4. Performance in Mathematics
- 60. Maths was assessed as a main domain in PISA in 2003 and 2012 with the 2006, 2009 and 2015 PISA cycles providing a briefer update.
- 61. Scotland's mean score in 2015 in the maths assessment of 491 was similar to the 2012 (498) figure.
- 62. Over time, Scotland's performance in maths fell significantly between 2003 and 2006, before stabilising. Nonetheless Scotland's performance in 2015 is statistically lower than in 2003 and 2006 ( Table A.8).
- 63. In 2015, the mean score for maths in Scotland was similar to the OECD average (490), as it has been since 2006.
- 64. Chart 4.1 below shows Scotland's score compared to the OECD average over the five waves of assessment since 2003 with 95-per-cent confidence intervals included.
Chart 4.1: Comparison of Scotland and OECD maths scores over time
Comparisons with other countries
- 65. Of the 34 other OECD countries, and three UK administrations, 14 were statistically above Scotland, 13 similar and 10 below. Of the UK administrations, England and Northern Ireland were similar to Scotland and Wales below. Table 4.1 below shows which countries performed above, similar to and below Scotland in 2015. Table A.9a, located in the annex, shows each country's score.
Table 4.1: OECD countries and UK administrations, higher than, similar to and lower than Scotland in maths
|Higher score than Scotland||Similar score to Scotland||Lower score than Scotland|
|Korea||Northern Ireland||United States|
- 66. The number of countries statistically above Scotland is the highest it has been since 2003 when comparisons became possible in maths. The number of countries statistically below Scotland is the smallest since 2003. The number of countries placed higher, below or similar to Scotland in the five waves since 2003 are shown in Chart 4.2 below.
Chart 4.2: Numbers of OECD countries and UK administrations scoring above or below Scotland in maths in PISA since 2003 
- 67. Although Scotland's performance in 2015 was similar to 2012, a number of changes in the relative position of other countries took place since the 2012 survey with countries in the following categories:
- Countries who improved their performance and moved ahead of Scotland. This applies to Denmark, Norway (previously behind Scotland) and Slovenia
- Countries which have maintained their performance, but moved ahead of Scotland as its observed (mean) score declined  . This applies to Ireland
- Countries who maintained their performance and moved from below to alongside Scotland. This applies to Italy, Luxembourg, Northern Ireland, Portugal and Spain
- Countries who improved their performance and moved from below to alongside Scotland. This applies to Sweden
- 68. Above Scotland, Korea experienced a significant decline in performance, while Australia declined in performance, but remained statistically similar to Scotland.
- 69. Among the participating non- OECD states, five were above Scotland: Singapore; Hong Kong-China; Macao-China; Chinese Tapei and B-S-J-G (China).
- 70. Two states were similar to Scotland: Viet Nam, (who moved from above Scotland following a decline in score - however the OECD believe that had the 2015 approach to scaling been applied to 2012, the apparent change for this country would have been smaller); and the Russian Federation (who improved score to move from below Scotland). Thirty countries were below Scotland.
- 71. Singapore achieved the highest score of all participating countries (as in science) ( Table A.9b). However, above Scotland, Singapore, Chinese Tapei and Hong Kong-China all experienced significant declines in their score. In the case of Singapore and Chinese Tapei, the OECD believe that the change between 2012 and 2015 would not have been as great if 2015 scaling had been applied to 2012. Further details on the countries affected by this are provided in the Annex to Volume I of the OECD report.
Distribution of scores
- 72. Scotland's spread of attainment, measured by the standard deviation (84 points) was similar to 2012, but continued to be less than the OECD average (89 points). Five countries had a narrower distribution, eight similar and 24 greater. Scotland's spread of attainment in 2015 was similar to 2012 (86 points) but was less than 2009 (93 points).
High and low achievers
Low performance (below Level 2)
- 73. The proportion of Scotland's students below Level 2, the OECD's baseline of ability to participate effectively in society, was 20.5 per cent, statistically smaller than the OECD average of 23.4 per cent. The proportion in Scotland in 2015 was similar to the proportion in 2012 (18.5 per cent).
High performance (Levels 5 and 6)
- 74. At the other end of the distribution, the proportion of Scotland's students who were higher achievers (Level 5 and above) was 8.6 per cent, lower than the OECD average of 10.6 per cent, and also lower than Scotland's proportion in 2012 (10.6 per cent).
- 75. Table A.10 shows each OECD country and UK administration's distribution of scores by proficiency level in maths.
- 76. Boys' and girls' performances in maths were statistically similar. The average score in maths was 488 for female students, and 495 for male students. The gap (seven points) was similar to the OECD average (eight points).
Change over time
- 77. The gap between boys and girls in maths was statistically significant in 2012, but this was no longer the case in 2015. Performance for boys fell 11 points compared to 2012. The three-point fall for girls was not significant.
High and low performers
- 78. In terms of the gender share of higher and lower achievers, 7.5 per cent of girls and 9.6 per cent of boys achieved Level 5 and above (no significant difference) and 19.6 per cent of boys and 21.4 per cent of girls were below Level 2 (no significant difference).
- 79. The share of higher performers among boys in Scotland was larger than the OECD (6.8 per cent), but girls had a smaller share than the OECD (9.9 per cent)
- 80. The share of lower performers among boys in Scotland was smaller than the OECD (24.4 per cent). However, for girls, lower performers had a significantly larger share than across the OECD (15.5 per cent).
- 81. The share of variation in test scores that was explained by students' background was 11.1 per cent. This was similar to the OECD average and 2012 (12.9 per cent), but was less than the 2009 figure of 16.3 per cent.
- 82. For maths, the OECD calculated the impact of a one-point improvement (the gradient) in the Index of Economic, Social & Cultural Status ( ESCS) to have been around 33 score points. This was similar to the OECD average (mean = 37 points). Scotland's figure was similar to 2012 but remained a reduction on the estimated impact in the 2009 survey (45 points) suggesting a sustained reduction in the gap between disadvantaged and more affluent pupils.
- 83. The average score gap between the 5 th and 95 th percentile by ESCS was 87 points - again equivalent to around three years of schooling.