Summary
summary mathematics education
- Course
- Institution
This document is a summary of the mathematical part of mathematics and language education thought by Torbeyns Joke. It will be usefull for the exams.
[Show more]
Seller
Follow
SDLstudent
Content preview
2debach
Mathematics education
SUMMARY
SERENA DE LEO
1
,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
CHAPTER 5: MATHEMATICAL MODELLING ................................................................................... 44
MATHEMATICAL MODELLING: DEFINITION, PROCESS, EDUCATION ................................................................ 44
MATHEMATICAL MODELLING: DEFINITION ...................................................................................................... 44
MATHEMATICAL MODELLING – EDUCATION .................................................................................................... 45
WORD PROBLEMS: FUNCTIONS.................................................................................................................... 45
APPLICATION............................................................................................................................................ 46
CONCEPT FORMATION – STARTING PROBLEM .................................................................................................. 46
3
, 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
CHAPTER 6 RATIONAL NUMBERS ................................................................................................ 58
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller SDLstudent. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.08. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
66579 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now