PISA Learning Mathematics for Life : A Perspective from PISA.

Foreword......Page 5
Table of Contents......Page 7
Introduction......Page 13
BACKGROUND......Page 14
ORGANISATION OF THE REPORT......Page 15
Reader’s Guide......Page 17
Main Features of the PISA Mathematics: Theoretical Framework......Page 19
INTRODUCTION......Page 20
MATHEMATICAL LITERACY......Page 21
MATHEMATICAL CONTENT IN PISA – THE USE OF OVERARCHING IDEAS......Page 23
OVERARCHING IDEAS AND TRADITIONAL TOPICS......Page 29
CONTEXT – SETTING THE MATHEMATICAL PROBLEM TO BE SOLVED......Page 30
THE COMPETENCIES......Page 33
COMPETENCY CLUSTERS......Page 36
CONCLUSION......Page 38
A Question of Difficulty: Questions from PISA 2003......Page 41
DESCRIBING GROWTH IN MATHEMATICAL LITERACY: HOW DIFFICULT IS THE QUESTION AND WHERE DOES IT FIT ON THE PISA MATHEMATICS SCALE?......Page 42
THE PISA SCALE AND DIFFICULTY......Page 43
EXAMPLES OF THE EASIEST MATHEMATICS QUESTIONS FROM PISA 2003......Page 48
EXAMPLES OF MODERATE TO DIFFICULT MATHEMATICS QUESTIONS FROM PISA 2003......Page 64
EXAMPLES OF DIFFICULT MATHEMATICS QUESTIONS FROM PISA 2003......Page 98
CONCLUSION......Page 117
Comparison o fCountry Level Results......Page 119
INTRODUCTION......Page 120
CROSS COUNTRY DIFFERENCES IN CURRICULUM......Page 121
GROUPINGS OF COUNTRIES BY PATTERNS IN ITEM RESPONSES......Page 122
PATTERNS IN MATHEMATICS CONTENT......Page 124
PERFORMANCE AND GRADE LEVELS......Page 131
COMPETENCY CLUSTERS AND MATHEMATICS PERFORMANCE......Page 134
CONTEXT AND MATHEMATICS PERFORMANCE......Page 137
CONCLUSION......Page 139
The Roles of Language and Item Formats......Page 141
THE USE OF LANGUAGE IN PISA MATHEMATICS QUESTIONS AND STUDENT PERFORMANCE......Page 142
WORD-COUNT AND QUESTION DIFFICULTY ACROSS COUNTRIES......Page 143
WORD-COUNT AND THE CONTEXT IN WHICH A QUESTION IS PRESENTED......Page 145
WORD-COUNT AND COMPETENCIES REQUIRED TO ANSWER THE QUESTION......Page 148
WORD-COUNT AND CONTENT......Page 149
ITEM-FORMAT AND MATHEMATICS PERFORMANCE......Page 151
ITEM-FORMAT AND ITEM DIFFICULTY ACROSS COUNTRIES......Page 152
ITEM-FORMAT, THE THREE C’S AND WORD-COUNT......Page 153
DIFFERENCES IN ITEM-FORMAT AND OMISSION RATES......Page 154
CONCLUSION......Page 156
Mathematical Problem Solving and Differences in Students’ Understanding......Page 159
GENERAL FEATURES OF MATHEMATICAL PROBLEM SOLVING IN PISA......Page 160
MAKING THE PROBLEM-SOLVING CYCLE VISIBLE THROUGH CASE STUDIES OF QUESTIONS......Page 162
STUDENTS’ MATHEMATICAL UNDERSTANDINGS AND ITEM SCORING......Page 169
STUDENTS’ UNDERSTANDING OF PROPORTIONAL REASONING......Page 179
STUDENTS’ UNDERSTANDING OF SYMBOLIC ALGEBRA......Page 184
STUDENTS’ UNDERSTANDING OF AVERAGE......Page 187
CONCLUSION......Page 189
REFERENCES......Page 191
Annex A1 - \rPISA 2003 MATHEMATICS ASSESSMENTS: CHARACTERISTICS OF QUESTIONS USED......Page 195
Annex A2 - \rOTHER EXAMPLES OF PISA MATHEMATICS QUESTIONS THAT WERE NOT USED IN THE PISA 2003 MATHEMATICS ASSESSMENT......Page 233
Annex A3 - TRADITIONAL DOMAINS AND PISA ITEMS\r......Page 237
Annex A4 - WORD-COUNT AND THE 3 Cs – ANALYSIS OF VARIANCE......Page 239
Annex A5 - ANALYSIS OF VARIANCE RELATED TO \rITEM FORMAT......Page 243
Annex A6 - Mathematics Expert Group\r......Page 247