,Table of contents
TABLE OF CONTENTS ..................................................................................................................... 2
CHAPTER 1: VIEWS ON AND APPROACHES TO (RESEARCH IN) MATHEMATICS EDUCATION .............. 5
1. MATHEMATICS: VIEWS, DEFINITIONS ............................................................................................... 5
MATHEMATICS: DIFFERENT VIEWS .................................................................................................................. 5
MATHEMATICS: DEFINING CHARACTERISTICS .................................................................................................... 5
DIFFERENT VIEWS AND DEFINITIONS ............................................................................................................... 6
2. MATHEMATICS EDUCATION: VIEWS, APPROACHES............................................................................... 6
LEARNING AND TEACHING: THREE PERSPECTIVES ............................................................................................... 6
LEARNING AND TEACHING MATHEMATICS: THREE VIEWS ..................................................................................... 7
1. MECHANISTIC APPROACH ...................................................................................................................... 7
2. STRUCTURAL APPROACH........................................................................................................................ 7
3. REALISTIC APPROACH ............................................................................................................................ 8
MATHEMATICAL PROFICIENCY........................................................................................................................ 9
THREE APPROACHES: SOME GENERAL COMMENTS ............................................................................................. 9
3. MATHEMATICS EDUCATION AS A RESEARCH DISCIPLINE....................................................................... 10
MATHEMATICS EDUCATION: RESEARCH DISCIPLINE ........................................................................................... 10
RESEARCH METHODS: RICH DIVERSITY ........................................................................................................... 10
CHAPTER 2: EARLY MATHEMATICAL ABILITIES .............................................................................. 10
1. EARLY MATHEMATICAL ABILITIES .................................................................................................. 10
MULTI-DIMENSIONAL ................................................................................................................................ 11
CONCLUSION ........................................................................................................................................... 14
2. DEVELOPMENT OF EARLY MATHEMATICAL ABILITIES ........................................................................... 14
DEVELOPMENTAL TRAJECTORIES .................................................................................................................. 14
NUMBER AND PATTERNING: EMPIRICAL EVIDENCE ........................................................................................... 15
CONCLUSION ........................................................................................................................................... 16
3. EARLY MATHEMATICS EDUCATION ................................................................................................. 17
LEARNING TRAJECTORIES APPROACH ............................................................................................................. 17
MATHEMATICAL INTERACTION AND DISCUSSION ............................................................................................. 19
CHAPTER 3: EARLY MATHEMATICAL FOCUSSING TENDENCIES ...................................................... 19
1. EARLY MATHEMATICAL FOCUSSING TENDENCIES: THEORETICAL FRAME WORK .......................................... 19
BASIS CLAIMS ........................................................................................................................................... 19
MECHANISM OF SELF-INITIATED PRACTICE ..................................................................................................... 20
2. EARLY MATHEMATICAL FOCUSSING TENDENCIES: COMPONENTS............................................................ 20
DIFFERENT TENDENCIES ............................................................................................................................. 20
SFON..................................................................................................................................................... 20
SFONS ................................................................................................................................................... 23
SFOR ..................................................................................................................................................... 24
SFOP ..................................................................................................................................................... 26
2
,3. CONCLUSION AND DISCUSSION .................................................................................................... 27
CONCEPTUAL ISSUES.................................................................................................................................. 27
MEASUREMENT ISSUES .............................................................................................................................. 28
DEVELOPMENT ISSUES ............................................................................................................................... 28
EDUCATIONAL ISSUES................................................................................................................................. 29
CHAPTER 4: MENTAL AND WRITTEN ARITHMETIC ........................................................................ 29
MENTAL AND WRITTEN ARITHMETIC: DEFINITION, TYPES OF STRATEGIES ....................................................... 29
DEFINITION.............................................................................................................................................. 29
PROCEDURAL STRATEGIES: MENTAL .............................................................................................................. 29
PROCEDURAL STRATEGIES: WRITTEN ............................................................................................................. 30
MULTI-DIGIT ADDITION AND SUBTRACTION .................................................................................................... 30
ALSO SINGLE-DIGIT OPERATIONS (MENTAL) ................................................................................................... 31
STRATEGY COMPETENCE: THEORETICAL, METHODOLOGICAL AND INSTRUCTIONAL RATIONALE ............................. 31
THEORETICAL RATIONALE ............................................................................................................................ 31
METHODOLOGICAL RATIONALE .................................................................................................................... 32
INSTRUCTIONAL RATIONALE ........................................................................................................................ 33
ROUTINE EXPERTISE (SINGLE-DIGIT ADDITION) ................................................................................................ 33
ADAPTIVE EXPERTISE (SINGLE-DIGIT ADDITION) ............................................................................................... 33
ROUTINE EXPERTISE (SINGLE-DIGIT MULTIPLICATION) ....................................................................................... 33
ADAPTIVE EXPERTISE (SINGLE-DIGIT MULTIPLICATION) ...................................................................................... 34
MULTI-DIGIT ADDITION AND SUBTRACTION ........................................................................................... 35
WHAT DO WE KNOW ABOUT STRATEGY COMPETENCE (EMPIRICAL STUDIES) ......................................................... 35
MULTI-DIGIT ADDITION AND SUBTRACTION OP TO 100 .................................................................................... 37
MULTI-DIGIT SUBTRACTION OP TO 1000 ....................................................................................................... 38
MULTI-DIGIT ADDITION AND SUBTRACTION: CONCLUSION ................................................................................. 39
MULTI-DIGIT DIVISION ..................................................................................................................... 40
WHAT DO WE KNOW ABOUT STRATEGY COMPETENCE? .................................................................................... 40
MULTI-DIGIT DIVISION (490:5) ................................................................................................................... 41
STUDY DESIGN .......................................................................................................................................... 41
RESULTS: STRATEGY USE ............................................................................................................................. 41
RESULTS: STRATEGY USE PROFILES ................................................................................................................ 42
RESULTS: COMPENSATION, REMAINDER ......................................................................................................... 43
MULTI-DIGIT DIVISION: CONCLUSION ............................................................................................................ 43
TAKE HOME................................................................................................................................... 43
MULTI-DIGIT ARITHMETIC: TAKE HOME ......................................................................................................... 43
MULTI-DIGIT ARITHMETIC: TAKE HOME ......................................................................................................... 43
, MATHEMATICAL MODELLING: EMPIRICAL EVIDENCE ................................................................................. 47
WHAT DO WE KNOW ABOUT MATHEMATICAL MODELLING IN ELEMENTARY SCHOOL CHILDREN? ............................... 47
WEAKNESSES IN MATHEMATICAL CONTENT KNOWLEDGE .................................................................................. 47
NO USE OF VALUABLE HEURISTICS ................................................................................................................ 48
NO USE OF VALUABLE METACOGNITIVE SKILLS ................................................................................................. 48
INADEQUATE CONCEPTIONS AND BELIEFS ....................................................................................................... 49
WORD PROBLEMS HAVE NOTHING TO DO WITH REALITY ................................................................................... 49
“AMPUTATED” PROCESS OF MATHEMATICAL MODELLING .................................................................................. 50
MATHEMATICAL MODELLING: INSTRUCTION .......................................................................................... 51
AMPUTATED PROCESS OF MATHEMATICAL MODELLING… INSTRUCTION? .............................................................. 51
NATURE OF THE PROBLEMS ......................................................................................................................... 51
PRACTISE AND CULTURE IN CURRENT INSTRUCTION .......................................................................................... 52
CF. VERSCHAFFEL ET AL., 1997 ................................................................................................................... 52
AMPUTATED PROCESS OF MATHEMATICAL MODELLING … INSTRUCTION ............................................................... 53
STRATEGY FOR WORD PROBLEM SOLVING....................................................................................................... 53
USEFUL HEURISTICS ................................................................................................................................... 53
APPROPRIATE BELIEFS AND ATTITUDES........................................................................................................... 54
TASKS ..................................................................................................................................................... 54
INSTRUCTIONAL TECHNIQUES ...................................................................................................................... 55
RESEARCH DESIGN..................................................................................................................................... 55
WORD PROBLEM TEST ............................................................................................................................... 55
CONCLUSION: INSTRUCTION ........................................................................................................................ 57
TAKE HOME................................................................................................................................... 57
MATHEMATICAL MODELLING: RELEVANNT BUT COMPLEX .................................................................................. 57
INSTRUCTION? ......................................................................................................................................... 57
RATIONAL NUMBERS AND THE “NATURAL NUMBER BIAS” ......................................................................... 58
RATIONAL NUMBERS: DEFINITION................................................................................................................. 58
RATIONAL NUMBERS: DIFFICULTIES ............................................................................................................... 59
NATURAL NUMBER BIAS ............................................................................................................................. 60
CONCEPTUAL CHANGE THEORY ........................................................................................................... 61
HOW TO UNDERSTAND NATURAL NUMBER BIAS?............................................................................................. 61
INSTRUCTION ........................................................................................................................................... 63
DUAL PROCESS THEORY .................................................................................................................... 64
PROCESSES UNDERLYING DIFFICULTIES ........................................................................................................... 64
NATURAL NUMBER BIAS IN ADULTS ............................................................................................................... 64
INSTRUCTION ........................................................................................................................................... 65
4
Les avantages d'acheter des résumés chez Stuvia:
Qualité garantie par les avis des clients
Les clients de Stuvia ont évalués plus de 700 000 résumés. C'est comme ça que vous savez que vous achetez les meilleurs documents.
L’achat facile et rapide
Vous pouvez payer rapidement avec iDeal, carte de crédit ou Stuvia-crédit pour les résumés. Il n'y a pas d'adhésion nécessaire.
Focus sur l’essentiel
Vos camarades écrivent eux-mêmes les notes d’étude, c’est pourquoi les documents sont toujours fiables et à jour. Cela garantit que vous arrivez rapidement au coeur du matériel.
Foire aux questions
Qu'est-ce que j'obtiens en achetant ce document ?
Vous obtenez un PDF, disponible immédiatement après votre achat. Le document acheté est accessible à tout moment, n'importe où et indéfiniment via votre profil.
Garantie de remboursement : comment ça marche ?
Notre garantie de satisfaction garantit que vous trouverez toujours un document d'étude qui vous convient. Vous remplissez un formulaire et notre équipe du service client s'occupe du reste.
Auprès de qui est-ce que j'achète ce résumé ?
Stuvia est une place de marché. Alors, vous n'achetez donc pas ce document chez nous, mais auprès du vendeur SDLstudent. Stuvia facilite les paiements au vendeur.
Est-ce que j'aurai un abonnement?
Non, vous n'achetez ce résumé que pour €7,49. Vous n'êtes lié à rien après votre achat.
