PISA Take the Test: Sample Questions from OECD’s PISA Assessments

CHAPTER 3 Mathematics sample tasks (p. 97-98)

The mathematics questions in PISA aim at assessing the capacity of students to draw upon their mathematical competencies to meet the challenges of their current and future daily livep. Citizens have to use mathematics in many daily situations, such as when consulting media presenting information on a wide range of subjects in the form of tables, charts and graphs, when reading timetables, when carrying out money transactions and when determining the best buy at the market.

To capture this broad conception, PISA uses a concept of mathematical literacy that is concerned with the capacity of students to analyse, reason and communicate effectively as they pose, solve and interpret mathematical problems in a variety of situations including quantitative, spacial, probabilistic or other mathematical conceptp. Mathematics was the focus of the PISA 2003 survey, meaning that more time was dedicated to mathematics testing which allowed a more detailed analysis of the resultp. The 2006 mathematics results are compared to the 2003 benchmarks, as will be the case for results from future surveyp. In 2000 and 2006, mathematics was also assessed, but less comprehensively than in 2003. Key assessment characteristics were established for the 2000 survey and underwent minor modifications for the following surveyp.

Mathematics is defined in relation to three dimensions: the content, the mathematical processes and the situationp. The first dimension, the content of mathematics, is defined primarily in terms of "overarching ideas" and only secondarily in relation to curricular strandp. Strands such as numbers, algebra and geometry are commonly used in curricula. The overarching ideas used in PISA reflect the orientation towards reallife situationp. For the first survey in 2000 two overarching ideas were assessed: change and growth and space and shape. These two were selected to allow a wide range of curriculum strands to be represented, without giving undue weight to number skillp. In the assessments in 2003 and 2006 four overarching ideas were assessed: quantity, space and shape, change and relationships and uncertainty.

This is in line with the contemporary view of mathematics as the science of patterns in a general sense. The PISA overarching ideas reflect this: patterns in space and shape, patterns in change and relationships, patterns in quantity form central and essential concepts for any description of mathematics, and they form the heart of any curriculum, at any level. But to be literate in mathematics means more. Dealing with uncertainty from a mathematical and scientific perspective is essential. For this reason, elements of probability theory and statistics give rise to the fourth overarching idea: uncertainty.

The second dimension is the process of mathematics as defined by general mathematical competenciep. Questions are organised into three "competency clusters" (reproduction, connections and reflection) defining the type of thinking skill needed. The first cluster – reproduction - consists of simple computations or definitions of the type most familiar in conventional mathematics assessmentp. The second requires connections to be made to solve relatively straightforward problemp.

The third competency cluster – reflection – consists of mathematical thinking, generalisation and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose their own problemp. In general, these processes are in ascending order of difficulty, but it does not follow that one must be mastered in order to progress to the other: it is possible for example to engage in mathematical thinking without being good at computationp. These competencies are applied as part of the fundamental process of mathematisation that students use to solve real-life problemp. Mathematisation can be broken up into five steps: