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Indicator 11: Performance of 15-Year-Old Students on Subscales in Mathematics Literacy

G-20 Countries Included: Argentina, Australia, Brazil, Canada, France, Germany, Indonesia, Italy, Japan, Mexico, Republic of Korea, Russian Federation, Turkey, United Kingdom, United States

The U.S. mean score on the change and relationships subscale was 488, lower than the scores of the Republic of Korea, Japan, Canada, Germany, and Australia; not measurably different from those of France, the United Kingdom, and the Russian Federation; and higher than those of six other G-20 countries.

In PISA 2012, the overall performance scale in mathematics literacy was composed of four subscales, allowing a more detailed look at student performance within mathematics content areas. (Mathematics, but not reading or science, had subscales because it was the focus in the 2012 assessment.) Indicator 1 examines the mean performance of 15-year-old students on these subscales in order to highlight the relative strengths and weaknesses in mathematics both within and across the participating G-20 countries.

The mathematics subscales in PISA relate to mathematics content domains and include change and relationships, space and shape, quantity, and uncertainty and data. The range of mean scores was similar for change and relationships and space and shape, with 194- and 192-point differences between the lowest and highest scoring G-20 countries, respectively (figure 11-1). Quantity had a 175-point difference between the lowest and highest scoring G-20 countries, and uncertainty and data had the smallest range, at 154 points.

The U.S. mean score on the change and relationships subscale was 488, lower than the scores of the Republic of Korea, Japan, Canada, Germany, and Australia; not measurably different from those of France, the United Kingdom, and the Russian Federation; and higher than those of six other countries. The performance of the United States was similar on the uncertainty and data subscale, with a mean score (488) below those of the Republic of Korea, Japan, Canada, Germany, Australia, and the United Kingdom; not measurably different from those of France and Italy; and higher than those of six other countries. Of the four subscales, the performance of U.S. students was the strongest on these two.

In contrast, on the quantity subscale, eight countries (the Republic of Korea, Japan, Germany, Canada, Australia, France, the United Kingdom, and Italy) had mean scores that were higher than the U.S. mean score of 478; one country (the Russian Federation) had a score that was not measurably different from the U.S. score; and five countries had scores that were lower. Similarly, the U.S. mean score on the space and shape subscale was 463, lower than the scores of nine countries (the Republic of Korea, Japan, Canada, Germany, Australia, the Russian Federation, France, Italy, and the United Kingdom) and higher than those of the other five countries.


Definitions and Methodologie

In PISA 2012, countries were required to sample students who were between the ages of 15 years and 3 months and 16 years and 2 months at the time of the assessment and who had completed at least 6 years of formal schooling, regardless of the type of institution in which they were enrolled.

PISA scores are reported on a scale from 0 to 1,000, with the scale average fixed at 500 and the standard deviation fixed at 100. The PISA achievement scales were designed to reliably measure student achievement over time, and the metric of the scales was established for reading in 2000, mathematics in 2003, and science in 2006.

The PISA assessment of mathematics literacy includes four domains that define the mathematic content covered: changeand relationships, space and shape, quantity, and uncertaintyand data. The change and relationships content subscale includes settings such as growth of organisms, music, the cycle of seasons, weather patterns, employment levels, and economic conditions and includes the use of algebraic expressions, equations and inequalities, and tabular and graphical representations. The space and shape content subscale encompasses phenomena encoun- tered in our visual world: patterns, properties of objects, positions and orientations, representations of objects, decoding of visual information, and navigation. It utilizes geometry, spatial visualization, measurement, and algebra. The quantity content subscale incorporates aspects of quantitative reasoning, such as number sense, multiple representations of numbers, computation, mental calculation, estimation, and assessment of the reasonableness of results. The uncertainty and data content subscale is based on the theory of probability and statistics and includes recognizing the place of variation in processes, having a sense of the quantification of that variation, acknowledging uncertainty and error in measurement, and knowing about chance.

In addition to the four domains, the PISA mathematics literacy assessment collects data on three mathematical processes: formulating, employing, and interpreting. Each mathematics item is classified into one of the four content domains as well as into one of the three mathematical processes.

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