The real world and the mathematical world

Abstract

This chapter describes the way in which PISA theorises and operationalises the links between the real world and the mathematical world that are essential to mathematical literacy. Mathematical modelling is described and illustrated and the chapter shows why it is used as the cornerstone to mathematical literacy. It discusses how this concept has developed over the PISA Frameworks from 2000 to 2012, culminating in the reporting in PISA 2012 of student proficiency in the three modelling processes of Formulate, Employ and Interpret. Consistent with the orientation to mathematical modelling and mathematisation, the authenticity of PISA items is given a high priority, so that students feel that they are solving worthwhile, sensible problems. The use of real–world contexts is regarded as essential to teaching and assessing mathematics for functional purposes and in assisting in motivation of students, but potential problems of cultural appropriateness and equity (through familiarity, relevance and interest) arise for an international assessment. This is the case for countries as a whole and also for subgroups of students. Relevant research and the PISA approach to minimising potential biases are discussed.