Proficiency at Level 2

At Level 2, students can use basic algorithms, formulae, procedures or conventions to solve problems involving whole numbers – e.g. to compute the approximate price of an object in a different currency or to compare the total distance across two alternative routes. They can interpret and recognise situations in contexts that require no more than direct inference, extract relevant information from a single source and make use of a single representational mode (such as graphs, tables, equations, etc). Students at this level are capable of making literal interpretations of results.

More than 90 % of students in Beijing, Shanghai, Jiangsu and Zhejiang (China) (hereafter “B-S-J-Z [China]), Hong Kong (China), Macao (China) and Singapore, and close to 90 % in Estonia achieved this benchmark. On average across OECD countries, 76 % of students attained Level 2 or higher (that is, were proficient at Level 2, 3, 4, 5 or 6; Figure I.6.1 and Table I.B1.2). Meanwhile, fewer than one in ten students in the Dominican Republic (9.4 %), and only 19 % of students in Panama and the Philippines attained this baseline level of mathematics proficiency. In 21 other countries, more than 20 % but less than 50 % of 15-year-old students attained this level of proficiency.

Proficiency at Level 3

At Level 3, students can execute clearly described procedures, including those that require sequential decisions. They typically show some ability to handle percentages, fractions and decimal numbers, and to work with proportional relationships. Their interpretations are sufficiently sound to be the basis for building a simple model or for selecting and applying simple problem-solving strategies. Students at this level can interpret and use representations based on different information sources and reason directly from them. Their solutions show that they have engaged in basic interpretation and reasoning.

Across OECD countries, 54 % of students were proficient at Level 3 or higher. More than 90 % of students were proficient at Level 3 or higher in B-S-J-Z (China); and at least two out of three students in Estonia, Hong Kong (China), Japan, Korea, Macao (China), Singapore and Chinese Taipei attained this level. This shows that in some education systems, virtually all children develop a solid foundation in mathematics. In contrast, in 24 countries and economies with comparable data, three out of four students did not attain this level (Figure I.6.1 and Table I.B1.2).

Proficiency at Level 4

At Level 4, students can work effectively with explicit models on complex, concrete situations that may involve constraints or call for making assumptions. They can select and integrate different representations, including symbolic representations (such as equations and formulae), linking them directly to aspects of real-world situations. Students at this level can reason with some insight. They can construct and communicate explanations and arguments based on their interpretations, reasoning and actions.

Across OECD countries, 29 % of students performed at proficiency Level 4, 5 or 6. More than one in two students in B-S-J-Z (China) (73 %), Singapore (63 %), Macao (China) (58 %) and Hong Kong (China) (55 %) performed at one of these levels. Between 40 % and 50 % of students in Chinese Taipei (47 %), Korea (44 %), Japan (43 %), the Netherlands (42 %) and Estonia (40 %) scored at or above Level 4. By contrast, in 27 participating countries and economies with comparable data – including all of the Latin American countries that participated in PISA 2018 – less than 10 % of students attained this level (Figure I.6.1 and Table I.B1.2).

Proficiency at Level 5

At Level 5, students can develop and work with models for complex situations, identifying constraints and specifying assumptions. They can select, compare and evaluate appropriate problem-solving strategies for dealing with complex problems related to these models. Students at this level can work strategically using broad, well-developed thinking and reasoning skills, appropriate linked representations, symbolic and formal characterisations, and insights pertaining to these situations. They have begun to develop the ability to reflect on their work, and to communicate conclusions and interpretations in written form.

Across OECD countries, 11 % of students were top performers in 2018, meaning that they were proficient at Level 5 or 6. Amongst all countries and economies that participated in PISA 2018, B-S-J-Z (China) had the largest proportion of top performers (44 %), followed by five other Asian countries and economies: Singapore (37 %), Hong Kong (China) (29 %), Macao (China) (28 %), Chinese Taipei (23 %) and Korea (21 %). The strong performance of these Asian countries dispels the notion that children in these countries merely memorise subject-matter content: Level 5 proficiency requires students to master a high level of conceptual understanding and mathematical reasoning. In all remaining countries and economies, less than 20 % of students attained this level of proficiency in mathematics.

Countries with similar mean performance may have significantly different shares of students who are able to perform at the highest levels in PISA (Figure I.6.1 and Table I.B1.2). A smaller share of top-performing students, compared to countries of similar average performance, means that student performance varies more narrowly around the mean. For example:

• Estonia (mean score: 523 points) had significantly fewer top-performing students (15.5 %) compared to Japan and Korea (mean scores: 527 and 526 points, respectively; top performers: 18.3 % and 21.4 %, respectively)

• Germany and Ireland performed similarly, on average (mean score of 500 points in both countries), but 13.3 % of students in Germany were top performers, compared to just 8.2 % in Ireland

• Croatia and Israel also performed similarly, on average (mean scores of 464 points and 463 points, respectively); yet 5.1 % of students in Croatia were top performers compared to 8.8 % of students in Israel.

Proficiency at Level 6

Students at Level 6 on the PISA mathematics scale can successfully complete the most difficult PISA items. These students can conceptualise, generalise and use information based on their investigations and modelling of complex problem situations, and can use their knowledge in relatively non-standard contexts. They can link different information sources and representations together and move flexibly amongst them. Students at this level are capable of advanced mathematical thinking and reasoning. These students can apply this insight and understanding, along with a mastery of symbolic and formal mathematical operations and relationships, to develop approaches and strategies for addressing novel situations. Students at this level can reflect on their actions, can formulate and precisely communicate those actions and reflections and can explain why they were applied to the original situation.

On average across OECD countries, only 2.4 % of students attained Level 6. About one in six students scored at this level in B-S-J-Z (China) (16 %), and about one in seven students in Singapore (14 %). In Hong Kong (China), Korea, Macao (China) and Chinese Taipei, between 5 % and 10 % of students attained proficiency Level 6. In 36 participating countries and economies, between 1 % and 5 % of students performed at this level; in 21 countries/economies, between 0.1 % and 1 % of students scored at Level 6; and in 15 other countries/economies, fewer than 1 in 1 000 students (0.1 %) performed at Level 6 (Figure I.6.1 and Table I.B1.2).

Proficiency at Level 1

At Level 1, students can answer mathematics questions involving familiar contexts where all of the relevant information is present and the questions are clearly defined. They are able to identify information and carry out routine procedures according to direct instructions. They can only perform actions that are obvious and that follow immediately from the given stimuli.

On average across OECD countries in 2018, 15 % of students were proficient only at Level 1. In B-S-J-Z (China) (2.4 %), Macao (China) (5.0 %), Singapore (7.1 %) and Hong Kong (China) (9.2 %), less than 10 % of students performed at or below Level 1 (Figure I.6.1 and Table I.B1.2). But in 21 countries and economies, Level 1 was the median level of proficiency, meaning that the score which divides 15-year-old students into two equal halves – 50 % scoring above it, and 50 % scoring below it – fell within the range of Level 1.

Proficiency below Level 1

Some 9.1 % of students on average across OECD countries scored below Level 1 in mathematics. By contrast, in the Dominican Republic (69 %), the Philippines (54 %) and Panama (54 %), more than one in two students scored below Level 1, the lowest described level of proficiency in PISA. In 26 participating countries and economies, between 20 % and 50 % of students did not reach Level 1 on the mathematics scale.

The PISA mathematics test included too few tasks of the appropriate difficulty that would help describe an additional level of proficiency below Level 1. However, based on the few PISA 2012 mathematics items whose difficulty lies below Level 1 (four of which were also included in the PISA 2018 mathematics assessment), students who score below Level 1, but not too far from it, can be expected to perform some direct and straightforward mathematical tasks. These include reading a single value from a well-labelled chart or table, where the labels on the chart match the words in the stimulus and question, so that the selection criteria are clear and the relationship between the chart and the aspects of the context depicted are evident. They may also be able to perform simple arithmetic calculations with whole numbers by following clear and well-defined instructions.

Given the large number of students who scored at these levels in many PISA-participating countries, the group of international experts working on the PISA 2021 test is trying to broaden the range of fundamental mathematical capabilities that PISA assesses, based partly on approaches piloted in the PISA for Development project (OECD, 2018_[6]).

All PISA-participating countries and economies have students who score at or below Level 1, but the largest proportions of students who score at these levels are found in the lowest-performing countries. In some cases, countries with similar mean performance may have significantly different shares of students who score below Level 2 in mathematics. For example, in Estonia, whose mean performance in 2018 (523 score points) was not significantly different from that of Korea or the Netherlands, only 10.2 % of students scored at or below Level 1, while 15.0 % did so in Korea and 15.8 % in the Netherlands. This shows that in Korea and the Netherlands, student performance in mathematics varied more widely than in Estonia, despite similar average performance. And while mean performance in Germany and Ireland was similar (500 score points), the percentage of low achievers in Germany (21.1 %) was about 5 percentage points higher than that in Ireland (15.7 %).