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In PISA 2012, the major subject was mathematics literacy, defined as:

An individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognize the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged, and reflective citizens(OECD 2013, p. 25).

More specifically, the PISA mathematics assessment looks at four mathematical content categories and three mathematical process categories:

Mathematical content categories (OECD 2013, pp. 33–35):

- Change and relationship: Can students model change and relationships with the appropriate functions and equations?
- Space and shape: Can students understand perspective, create and read maps, and manipulate 3D objects?
- Quantity: Are 15-year-olds able to comprehend multiple representations of numbers, engage in mental calculation, employ estimation, and assess the reasonableness of results?
- Uncertainty and data: Can students use probability and statistics and other techniques of data representation and description to mathematically describe, model, and interpret uncertainty?

Mathematical process categories (OECD 2013, pp. 28–30):

- Formulate: Can 15-year-olds recognize and identify opportunities to use mathematics and then provide mathematical structure to a problem presented in some contextualized form in order to formulate situations mathematically?
- Employ: Are students able to employ mathematical concepts, facts, procedures, and reasoning to solve mathematically formulated problems and obtain mathematical conclusions?
- Interpret: Can students interpret, apply, and evaluate mathematical outcomes in order to determine whether results are reasonable and make sense in the context of the problem?

The PISA mathematics framework was updated for the 2012 assessment. The revised framework is intended to clarify the mathematics relevant to 15-year-old students, while ensuring that the items developed remain set in meaningful and authentic contexts, and defines the mathematical processes in which students engage as they solve problems. These processes, described above, are being used for the first time in 2012 as a primary reporting dimension. Although the framework has been updated, it is still possible to measure trends in mathematics literacy over time, as the underlying construct is intact.

Mathematics literacy is reported both in terms of proficiency levels and scale scores (reported on a scale of 0–1,000). Exhibit M1 describes the six mathematics literacy proficiency levels and their respective cut scores for both the paper-based mathematics literacy assessment and the computer-based mathematics assessment.

**Exhibit M1. Description of PISA proficiency levels on mathematics literacy scale: 2012**

Proficiency level and lower cut score | Task descriptions |

Level 6 669 | At level 6, students can conceptualize, generalize, and utilize information based on their investigations and modeling of complex problem situations, and can use their knowledge in relatively non-standard contexts. They can link different information sources and representations and flexibly translate among 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 new approaches and strategies for attacking novel situations. Students at this level can reflect on their actions, and can formulate and precisely communicate their actions and reflections regarding their findings, interpretations, arguments and the appropriateness of these to the original situations. |

Level 5 607 | 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 characterizations, and insight pertaining to these situations. They begin to reflect on their work and can formulate and communicate their interpretations and reasoning. |

Level 4 545 | At level 4, students can work effectively with explicit models for complex concrete situations that may involve constraints or call for making assumptions. They can select and integrate different representations, including symbolic, linking them directly to aspects of real-world situations. Students at this level can utilize their limited range of skills and can reason with some insight, in straightforward contexts. They can construct and communicate explanations and arguments based on their interpretations, arguments, and actions. |

Level 3 482 | At level 3, students can execute clearly described procedures, including those that require sequential decisions. Their interpretations are sufficiently sound to be a base 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. They typically show some ability to handle percentages, fractions and decimal numbers, and to work with proportional relationships. Their solutions reflect that they have engaged in basic interpretation and reasoning. |

Level 2 420 | At level 2, students can interpret and recognize situations in contexts that require no more than direct inference. They can extract relevant information from a single source and make use of a single representational mode. Students at this level can employ basic algorithms, formulae, procedures, or conventions to solve problems involving whole numbers. They are capable of making literal interpretations of the results. |

Level 1 358 | At level 1, students can answer questions involving familiar contexts where all relevant information is present and the questions are clearly defined. They are able to identify information and to carry out routine procedures according to direct instructions in explicit situations. They can perform actions that are almost always obvious and follow immediately from the given stimuli. |

NOTE: To reach a particular proficiency level, a student must correctly answer a majority of items at that level. Students were classified into mathematics literacy levels according to their scores. Cut scores in the exhibit are rounded; exact cut scores are provided in table AA2. Scores are reported on a scale from 0 to 1,000.

SOURCE: Organization for Economic Cooperation and Development (OECD), Program for International Student Assessment (PISA), 2012.

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