People from many countries have expressed interest in the tests students take for the Programme for International Student Assessment (PISA). Learning Mathematics for Life examines the link between the PISA test requirements and student performance. It focuses specifically on the proportions of students who answer questions correctly across a range of difficulty. The questions are classified by content, competencies, context and format, and the connections between these and student performance are then analysed.
This analysis has been carried out in an effort to link PISA results to curricular programmes and structures in participating countries and economies. Results from the student assessment reflect differences in country performance in terms of the test questions. These findings are important for curriculum planners, policy makers and in particular teachers - especially mathematics teachers of intermediate and lower secondary school classes.
-Foreword Chapter 1. PISA 2003: Introduction -Introduction -Purpose -Background -Organisation of the report Reader's Guide -Abbreviations used in this report -Technical definitions -Further documentation Chapter 2. Main Features of the PISA Mathematics Theoretical Framework -Introduction -Mathematical literacy -Mathematical content in PISA - the use of overarching ideas --Change and relationships --Space and shape --Quantity --Uncertainty -Overarching ideas and traditional topics -Context - setting the mathematical problem to be solved -The competencies --Mathematical thinking and reasoning --Mathematical argumentation --Modelling --Problem posing and solving --Representation --Symbols and formalism --Communication --Aids and tools -Competency clusters --Reproduction cluster --Connections cluster --Reflection cluster -Conclusion Chapter 3. A Question of Difficulty - Questions from PISA 2003 -Introduction -Describing growth in mathematical literacy -The PISA scale and difficulty -Examples of the easiest mathematical questions from PISA 2003 -Examples of moderate to difficult mathematics questions fro PISA 2003 -Examples of difficult mathematics questions from PISA 2003 -Conclusion Chapter 4. Comparison of Country Level Results -Introduction -Cross-country differences in curriculum -Groupings of countries by patterns in item responses -Patterns in mathematics context -Performance and grade levels -Competency clusters and mathematics performance -Context and mathematics performance -Conclusion Chapter 5. The Roles of Language and Item Formats -Introduction -The use of language in PISA mathematics questions and student performance -Word-count and question difficulty across countries -Word-count and the context in which a question is presented -Word-count and competencies required to answer a question -Word-count and content -Item-format and mathematics performance -Item format, the three C's and word-count -Differences in item-format and omission rates -Conclusion Chapter 6. Mathematical Problem Solving and Differences in Students' Understanding -Introduction -General features of mathematical problem solving in PISA -Making the problem-solving cycle visible throughcase studies of questions -Students' mathematical understandings and item scoring -Students' understanding of proportional reasoning -Students' understanding of symbolic algebra -Students' understanding of average -Conclusion References Annex A1 - Pisa 2003 Mathematics Assessments - Characteristics of Questions Used Annex A2 - Other Examples of Pisa Mathematics Questions that were not Used in the Pisa 2003 Mathematics Assessment Annex A3 - Traditional Domains and Pisa Items Annex A4 - Word-Count and the 3 Cs - Analysis of Variance Annex A5 - Analysis of Variance Related to Item Format Annex A6 - Mathematics Expert Group