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

### International Benchmarks

Table 14a. Change in percentage of 8th-grade students reaching the TIMSS international benchmarks in mathematics by education system: 1995-2015 and 2011-2015
Education system Percentage of students reaching each international benchmark 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) Intermediate (475) Low (400) Advanced (625) High (550) Intermediate (475) Low (400) Advanced (625) High (550) Intermediate (475) Low (400) Advanced (625) High (550) Intermediate (475) Low (400) Advanced (625) High (550) Intermediate (475) Low (400)

Average percentage is larger than U.S. percentage at the .05 level of statistical significance.

Average percentage is smaller than U.S. percentage at the .05 level of statistical significance.

― Not available.

# Rounds to zero.

*p<.05. Percentage is significantly different from the U.S. percentage at the .05 level of statistical significance.

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

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

5 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.

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

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

8 Reservations about reliability because the percentage of students with achievement too low for estimation exceeds 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 also is 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, the Russian Federation 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); England-GBR and the United States met guidelines for sample participation rates only after replacement schools were included; and Australia nearly satisfied guidelines for sample participation rates after replacement schools were included.

For 2011, Georgia and Florida-USA had a National Target Population that did not include all of the International Target Population; the Russian Federation, Singapore, the United States, Ontario-CAN, and Florida-USA had a National Defined Population that covered 90-95 percent of the National Target Population; Israel had a National Defined Population that covered less than 90 percent of the National Target Population (but at least 77 percent); England-GBR nearly satisfied guidelines for sample participation rates after replacement schools were included; and Bahrain tested the same cohort of students as other education systems, but later in the assessment year at the beginning of the next school year. In Bahrain, the Islamic Republic of Iran, Jordan, Oman, Qatar, and Saudi Arabia 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.

The standard errors for the estimates shown in this table are in table 14b available at http://nces.ed.gov/timss/timss2015/timss2015_table14b.asp.

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

Singapore2 40 84 98 100 48 78 92 99 54 81 94 99 14 * -3 -5 * -1 * 7 * 3 1 #
Chinese Taipei-CHN 49 73 88 96 44 72 88 97 -5 * -1 # #
Korea, Republic of 31 67 89 97 47 77 93 99 43 75 93 99 12 * 8 * 4 * 2 * -4 -1 # #
Hong Kong-CHN 23 65 88 96 34 71 89 97 37 75 92 98 14 * 10 * 4 2 2 4 3 1
Japan 29 67 91 98 27 61 87 97 34 67 89 98 5 * # -2 -1 7 * 6 * 2 * 1
Kazakhstan 3 23 57 85 15 41 71 91 12 * 19 * 14 * 5 *
Russian Federation 9 38 73 93 14 47 78 95 14 46 78 95 5 * 7 * 4 2 # -1 -1 #
Israel3 12 40 68 87 13 38 65 84 # -1 -3 -2
Hungary 10 40 74 94 8 32 65 88 12 37 67 88 2 -3 -8 * -6 * 4 * 5 * 1 1
United States4 4 26 61 86 7 30 68 92 10 37 70 91 5 * 11 * 9 * 6 * 3 * 6 * 2 #
England-GBR 6 27 61 87 8 32 65 88 10 36 69 93 3 * 9 * 8 * 6 * 2 4 4 5 *
Australia 7 33 68 90 9 29 63 89 7 30 64 89 # -3 -3 # -2 2 1 #
Ireland 8 37 73 91 7 38 76 94 -2 1 3 3
New Zealand4 6 28 64 89 5 24 57 84 6 27 58 85 # -1 -5 * -4 * 1 3 2 1
Turkey 7 20 40 67 6 20 42 70 -1 # 2 3
Slovenia 4 22 60 90 4 27 67 93 6 32 73 95 2 * 10 * 12 * 5 * 2 * 5 * 6 * 2 *
United Arab Emirates 2 14 42 73 5 20 46 73 2 * 6 * 4 * #
Sweden 12 46 81 96 1 16 57 89 3 26 65 91 -9 * -20 * -16 * -5 * 2 * 10 * 8 * 3 *
Qatar5 2 10 29 54 3 14 36 63 1 4 * 7 * 9 *
Malaysia 2 12 36 65 3 18 45 76 2 * 5 * 9 * 10 *
Italy2 3 24 64 90 3 24 62 89 # -1 -1 -1
Thailand 2 8 28 62 3 10 29 62 1 2 1 #
Iran, Islamic Republic of5 # 4 24 59 2 8 26 55 2 12 34 63 2 * 8 * 10 * 4 # 4 * 9 * 9 *
Georgia2, 6 3 13 36 62 2 15 42 72 # 2 6 * 10 *
Bahrain 1 8 26 53 2 12 39 75 1 4 * 13 * 21 *
Norway (8)7 4 26 64 90 1 12 51 87 1 17 59 90 -3 * -9 * -5 * # # 5 * 8 * 3 *
Oman5 # 4 16 39 1 6 23 52 # 2 * 7 * 13 *
Chile5 1 5 23 57 1 7 28 63 # 1 5 * 6 *
Lebanon 1 9 38 73 # 8 35 71 # -2 -3 -3
Saudi Arabia8 1 5 20 47 # 2 11 34 # -3 * -9 * -13 *
Jordan8 # 6 26 55 # 3 18 45 # -3 * -9 * -10 *
Morocco8 # 2 12 36 # 2 14 41 # # 2 * 5 *
Benchmarking participants
Dubai-UAE 5 23 53 79 10 36 67 88 5 * 13 * 14 * 9 *
Quebec-CAN9 14 54 90 99 6 40 82 98 9 47 86 98 -5 -6 -4 -1 4 * 7 * 4 #
Florida-USA6 8 31 68 94 7 28 57 84 -1 -4 -10 * -9 *
Ontario-CAN 3 26 65 91 4 31 71 94 6 37 75 95 3 * 11 * 10 * 4 * 2 * 6 * 5 * 1
Abu Dhabi-UAE 2 12 39 71 3 14 37 65 1 2 -2 -6 *