The PISA 2012 mathematics framework explains the theoretical underpinnings of the PISA mathematics assessment, including a new formal definition of mathematical literacy, the mathematical processes which students undertake when using mathematical literacy, and the fundamental mathematical capabilities which underlie those processes. The framework describes how mathematical content knowledge is organised into four content categories and outlines the content knowledge that is relevant to an assessment of 15-year-old students. It describes four categories of contexts in which students will face mathematical challenges. The framework specifies the proportions of items from each of the four content and context categories, each response format and each process, and describes the rotating booklet designs and questionnaires. Items of a range of difficulty are required. The optional computer-based assessment for mathematics is described, with discussion of the rationale and potential for future development. The categorisations are illustrated with seven units used in PISA surveys and field trials. Multiple quality control measures are described. The PISA assessment will measure how effectively countries are preparing students to use mathematics in every aspect of their personal, civic and professional lives, as part of their constructive, engaged and reflective citizenship.