessment. However, there was a considerable difference between the highest average achievement and the lowest. Also, the scale score distributions in Exhibit 3.1 show that there is wide variation in achievement in every country. Every country has some higher achieving and some lower achieving students.

+ Read More### Mathematics Grade 8

#### Trends in Average Achievement

Exhibit 3.3 graphs the differences in average mathematics achievement between the assessment cycles for TIMSS 2019 countries that have comparable data from previous assessments, while Exhibit 3.4 provides more details. The countries are presented in alphabetical order in both exhibits. The trends in mathematics achievement at the eighth grade signal more improvements than downturns across the assessment cycles internationally.

Most recently, for the 33 countries that participated in both TIMSS 2015 and 2019, 13 had increases in average achievement and 4 had decreases. The trends between 2007 and 2019, as well as between 1995 and 2019, also show more increases than decreases in average mathematics achievement over the long term. In 2019, compared with 2007, for the 23 countries in both assessments, there were 16 increases and only 2 decreases. In 2019, compared with 1995, for the 18 countries in both assessments, there were 9 increases and 4 decreases.

+ Read More### Mathematics Grade 8

#### Average Achievement by Gender

Exhibit 3.5 shows the differences in average mathematics achievement between girls and boys. In TIMSS 2019, there was considerable gender equity in average achievement. Girls had higher average achievement than boys in 7 countries, there was gender equity in average mathematics achievement in 26 countries, and boys had higher average achievement than girls in 6 countries.

### Mathematics Grade 8

#### Trends in Average Achievement by Gender

For the TIMSS 2019 countries with comparable data from previous TIMSS assessments, Exhibit 3.6 contains graphs of average mathematics achievement across assessments by gender. The countries are presented in alphabetical order. The difference in average mathematics achievement between boys and girls has remained relatively stable in most countries, with any overall increases or decreases in achievement from assessment to assessment occurring similarly for both girls and boys. However, several countries with no gender gap in TIMSS 2015 had a gap favoring boys in TIMSS 2019, including Israel and Morocco, while Saudi Arabia and South Africa (ninth grade) had a gap favoring girls in 2019. Gender gaps in average achievement favoring boys in TIMSS 2015 were closed in Chile, the Russian Federation, and Sweden, and a gap favoring girls was closed in Singapore.

### Mathematics Grade 8

#### TIMSS 2019 International Benchmarks

To provide an interpretation of the results on the TIMSS eighth grade mathematics achievement scale in relation to the students’ performance on the assessment items, TIMSS describes achievement at four points along the scale as International Benchmarks: Advanced International Benchmark (625), High International Benchmark (550), Intermediate International Benchmark (475), and Low International Benchmark (400). The descriptions of mathematics achievement at the International Benchmarks were updated from TIMSS 2015 based on an analysis of the items that students with average achievement at each of the benchmarks answered successfully in TIMSS 2019.

Exhibit 3.7 summarizes what eighth grade students who reached each of the TIMSS International Benchmarks in 2019 could do in mathematics. The progression in mathematics achievement is evident from benchmark to benchmark, from demonstrating some knowledge of whole numbers and basic graphs at the Low International Benchmark to applying and reasoning in a variety of complex situations at the Advanced International Benchmark. As much as possible, each description references achievement in the four content areas covered in the assessment at the eighth grade: number, algebra, geometry, and data and probability. The following tables show the target percentages for the content and cognitive domains.

The interactive map of the benchmark descriptions links to example items. It provides an overview of the mathematics understanding demonstrated by the eighth grade students who performed at the four levels of the achievement scale. The following sections provide more information about students’ achievement in TIMSS 2019 at each International Benchmark as well as more detailed descriptions of each level together with example items.

+ Read MoreINTERNATIONAL BENCHMARKS | EXAMPLE ITEMS |

### Mathematics Grade 8

#### Percentages of Students Reaching International Benchmarks

Exhibit 3.8 presents the percentage of students reaching each TIMSS 2019 International Benchmark. The results are presented in descending order according to the percentage of students reaching the Advanced International Benchmark, which is indicated in the bar graph with black dots. Because students who reached the Advanced Benchmark also reached the other benchmarks, the percentages illustrated in the exhibit and shown in the columns to the right are cumulative.

The five high-performing East Asian countries had the highest percentages of students reaching the Advanced International Benchmark. Half the eighth grade students reached the Advanced International Benchmark in Singapore (51%) and Chinese Taipei (49%), as well as 45 percent in Korea, 37 percent in Japan, and 32 percent in Hong Kong SAR. Eight countries had 10 to 16 percent, but most countries had fewer than 10 percent of their eighth grade students reaching the Advanced International Benchmark.

As a point of reference, Exhibit 3.8 provides the international median percentage of students reaching each benchmark at the bottom of the four right-hand columns. By definition, half the countries have a percentage in that column above the median and half below the median. The median percentages of students reaching the International Benchmarks were as follows: Advanced—5 percent, High—25 percent, Intermediate—56 percent, and Low—87 percent. Japan had 99 percent of its students reach the Low Benchmark, Singapore and Chinese Taipei had 98 percent, and Korea had 97 percent.

Not only are Singapore, Chinese Taipei, Korea, and Japan educating high percentages of their students to an advanced level, they are educating almost all of their students to a level of minimal proficiency.

+ Read More### Mathematics Grade 8

#### Trends in Percentages of Students Reaching International Benchmarks

Exhibit 3.9 shows the changes in percentages of students reaching the benchmarks for countries that have comparable data from previous assessments. The trends paint a positive picture of improvement across all four benchmarks. Of the 33 countries participating in both 2015 and 2019, 9 increased and none decreased at the Advanced International Benchmark, 7 increased and 3 decreased at the High Benchmark, 10 increased and 6 decreased at the Intermediate Benchmark, and 10 increased and 4 decreased at the Low Benchmark.

The longer-term trends also show considerable improvement across the percentages of students reaching all four of the benchmarks. Between 2007 and 2019, the 23 countries participating in those two assessments had 15 increases and only 1 decrease at the Advanced level, 16 increases and 2 decreases at the High level, 15 increases and 3 decreases at the Intermediate level, and 12 increases and 3 decreases at the Low level. Between 1995 and 2019, the 18 countries participating in both assessments had 13 increases and 2 decreases at the Advanced level, 9 increases and 4 decreases at the High level, 6 increases and 5 decreases at the Intermediate level, and 5 increases and 5 decreases at the Low level.

+ Read More### Mathematics Grade 8

#### Low Benchmark: Full Description

Exhibit 3.10 presents the description of eighth grade students’ achievement at the Low International Benchmark. The few eighth grade items in TIMSS 2019 at the Low level indicated that students had some understanding of whole numbers and basic graphs.

### Mathematics Grade 8

#### Intermediate Benchmark: Full Description and Example Items

Exhibit 3.11 provides the description of student achievement at the Intermediate International Benchmark. At this level, students could apply basic mathematical knowledge in a variety of situations.

Exhibit 3.11.1 presents an item from the number domain. As shown in this item, students reaching the Intermediate Benchmark demonstrated familiarity with negative numbers. The international average was 59 percent. The highest performance on the item was in Finland—85 percent of the students responded correctly.

Exhibit 3.11.2 presents a geometry item. Fifty-six percent of the eighth grade students, on average, were able to use the properties of angles to determine the size of a fourth angle in a quadrilateral when given the values of the other three angles. The Singaporean students had the highest achievement, with 90 percent correct.

Exhibit 3.11.3 shows a multi-part item from the data and probability domain. Eighty-three percent of the students in Singapore were able to compute and compare three unit prices based on advertisements. The international average was 56 percent.

+ Read More### Mathematics Grade 8

#### High Benchmark: Full Description and Example Items

Exhibit 3.12 presents the description of achievement at the High International Benchmark. Eighth grade students reaching this benchmark could apply their mathematics understanding in a variety of relatively complex situations.

Exhibit 3.12.1 provides an example from the number domain. Fifty-four percent of the eighth grade students, on average, were able to use a ratio to solve a problem. With 87 percent correct, Singapore had the highest percentage correct.

Exhibit 3.12.2 provides an example from the algebra domain. In this item, students were asked to solve a problem by evaluating a formula with exponents. The international average was 35 percent. Seventy-three percent of the Singaporean eighth grade students answered correctly.

Exhibit 3.12.3 shows a reasoning item from the geometry domain. On average, 41 percent of eighth grade students were able to visualize two different cylinders. The highest achievement was in Japan, with 79 percent of the students answering this item correctly.

Exhibit 3.12.4 shows a data interpretation item from the data and probability domain. Eighty-three percent of the Japanese eighth grade students were able to match different types of data to the appropriate graphic displays. The international average was 47 percent.

Exhibit 3.12.5 shows another example item from the data and probability domain, involving outcomes and probabilities. Eighth grade students in Korea posted the highest percentage correct—70 percent. The international average was 43 percent.

+ Read More### Mathematics Grade 8

#### Advanced Benchmark: Full Description and Example Items

Exhibit 3.13 presents the description of eighth grade performance at the Advanced International Benchmark. Students could apply and reason to solve a variety of problems as well as solve linear equations and make generalizations.

Exhibit 3.13.1 shows a multistep problem involving fractions from the number domain. This problem was relatively difficult for eighth grade students, with an international average of 18 percent. The top performances were in Chinese Taipei and Korea, where just over half the students answered correctly (52–53%).

Exhibit 3.13.2 involved students constructing a linear equation to solve a problem about perimeter. The international average was 26 percent. Almost three-fourths (74%) of the Singaporean students successfully completed this task.

Exhibit 3.13.3 shows a reasoning item from the geometry domain, which was based on properties of supplementary angles. Seventy-seven percent of eighth grade students answered correctly in both Japan and Korea. The international average was 26 percent.

Exhibit 3.13.4 presents an item from the data and probability domain that required students to interpret the change in a mean, using decimals and rounding. The international average was 36 percent. The highest percentage correct—71 percent—was in Korea.

+ Read More### Mathematics Grade 8

#### TIMSS 2019 Mathematics Content and Cognitive Domains

TIMSS 2019 assessed four content areas in mathematics at the eighth grade: number, algebra, geometry, and data and probability.

The 30 percent of the eighth grade assessment devoted to number consisted of integers (10%); fractions and decimals (10%); and ratio, proportion, and percent (10%). Building on the number content domain at the fourth grade, eighth grade students were asked to compute and solve problems involving more advanced whole number concepts and procedures as well as integers, fractions, and decimals.

Thirty percent of the assessment also was devoted to algebra, which included expressions, operations, and equations (20%) and relationships and functions (10%). Students were asked to solve real world problems using algebraic models and explain relationships involving algebraic concepts. For example, when given one quantity in a formula involving two quantities, they were asked to find the other quantity. They also were given problems involving linear equations and functions.

Twenty percent of the assessment was devoted to geometry. Extending the understanding of shapes and measures assessed at the fourth grade, eighth grade students were asked to analyze the properties of a variety of two- and three-dimensional figures and calculate perimeters, areas, and volumes. They were asked to solve problems and provide explanations based on geometric relationships, such as congruence, similarity, and the Pythagorean theorem.

The remaining 20 percent of the assessment was devoted to the data and probability content domain, which consisted of two topic areas: data (15%) and probability (5%). Students were asked to read and extract the important meaning from a variety of visual displays, demonstrate familiarity with the statistics underlying data distributions, and organize and represent data. There also were some questions related to basic probability concepts.

Eighth grade students also needed to draw on a range of cognitive skills across the content domains described above. These skills were categorized into three broad cognitive domains—knowing, applying, and reasoning. Thirty-five percent of the eighth grade assessment was devoted to the knowing cognitive domain, 40 percent to applying, and 25 percent to reasoning. The knowing domain covers the facts, concepts, and procedures students need to know, while the second domain, applying, focuses on students’ ability to apply knowledge and conceptual understanding to solve problems or answer questions. The reasoning domain goes beyond the solution of routine problems to encompass unfamiliar situations, complex contexts, and multistep problems.

+ Read More### Mathematics Grade 8

#### Average Achievement in Content Domains

Exhibit 3.14 shows countries’ average mathematics achievement in each of the four content domains relative to their overall average achievement (presented from highest to lowest overall average achievement). Based on students’ relative strengths and weaknesses at the eighth grade, the TIMSS 2019 countries appear to be placing relatively more instructional emphasis on the algebra content domain and less on the number and data and probability domains. Of the 36 participating countries for which content domain scores were estimated, 7 had a relative strength in number and 14 had a relative weakness; 19 had a relative strength in algebra and 14 had a relative weakness; 14 had a relative strength in geometry, and 17 had relative weakness; and 10 had a relative strength in data and probability, and 21 had a relative weakness. All countries had at least one relative strength or relative weakness compared with their overall achievement.

### Mathematics Grade 8

#### Trends in Average Achievement in Content Domains

Exhibit 3.15 presents trends in average achievement for the four mathematics content domains. The results are very positive, showing more increases than decreases in all four content areas, especially geometry. Thirty TIMSS 2019 countries also participated in TIMSS 2015 and had comparable data for the content domains. In the number content area, 8 showed improvement and 6 showed declines; in algebra, 8 showed improvement and 3 showed declines; in geometry, 12 showed improvement and 2 showed declines; and in data and probability, 8 showed improvement and 5 showed declines.

TIMSS began providing scaled results in the content domains in 2007, with 23 countries having trends between 2007 and 2019. Compared with 2007, there was considerable improvement in TIMSS 2019 across the content domains in these countries—13 had higher average achievement in number, 13 in algebra, 18 in geometry, and 10 in data and probability. Only several of the countries had lower average achievement—2 in number, 1 in algebra, 2 in geometry, and 3 in data and probability.

+ Read More### Mathematics Grade 8

#### Average Achievement in Content Domains by Gender

Exhibit 3.16 shows the differences in average achievement between girls and boys in the four mathematics content domains. Boys had a substantial advantage in number (as they did at fourth grade) and girls did in algebra. In the number content domain, girls had higher average achievement than boys in only 4 countries, and boys had higher average achievement in 14 countries. In algebra, girls had higher average achievement than boys in 16 countries, and in no country did boys have higher average achievement. In geometry, girls had higher average achievement than boys in 7 countries, and boys had higher average achievement in 3 countries. In data and probability, girls had higher average achievement than boys in 7 countries, and boys had higher average achievement in 9 countries.

### Mathematics Grade 8

#### Average Achievement in Cognitive Domains

Exhibit 3.17 shows countries’ average achievement in the knowing, applying, and reasoning cognitive domains relative to their overall average achievement (from highest to lowest overall average achievement). Interestingly, fewer countries had a relative strength in the knowing and applying cognitive domains than they did in the reasoning domain. More countries had a weakness in the knowing domain than in the applying and reasoning domains. Eight countries had a relative strength in the knowing cognitive domain, and 17 had a relative weakness. Six countries had a relative strength in the applying cognitive domain, and 14 had a relative weakness. Sixteen countries had a relative strength in the reasoning cognitive domain, and 9 had a relative weakness. Kazakhstan was the only country with no relative strengths or weaknesses in the cognitive domains.

### Mathematics Grade 8

#### Trends in Average Achievement in Cognitive Domains

Exhibit 3.18 presents differences in average achievement for the three cognitive domains across four assessment cycles back to 2007, when TIMSS first began providing scaled results in the cognitive domains. Trends for countries with comparable data between assessment cycles show more countries have had increases than decreases in average achievement in each of the cognitive domains. Twenty-nine countries had comparable data in the TIMSS 2015 and TIMSS 2019 assessments for the cognitive domains. The recent trends in the knowing cognitive domain showed increases in 9 countries and decreases in 4 countries. In the applying domain, 9 countries showed increases and 3 showed decreases. In the reasoning domain, 13 showed increases and 3 showed decreases.

Between 2007 and 2019, in the knowing, applying, and reasoning domains, there were increases in average achievement in 14 countries, 14 countries, and 16 countries, respectively. There were decreases in average achievement in only 1 country in knowing and reasoning, and 2 countries in applying.

+ Read More### Mathematics Grade 8

#### Average Achievement in Cognitive Domains by Gender

Exhibit 3.19 shows the differences between girls’ and boys’ average achievement in the cognitive domains of knowing, applying, and reasoning. In the knowing domain, girls had higher average achievement than boys in 8 countries, and boys had higher achievement than girls in 5 countries. In the applying domain, girls had higher average achievement than boys in 5 countries, and boys had higher average achievement than girls in 8 countries. In reasoning, girls had higher average achievement than boys in 8 countries compared with 3 countries where boys had higher average achievement.

### Science Grade 8

#### Average Achievement and Scale Score Distributions

The TIMSS 2019 eighth grade science assessment was based on a comprehensive assessment framework developed collaboratively with the participating countries to reflect their curricular goals. The eighth grade science assessment included four content areas—biology (35%), chemistry (20%), physics (25%), and Earth science (20%). In accordance with the framework, the majority of TIMSS 2019 science items assessed eighth grade students’ applying and reasoning skills, and there is a cross-cutting inquiry strand. To cover the framework at the eighth grade, the TIMSS 2019 science assessment comprised 220 assessment items.

This cycle marked the beginning of the transition to a computer-based assessment system. More than half of the TIMSS 2019 countries administered the assessment in an “e” (electronic) format and almost half administered the assessment in a paper format, as in TIMSS 2015. The “e” countries also administered the trend items in the paper format to provide a bridge to the TIMSS 2015 and TIMSS 2019 paper-based assessments. The assessment was carefully designed and analyzed, so that the TIMSS 2019 science achievement results for all 39 countries are reported on the same TIMSS eighth grade science scale.

Exhibit 4.1 presents the average achievement at the eighth grade for each participating country (from highest to lowest) together with the scale score distribution underlying the average scale score. Exhibit 4.2 shows whether relatively small differences in average achievement between one country and the next are statistically significant.

Singapore had the highest average achievement, followed by Chinese Taipei and Japan, whose students performed similarly and had higher average achievement than all of the other countries. These three countries were followed by Korea, whose eighth grade students had higher average achievement than students in all of the other countries except the three top-performing countries. Next, the Russian Federation and Finland, followed by Lithuania, and then by Hungary and Australia, and then Ireland and the United States, all performed very well. Essentially, Exhibit 4.2 shows clusters of several similarly performing countries, followed by the next highest achieving clusters of similarly performing countries, and so on.

A number of eighth grade TIMSS 2019 participants performed well. Sixteen countries (including those discussed above) had higher average achievement than the centerpoint of 500 (Exhibit 4.1), which is a point of reference on the TIMSS eighth grade science scale that remains constant from TIMSS assessment to TIMSS assessment. However, there was a considerable difference between the highest average achievement and the lowest. Also, the scale score distributions in Exhibit 4.1 show that there is wide variation in achievement in every country. Every country has some higher achieving and some lower achieving students.

+ Read More### Science Grade 8

#### Trends in Average Achievement

Exhibit 4.3 graphs the differences in average science achievement between the assessments for TIMSS 2019 countries that have comparable data from previous assessments, while Exhibit 4.4 provides more details. The countries are presented in alphabetical order in both exhibits. The trends in science achievement at the eighth grade signal more improvements than downturns across the assessment cycles internationally. However, across the seven assessment cycles since 1995, most countries have had some periods of increases and decreases in average achievement as well as periods of stability.

Most recently, for the 33 countries that participated in both TIMSS 2015 and 2019, 11 had increases in average achievement and 5 had declines. Looking at trends between 2007 and 2019 as well as between 1995 and 2019 also shows moderate progress in average science achievement at the eighth grade over the long term, with more countries having increases than decreases. In 2019 compared with 2007, for the 23 countries in both assessments, there were 12 increases and 6 decreases. In 2019 compared with 1995, for the 18 countries in both assessments, there were 8 increases and 4 decreases.

+ Read More### Science Grade 8

#### Average Achievement by Gender

Exhibit 4.5 shows the differences in average science achievement between girls and boys. In TIMSS 2019, girls had higher average achievement than boys in 15 countries, there was gender equity in average science achievement in 18 countries, and boys had higher average achievement than girls in 6 countries.

### Science Grade 8

#### Trends in Average Achievement by Gender

For the TIMSS 2019 countries with comparable data from previous TIMSS assessments, Exhibit 4.6 contains graphs of average science achievement across assessments by gender. The countries are presented in alphabetical order. The difference in average science achievement between boys and girls has remained relatively stable in most countries, with any overall increases or decreases in achievement from assessment to assessment occurring similarly for both girls and boys. However, consistent with girls having average higher achievement than boys in more countries than the other way around, a number of countries with no gender gap in TIMSS 2015 had a gap favoring girls in TIMSS 2019, including Egypt, Iran, South Africa (ninth grade), and Sweden. (Finland, Kazakhstan, and Romania did not have comparable data from 2015, but had a gap favoring girls in TIMSS 2019 that did not exist in 2011.) The gender gap in average achievement favoring girls in TIMSS 2015 was closed in Lebanon, Malaysia, Morocco, and Turkey. Japan and Korea had no gender gap in 2015, but had a gap favoring boys in 2019. The gender gap in average achievement favoring boys in TIMSS 2015 was closed in Hong Kong SAR and the United States.

### Science Grade 8

#### TIMSS 2019 International Benchmarks

To provide an interpretation of the results on the TIMSS eighth grade science achievement scale in relation to the students’ performance on the assessment items, TIMSS describes achievement at four points along the scale as International Benchmarks: Advanced International Benchmark (625), High International Benchmark (550), Intermediate International Benchmark (475), and Low International Benchmark (400). The descriptions of science achievement at the International Benchmarks were updated from TIMSS 2015 based on an analysis of the items that students with average achievement at each of the benchmarks answered successfully in TIMSS 2019.

Exhibit 4.7 summarizes what eighth grade students who reached each of the TIMSS International Benchmarks in 2019 could do in science. The progression in science achievement is evident from benchmark to benchmark, from limited knowledge of science facts at the Low International Benchmark to communicating conceptual understanding in a variety of science contexts at the Advanced International Benchmark. As much as possible, each description references achievement in the four content areas covered in the assessment at the eighth grade— biology, chemistry, physics, and Earth science—as well as science practices assessed by TIMSS. Science practices include skills from daily life and school studies that students use systematically to conduct scientific inquiry and investigation. The following tables show the target percentages for the content and cognitive domains.

The interactive map of the benchmark descriptions links to example items. It provides an overview of the science understanding demonstrated by the eighth grade students who performed at the four different levels on the achievement scale. The following sections provide more information about students’ achievement in TIMSS 2019 at each International Benchmark as well as more detailed descriptions of each level together with example items.

+ Read MoreINTERNATIONAL BENCHMARKS | EXAMPLE ITEMS |

### Science Grade 8

#### Percentages of Students Reaching International Benchmarks

Exhibit 4.8 presents the percentage of students reaching each TIMSS 2019 International Benchmark. The results are presented in descending order according to the percentage of students reaching the Advanced International Benchmark and are indicated in the graph with black dots. Because students who reached the Advanced Benchmark also reached the other benchmarks, the percentages illustrated in the exhibit and shown in the columns to the right are cumulative.

Consistent with Singapore being the highest performing country, nearly half of their eighth grade students (48%) reached the Advanced International Benchmark. The next highest percentages reaching the Advanced level were in Chinese Taipei (29%), Japan (22%), and Korea (22%). Twelve countries had 10 to 16 percent, and the rest of the countries had fewer than 10 percent of their eighth grade students reaching the Advanced International Benchmark.

As a point of reference, Exhibit 4.8 provides the international median percentage of students reaching each benchmark at the bottom of the four right-hand columns. By definition, half the countries have a percentage in that column above the median and half below the median. The median percentages of students reaching the International Benchmarks were as follows: Advanced—7 percent, High—29 percent, Intermediate—61 percent, and Low—85 percent. The Low International Benchmark can be considered a level of minimum proficiency, with Japan (99%) and Singapore (98%) having nearly all of their students reaching this level.

+ Read More### Science Grade 8

#### Trends in Percentages of Students Reaching International Benchmarks

Exhibit 4.9 shows the changes in percentages of students reaching the benchmarks for countries that have comparable data from previous assessments. The trends indicate more improvement at the two higher benchmarks than declines, in contrast to similar improvements but more declines at lower benchmarks. Of the 33 countries participating in both 2015 and 2019, 10 increased and only 1 decreased at the Advanced International Benchmark, 9 increased and 4 decreased at the High Benchmark, 10 increased and 8 decreased at the Intermediate Benchmark, and 8 increased and 8 decreased at the Low Benchmark.

The longer-term trends also show a similar pattern. Between 2007 and 2019, the 23 countries participating in those two assessments had 13 increases and 2 decreases at the Advanced level, 12 increases and 4 decreases at the High level, 10 increases and 5 decreases at the Intermediate level, and 8 increases and 9 decreases at the Low level. Between 1995 and 2019, the 18 countries participating in both assessments had 7 increases and 2 decreases at the Advanced level, 8 increases and 2 decreases at the High level, and 7 increases and 3 decreases at the Intermediate level, as well as 5 increases and 6 decreases at the Low level.

+ Read More### Science Grade 8

#### Low Benchmark: Full Description

Exhibit 4.10 presents the description of eighth grade students’ achievement at the Low International Benchmark. The very few items that anchored at the Low level indicated students had limited understanding of scientific principles and concepts and limited knowledge of science facts.

### Science Grade 8

#### Intermediate Benchmark: Full Description and Example Items

Exhibit 4.11 provides the description of students’ achievement at the Intermediate International Benchmark. At this level, the eighth grade students showed and applied some knowledge of biology and physical science.

Exhibit 4.11.1 presents an item from the biology content domain about the advantages of a crocodile’s field of vision. On average, 55 percent of the eighth grade students could provide an explanation. The highest achievement was in Japan and Singapore with 84–85 percent correct.

Exhibit 4.11.2 presents an item from the chemistry content domain asking students to distinguish between elements and compounds. Finland and Lithuania had the highest performance—88–89 percent correct. The international average was 61 percent.

Exhibit 4.11.3 shows an example item from physics. Students were able to identify the difference in gravitational attraction as the reason why a rover weighs a different amount on Mars than it does on Earth. With 90 percent correct, the Singaporean eighth graders had the highest achievement. The international average was 69 percent.

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#### High Benchmark: Full Description and Example Items

Exhibit 4.12 presents the description of science achievement at the High International Benchmark. Eighth grade students reaching this level demonstrated conceptual understanding of topics related to biology, chemistry, physics, and Earth science.

Exhibit 4.12.1 provides an example from the biology domain. Forty-eight percent of the eighth grade students, on average, were able to explain why increasing the number of gardens reduces the amount of carbon dioxide in the air. With 85 percent success, Singapore had the highest percentage correct.

Exhibit 4.12.2 provides an example from the chemistry domain. In this item, students were asked to interpret the results of a science experiment shown in a diagram and provide evidence. Students in the Russian Federation were the most successful—69 percent correct. The international average was 39 percent.

A physics example is shown in Exhibit 4.12.3. Seventy-eight percent of the students in Chinese Taipei—by far the highest percentage correct—explained that you cannot hear a phone ring in a vacuum because there is no air. The international average was 38 percent.

Exhibit 4.12.4 provides an example from Earth science asking students to identify the shrinking size of polar ice caps as evidence that the Earth is becoming warmer. Chinese Taipei had the highest achievement with 87 percent correct, and 57 percent of eighth grade students internationally answered correctly, on average.

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#### Advanced Benchmark: Full Description and Example Items

Exhibit 4.13 presents the description of eighth grade performance at the Advanced International Benchmark. Students reaching the Advanced level communicated conceptual understanding of concepts related to biology, chemistry, physics, and Earth science in a variety of contexts.

Exhibit 4.13.1 shows an item from the biology domain asking students to correctly classify seven animals as mammals or non-mammals. On average, 30 percent of the eighth grade students were successful. Japan was the highest achieving country with 75 percent correct.

Exhibit 4.13.2 presents an item from the chemistry domain about the periodic table of elements. The international average was 29 percent correct, and top-achieving Singapore had 60 percent on this item.

Exhibit 4.13.3 shows a physics item that asked what happens to gas molecules inside a balloon when the balloon is heated. Singapore and Israel had the highest performance on this item with 68–69 percent correct. The international average was 41 percent.

The last example item is shown in Exhibit 4.13.4. From the Earth science content domain, the item asked students to recognize what causes a weather balloon to expand as it rises above the ground. On average, 42 percent of the eighth grade students correctly answered that the atmospheric pressure decreases. The highest percentage correct, 68 percent, was posted by Japan.

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#### TIMSS 2019 Science Content and Cognitive Domains

TIMSS 2019 assessed four content areas in science at the eighth grade: biology, chemistry, physics, and Earth science.

Thirty-five percent of the eighth grade science assessment was devoted to biology, including characteristics and life processes of organisms; cells and their functions; life cycles, reproduction, and heredity; diversity, adaptation, and natural selection; ecosystems; and human health. Eighth grade students were asked about how structure relates to function in organisms, cell structure and function, and the processes of photosynthesis and cellular respiration. Other areas assessed included reproduction and heredity, molecular biology and molecular genetics, adaptation and natural selection, and processes and interactions in ecosystems.

Twenty percent of the assessment covered three chemistry topics—composition of matter, properties of matter, and chemical change. Students were asked about elements, compounds, and mixtures; the use of the periodic table; physical and chemical properties of matter; as well as the properties of mixtures and solutions and the properties of acids and bases. The chemical change topic focused on the characteristics of chemical changes and the conservation of matter during chemical changes.

Twenty-five percent of the assessment was devoted to physics, which consisted of five topics: physical states and changes in matter, energy transformation and transfer, light and sound, electricity and magnetism, and motion and forces. For example, eighth grade students were asked to describe processes involved in changes in the state of matter, to identify different forms of energy and describe simple energy transformations, to apply the principle of conservation of total energy in practical situations, and to understand the difference between thermal energy (heat) and temperature.

The remaining 20 percent of the assessment was devoted to Earth science topics. Students were asked about the structure and physical features of Earth, including Earth’s structural layers, and the atmosphere, as well as processes, cycles, and patterns, including geological processes that have occurred over Earth’s history, the water cycle, and patterns of weather and climate. Earth’s resources and their use and conservation also were covered. The area of Earth in the Solar System included identifying how observable phenomena relate to the movements of Earth and the Moon, and describing the features of Earth, the Moon, and other planets.

Eighth grade students also needed to draw on a range of cognitive skills across the content domains already described above. There are three cognitive domains. Thirty-five percent of the eighth grade assessment was devoted to the knowing cognitive domain, 35 percent to applying, and 30 percent to reasoning. The knowing domain covers the facts, concepts, and procedures students need to know, while the applying domain focuses on students’ ability to apply knowledge and conceptual understanding to solve practical problems or answer questions. The reasoning domain goes beyond the solution of familiar problems to encompass unfamiliar situations, complex contexts, and multistep problems. Also, five science practices fundamental to scientific inquiry were assessed within the content areas and cognitive domains.

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#### Average Achievement in Content Domains

Exhibit 4.14 shows countries’ average science achievement in each of the four content domains relative to their overall average achievement (presented from highest to lowest overall average achievement). Based on countries’ strengths and weaknesses, the TIMSS 2019 countries appear to be placing relatively less instructional emphasis on the chemistry and physics domains. Of the 37 participating countries for which cognitive domain scores were estimated, 11 had a relative strength in biology and 8 had a relative weakness. In chemistry, 10 had a relative strength and 16 had a relative weakness; in physics, 9 had a relative strength and 14 had a relative weakness. In most countries, Earth science tended to be either a relative strength (12 countries) or a relative weakness (19 countries). England and Hungary were the only two countries without at least one relative strength or relative weakness compared with its overall achievement.

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#### Trends in Average Achievement in Content Domains

Exhibit 4.15 presents trends in average achievement for the four science content domains assessed by TIMSS 2019—biology, chemistry, physics, and Earth science. The results are moderately positive, showing more increases than decreases in all four content areas, especially most recently in biology. Thirty-one TIMSS 2019 countries also participated in TIMSS 2015 and have comparable data in the content domains. In the biology content area, 13 showed improvement and 5 showed declines; in chemistry, 8 showed improvement and 8 showed declines; in physics, 9 showed improvement and 5 showed declines; and in Earth science, 10 showed improvement and 5 showed declines.

TIMSS began providing scaled results in the content domains in 2007, with 23 countries having trends between 2007 and 2019. Compared with 2007, in TIMSS 2019, 11 countries showed improvement and 5 showed declines in biology, 8 countries showed improvement and 6 showed declines in chemistry, 11 showed improvement and 6 showed declines in physics, and 12 showed improvement and 6 showed declines in Earth science.

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#### Average Achievement in Content Domains by Gender

Exhibit 4.16 shows the differences in average achievement between girls and boys in the four science content domains. Across the TIMSS 2019 countries, girls had a substantial advantage in biology and chemistry whereas boys had the edge in physics and Earth science. In the biology content domain, girls had higher average achievement than boys in 17 countries, and boys had higher average achievement in 3 countries. In chemistry, girls had higher average achievement than boys in 21 countries, and boys had higher average achievement in only 1 country. In physics, girls had higher average achievement than boys in 6 countries, and boys had higher average achievement in 13 countries. In Earth science, girls had higher average achievement than boys in 4 countries, and boys had higher average achievement in 15 countries.

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#### Average Achievement in Cognitive Domains

Exhibit 4.17 shows countries’ average achievement in the knowing, applying, and reasoning cognitive domains relative to their overall average achievement (from highest to lowest overall average achievement). Interestingly, in the knowing and reasoning domains, about the same number of countries had relative strengths as had relative weaknesses, but in the applying domain, fewer countries had strengths than weaknesses. Eleven countries had a relative strength in the knowing cognitive domain, and 12 had a relative weakness. Only 6 countries had a relative strength in the applying domain, although 14 had a relative weakness. Thirteen countries had a relative strength in the reasoning cognitive domain, and 16 had a relative weakness. The Russian Federation and Hong Kong SAR were well balanced, with no relative strengths or weaknesses in the cognitive domains.

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#### Trends in Average Achievement in Cognitive Domains

Exhibit 4.18 presents differences in average achievement for the three cognitive domains across four assessment cycles back to 2007, when TIMSS first began providing scaled results in the cognitive domains. Trends show more countries have had increases than decreases in average achievement in each of cognitive domains, particularly in the knowing domain. Thirty-one countries participated in both the TIMSS 2015 and TIMSS 2019 assessments and have comparable data in the cognitive domains. The recent trends in the knowing cognitive domain showed increases in 10 countries and decreases in 8 countries. In the applying and reasoning domains, 7 countries showed increases, and 6 showed decreases.

Between 2007 and 2019, in the knowing domain, there were increases in 13 countries compared with declines in 6 countries. In the applying domain, there were increases in 11 countries and declines in 6 countries. In the reasoning domain, 9 countries had increases and 6 had decreases.

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#### Average Achievement in Cognitive Domains by Gender

Exhibit 4.19 shows the differences between girls’ and boys’ average achievement in the cognitive domains of knowing, applying, and reasoning. Reflecting the overall results where girls had higher average achievement in more countries than the reverse, girls had higher average achievement than boys in more countries than the reverse in all three cognitive domains, especially applying and reasoning. In the knowing domain, girls had higher average achievement than boys in 10 countries, and boys had higher achievement than girls in 8 countries. In the applying domain, girls had higher average achievement than boys in 13 countries, and boys had higher average achievement than girls in 4 countries. In reasoning, girls had higher average achievement than boys in 13 countries, compared with 2 countries where boys had higher average achievement.