' Streefland is to be congratulated on his thoroughness in presenting a far reaching study with many ramifications. I predict that any reader will find many of the author's premises as well as generalizations thought evoking. ' Zentrallblatt fur Didaktik der Mathematik, 5

• and overview.- Notes Introduction.- 1 Description of the fraction problem.- 1.1 Introduction and overview.- 1.2 Pointing out the problem.- 1.3 Description of the problem.- 1.4 Overview and outlook.- Notes chapter 1.- 2 Currents-standpoint-proposal.- 2.1 Introduction and overview.- 2.2 Currents.- 2.3 Standpoint.- 2.4 Proposal.- 2.5 Review and outlook.- Notes chapter 2.- 3 The context of the research.- 3.1 Introduction and overview.- 3.2 Starting from the construction principle.- 3.3 Development research.- 3.4 Design and method.- 3.5 The research group.- 3.6 The researcher’s position.- 3.7 Conclusion.- Notes chapter 3.- 4 The course in theory and practice.- 4.1 Introduction and overview.- 4.2 Global outline of the fraction course.- 4.3 Producing fractions: the teaching experiment.- 4.4 In view of mathematization.- 4.5 Review and outlook.- Notes chapter 4.- 5 Individual portraits of the fraction researchers.- 5.1 Introduction and overview.- 5.2 Indicators for the (improvement in) quality of the individual learning processes.- 5.3 The student portraits.- 5.4 Review and outlook.- Notes chapter 5.- 6 Internal evaluation of the learning process.- 6.1 Introduction and overview.- 6.2 Yielding to and building up resistance to IN-distractors.- 6.3 Progression in schematizating through abbreviations.- 6.4 Models and diagrams.- 6.5 Acquiring representations fitting formally posed problems.- 6.6 Constructions and productions on a symbolic level.- 6.7 The framework of the level-theory and the course construction.- 6.8 Review and outlook.- Notes chapter 6.- 7 External or summative evaluation.- 7.1 Introduction and overview.- 7.2 Weighing the groups.- 7.3 Comparing and characterizing the programs.- 7.4 The tests.- 7.5 Results.- 7.6 Summary and conclusions.- 7.7 Realistic andmechanistic: a difference in effects?.- 7.8 A look ahead.- Notes chapter 7.- 8 Theoretical review.- 8.1 Introduction and overview.- 8.2 Teaching and learning fractions.- 8.3 Conclusion.- Notes chapter 8.- Epilogue: Sketch of a new course -fractions, an integrated perspective-.

' Streefland is to be congratulated on his thoroughness in presenting a far reaching study with many ramifications. I predict that any reader will find many of the author's premises as well as generalizations thought evoking. ' Zentrallblatt fur Didaktik der Mathematik, 5

• and overview.- Notes Introduction.- 1 Description of the fraction problem.- 1.1 Introduction and overview.- 1.2 Pointing out the problem.- 1.3 Description of the problem.- 1.4 Overview and outlook.- Notes chapter 1.- 2 Currents-standpoint-proposal.- 2.1 Introduction and overview.- 2.2 Currents.- 2.3 Standpoint.- 2.4 Proposal.- 2.5 Review and outlook.- Notes chapter 2.- 3 The context of the research.- 3.1 Introduction and overview.- 3.2 Starting from the construction principle.- 3.3 Development research.- 3.4 Design and method.- 3.5 The research group.- 3.6 The researcher’s position.- 3.7 Conclusion.- Notes chapter 3.- 4 The course in theory and practice.- 4.1 Introduction and overview.- 4.2 Global outline of the fraction course.- 4.3 Producing fractions: the teaching experiment.- 4.4 In view of mathematization.- 4.5 Review and outlook.- Notes chapter 4.- 5 Individual portraits of the fraction researchers.- 5.1 Introduction and overview.- 5.2 Indicators for the (improvement in) quality of the individual learning processes.- 5.3 The student portraits.- 5.4 Review and outlook.- Notes chapter 5.- 6 Internal evaluation of the learning process.- 6.1 Introduction and overview.- 6.2 Yielding to and building up resistance to IN-distractors.- 6.3 Progression in schematizating through abbreviations.- 6.4 Models and diagrams.- 6.5 Acquiring representations fitting formally posed problems.- 6.6 Constructions and productions on a symbolic level.- 6.7 The framework of the level-theory and the course construction.- 6.8 Review and outlook.- Notes chapter 6.- 7 External or summative evaluation.- 7.1 Introduction and overview.- 7.2 Weighing the groups.- 7.3 Comparing and characterizing the programs.- 7.4 The tests.- 7.5 Results.- 7.6 Summary and conclusions.- 7.7 Realistic andmechanistic: a difference in effects?.- 7.8 A look ahead.- Notes chapter 7.- 8 Theoretical review.- 8.1 Introduction and overview.- 8.2 Teaching and learning fractions.- 8.3 Conclusion.- Notes chapter 8.- Epilogue: Sketch of a new course -fractions, an integrated perspective-.

' Streefland is to be congratulated on his thoroughness in presenting a far reaching study with many ramifications. I predict that any reader will find many of the author's premises as well as generalizations thought evoking. ' Zentrallblatt fur Didaktik der Mathematik, 5

• and overview.- Notes Introduction.- 1 Description of the fraction problem.- 1.1 Introduction and overview.- 1.2 Pointing out the problem.- 1.3 Description of the problem.- 1.4 Overview and outlook.- Notes chapter 1.- 2 Currents-standpoint-proposal.- 2.1 Introduction and overview.- 2.2 Currents.- 2.3 Standpoint.- 2.4 Proposal.- 2.5 Review and outlook.- Notes chapter 2.- 3 The context of the research.- 3.1 Introduction and overview.- 3.2 Starting from the construction principle.- 3.3 Development research.- 3.4 Design and method.- 3.5 The research group.- 3.6 The researcher’s position.- 3.7 Conclusion.- Notes chapter 3.- 4 The course in theory and practice.- 4.1 Introduction and overview.- 4.2 Global outline of the fraction course.- 4.3 Producing fractions: the teaching experiment.- 4.4 In view of mathematization.- 4.5 Review and outlook.- Notes chapter 4.- 5 Individual portraits of the fraction researchers.- 5.1 Introduction and overview.- 5.2 Indicators for the (improvement in) quality of the individual learning processes.- 5.3 The student portraits.- 5.4 Review and outlook.- Notes chapter 5.- 6 Internal evaluation of the learning process.- 6.1 Introduction and overview.- 6.2 Yielding to and building up resistance to IN-distractors.- 6.3 Progression in schematizating through abbreviations.- 6.4 Models and diagrams.- 6.5 Acquiring representations fitting formally posed problems.- 6.6 Constructions and productions on a symbolic level.- 6.7 The framework of the level-theory and the course construction.- 6.8 Review and outlook.- Notes chapter 6.- 7 External or summative evaluation.- 7.1 Introduction and overview.- 7.2 Weighing the groups.- 7.3 Comparing and characterizing the programs.- 7.4 The tests.- 7.5 Results.- 7.6 Summary and conclusions.- 7.7 Realistic andmechanistic: a difference in effects?.- 7.8 A look ahead.- Notes chapter 7.- 8 Theoretical review.- 8.1 Introduction and overview.- 8.2 Teaching and learning fractions.- 8.3 Conclusion.- Notes chapter 8.- Epilogue: Sketch of a new course -fractions, an integrated perspective-.