## Mathematics for Grades 4 and 8: Trends Over Three Time Points

### International Benchmarks

Table 13b. Standard errors for change in percentage of 4th-grade students reaching the TIMSS international benchmarks in mathematics, by education system: 1995-2015 and 2011-2015
Education system Standard errors for percentage of students reaching each international benchmark Standard errors for change in percentage reaching each international benchmark1
1995 2011 2015 Percentage point difference: 1995 to 2015 Percentage point difference: 2011 to 2015
Advanced (625) High (550) Inter-mediate (475) Low (400) Advanced (625) High (550) Inter-mediate (475) Low (400) Advanced (625) High (550) Inter-mediate (475) Low (400) Advanced (625) High (550) Inter-mediate (475) Low (400) Advanced (625) High (550) Inter-mediate (475) Low (400)

† Not applicable.

1 The change in average percentage is calculated by subtracting the 1995 or 2011 estimate, respectively, from the 2015 estimate using unrounded numbers.

2 National Defined Population covers 90 to 95 percent of the National Target Population in 2015.

3 Met guidelines for sample participation rates only after replacement schools were included in 2015.

4 Nearly satisfied guidelines for sample participation rates after replacement schools were included in 2015.

5 National Defined Population covers less than 90 percent of the National Target Population (but at least 77 percent) in 2015.

6 The number in parentheses indicates years of school not grade in schooling.

7 National Target Population does not include all of the International Target Population in 2015.

8 Reservations about reliability because the percentage of students with achievement too low for estimation exceeds 15 percent but does not exceed 25 percent in 2015.

9 Did not satisfy guidelines for sample participation rates in 2015.

NOTE: Education systems are ordered by the percentage of students reaching the Advanced international benchmark in 2015. Education systems that are not countries are designated by the appended three-letter international abbreviation for their country. Participants that did not administer TIMSS at the target grade are not shown; see the international report for their results. For cross-education system trend tables, data are shown for the first available and most recent year; 1995 is the first year for the overall mathematics scale and benchmark data and 2007 is the first year for the content and cognitive subscales. Participants that only participated in one of the three time points are also excluded. Lithuania and Kuwait also are excluded because full trend data are not available. U.S. state data are based on public school students only. For TIMSS 2015, Norway revised its assessed population to students in their 5th and 9th years of schooling to obtain better comparisons with Sweden and Finland. However, in previous TIMSS cycles Norway assessed students in their 4th and 8th years of schooling, which were defined as 4th and 8th grades but have been redefined as 3rd and 7th grades because year 1 in Norway is now considered the equivalent of a year of kindergarten. To maintain trend with previous TIMSS cycles, in 2015 Norway also collected data from students in their 4th and 8th years of schooling, which is used in trend tables.

For 1995, Ireland, the Republic of Korea, Portugal, and Ontario-CAN had a National Defined Population that covered 90-95 percent of the National Target Population; England-GBR had a National Defined Population that covered less than 90 percent of the National Target Population (but at least 77 percent) and met guidelines for sample participation rates only after replacement schools were included; and Australia and the Netherlands did not satisfy guidelines for sample participation rates.

For 2011, Georgia and Florida-USA had a National Target Population that did not include all of the International Target Population; Croatia, Denmark, Hong Kong-CHN, Kazakhstan, Qatar, Serbia, Singapore, and the United States had a National Defined Population that covered 90-95 percent of the National Target Population; Florida-USA had a National Defined Population that covered less than 90 percent of the National Target Population (but at least 77 percent); the Netherlands and Northern Ireland-GBR met guidelines for sample participation rates only after replacement schools were included; and Norway (4) nearly satisfied guidelines for sample participation rates after replacement schools were included. In Oman in 2011, there were reservations about reliability because the percentage of students with achievement too low for estimation exceeded 15 percent but did not exceed 25 percent; in Morocco there were reservations about reliability because the percentage of students with achievement too low for estimation exceeded 25 percent.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995, 2011, and 2015.

Singapore2 2.2 1.6 0.9 0.4 2.0 1.4 0.7 0.2 2.1 1.7 0.9 0.3 3.0 2.3 1.3 0.5 2.9 2.2
Hong Kong-CHN3 1.7 2.3 1.3 0.5 1.8 1.5 1.2 0.5 2.0 1.3 0.4 0.1 2.6 2.6 1.4 0.6 2.7 2.0 1.2 0.5
Korea, Republic of 1.1 1.3 0.5 0.2 1.4 0.8 0.4 0.1 1.3 1.0 0.4 0.1 1.7 1.6 0.7 1.9 1.3
Chinese Taipei-CHN 1.1 1.1 0.6 0.2 1.5 1.0 0.4 0.2 1.9 1.5 0.8 0.3
Japan 1.0 1.2 0.7 0.2 1.0 1.0 0.5 0.2 1.1 1.0 0.4 0.1 1.5 1.5 0.9 0.3 1.5 1.4 0.7
Northern Ireland-GBR4 1.2 1.4 1.1 0.6 1.3 1.5 1.1 0.6 1.8 2.1 1.5 0.8
Russian Federation 1.3 2.1 1.3 0.5 1.8 1.8 1.1 0.4 2.2 2.8 1.7 0.6
England-GBR 0.8 1.5 1.5 1.0 1.3 1.7 1.4 0.7 1.2 1.5 1.2 0.7 1.5 2.1 1.9 1.2 1.7 2.3 1.9 1.0
Kazakhstan 1.1 2.1 2.4 1.2 1.8 2.6 1.5 0.5 2.1 3.3 2.8 1.3
United States2, 3 0.9 1.6 1.2 0.7 0.8 1.1 0.8 0.3 0.8 1.1 1.0 0.5 1.2 1.9 1.6 0.8 1.1 1.3 0.6
Ireland 1.0 1.7 1.6 1.0 0.9 1.6 1.3 0.6 1.0 1.6 1.0 0.4 1.4 2.3 1.9 1.1 1.3 2.2 1.7 0.7
Hungary 1.1 1.8 1.5 0.9 0.8 1.4 1.5 1.0 0.9 1.5 1.5 0.9 1.4 2.4 2.1 1.2 2.1 2.1 1.3
Portugal2 0.3 0.8 1.6 1.8 1.2 1.9 1.6 0.7 0.9 1.3 1.1 0.4 0.9 1.5 1.9 1.9 1.5 2.3 1.9
Denmark2, 3 1.0 1.5 1.2 0.6 0.9 1.6 1.3 0.6 2.2 1.8
Serbia5 0.7 1.5 1.4 1.0 0.8 1.4 1.6 1.2 2.1 2.1 1.5
Belgium (Flemish)-BEL3 0.7 1.4 0.8 0.2 0.8 1.5 0.9 0.3 2.0 1.2
Cyprus 0.6 1.3 1.4 1.3 0.7 1.5 1.3 0.6 1.0 1.9 1.9 1.4
Australia 0.7 1.4 1.6 1.2 0.9 1.3 1.4 1.0 0.9 1.6 1.3 0.9 1.1 2.1 2.1 1.5 1.3 2.1 1.3
Finland 0.8 1.4 1.2 0.4 0.7 1.3 1.0 0.4 1.1 1.9 1.5 0.6
Czech Republic 1.3 1.6 1.1 0.5 0.5 1.5 1.3 0.8 0.7 1.4 1.1 0.5 1.5 2.1 0.7 0.9 2.1 1.7 0.9
New Zealand 0.7 1.4 2.0 1.7 0.5 1.1 1.4 0.9 0.5 0.9 1.2 0.9 0.9 1.7 2.3 1.9 0.7 1.5 1.8 1.3
Slovenia 0.4 1.1 1.9 1.5 0.5 1.3 1.4 0.5 0.5 1.4 1.2 0.5 0.7 1.8 2.2 1.6 0.7 1.9 1.9 0.8
Germany 0.5 1.4 1.3 0.5 0.5 1.3 1.1 0.6 1.9 1.7 0.8
Sweden2 0.4 1.2 1.3 0.6 0.5 1.6 1.6 0.8 0.7 2.0 2.1 1.0
United Arab Emirates 0.2 0.5 0.9 1.0 0.4 0.8 1.0 0.9 0.4 0.9 1.3 1.3
Turkey 0.5 1.4 1.7 1.5 0.5 1.2 1.3 1.1 0.7 1.8 2.2 1.9
Italy2 0.6 1.5 1.4 0.8 0.6 1.3 1.4 0.8
Slovak Republic 0.7 1.6 1.6 1.3 0.4 1.1 1.4 0.9 0.8 2.0 2.1 1.6
Netherlands3 1.1 1.9 1.3 0.5 0.6 1.4 0.8 0.2 0.6 1.3 1.0 0.3 1.3 2.3 1.7 0.9 1.9 1.3 0.3
Spain2 0.3 1.1 1.8 1.3 0.4 1.1 1.4 0.9 0.4 1.5 2.3 1.6
Norway (4)6 0.4 1.2 1.9 1.2 0.4 1.5 1.9 0.9 0.4 1.1 1.5 1.1 0.6 1.6 2.4 1.6 2.4 1.4
Croatia 0.3 1.0 1.2 0.9 0.4 1.1 1.2 0.6 0.5 1.5 1.7 1.1
Qatar 0.4 0.9 1.3 1.5 0.5 1.1 1.4 1.4 0.6 1.4 1.9 2.1
Georgia7 0.5 1.0 1.7 1.7 0.6 1.4 1.7 1.6 1.7 2.4 2.4
Oman 0.1 0.3 0.9 1.2 0.3 0.6 1.1 1.0 0.3 0.7 1.4 1.6
Bahrain2 0.3 0.9 1.4 1.4 0.2 0.5 0.8 0.8 1.0 1.6 1.6
Iran, Islamic Republic of 0.8 1.8 2.4 0.2 0.8 1.5 1.5 0.3 0.7 1.1 1.4 0.3 1.0 2.1 2.8 1.1 1.9 2.0
Chile 0.3 0.7 1.1 1.2 0.2 0.7 1.4 1.5 0.4 1.0 1.8 2.0
Saudi Arabia8 0.7 1.2 1.9 1.8 0.7 1.2 1.7 0.8 1.4 2.2 2.5
Morocco 0.7 1.1 1.6 0.5 1.1 1.6 0.8 1.6 2.2
Benchmarking participants
Florida-USA7 1.3 1.8 1.3 0.4 2.1 2.7 1.7 0.7 2.4 3.3 2.2 0.8
Dubai-UAE 0.4 0.8 0.9 0.9 0.5 0.9 0.8 0.5 0.7 1.2 1.2 1.0
Quebec-CAN9 1.8 3.4 1.8 0.6 0.7 1.7 1.2 0.3 1.3 2.5 1.8 0.6 2.2 4.3 2.5 0.8 1.5 3.0 2.1 0.7
Ontario-CAN 0.5 1.4 1.9 1.3 0.7 1.6 1.6 0.7 0.6 1.4 1.3 0.6 0.8 2.0 2.3 1.4 1.0 2.1 2.1 1.0
Abu Dhabi-UAE2, 8 0.3 1.0 1.9 2.1 0.7 1.4 1.9 1.8 0.8 1.7 2.7 2.8