Average score is higher than U.S. average score at the .05 level of statistical significance.

Average score is lower than U.S. average score at the .05 level of statistical significance.

― Not available.

† Not applicable.

# Rounds to zero.

*p<.05. Change in average scores is significant at the .05 level of statistical significance.

¹ The change in average score is calculated by subtracting the 2007 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 National Defined Population covers less than 90 percent of the National Target Population (but at least 77 percent) in 2015.

⁵ The number in parentheses indicates years of school not grade in schooling.

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

⁷ Reservations about reliability because the percentage of students with achievement too low to estimate exceeds 15 percent but does not exceed 25 percent in 2015.

⁸ Reservations about reliability because the percentage of students with achievement too low to estimate exceeds 25 percent in 2015.

⁹ Did not satisfy guidelines for sample participation in 2015.

NOTE: Education systems are ordered by 2015 average score in reasoning. 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. 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. Trend results for Kuwait do not include private schools. Trend results for Lithuania do not include students taught in Polish or in Russian.

  For 2007, Georgia and Lithuania had a National Target Population that did not include all of the International Target Population; the United States and Ontario-CAN had a National Defined Population that covered 90-95 percent of the National Target Population; Quebec-CAN had a National Defined Population that covered less than 90 percent of the National Target Population (but at least 77 percent); England-GBR, Hong Kong-CHN, and the United States met guidelines for sample participation only after replacement schools were included; Dubai-UAE nearly satisfied guidelines for sample participation rates after replacement schools were included; and Kuwait and Dubai-UAE tested the same cohort of students as other education systems, but later in the assessment year at the beginning of the next school year.

  For 2011, Georgia, Lithuania, 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 12b available at http://nces.ed.gov/timss/timss2015/timss2015_table12b.asp.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007, 2011, and 2015.