Mathematics and language education AJ 21-22 Anke Van der Schoot
Hoofdstuk 1: views and approaches to math. Education
Verschaffel What is mathematics?
- The nature of math.
- Nature of mathematical objects and
truth
Views of the purposes of math. Teaching and
learning
Views on and approaches to learning and
teaching (elementary) math.
- Mechanistic
o Skills or drill (baroody)
- Structural
o New math
- Constructivistic/realisqtic
o Freudenthal
o 2 types of mathemazation
Mathematics education as a research field on
its own
Van den Heuvel What is RME
Freudenthals’s guiding ideas about math en
math education
Core teaching principles of RME
- Activity principe,
- Reality principe
- Leven principe
- Interactivity principe
- Guidance principe
What is recontextualization
- Social activity method (SAM)
What is reflective practice
- Reflective practitioner
- Knowing in action
- Reflection in action
Kilpatrick “ all young Americans must learn to think
mathematically and they must think
mathematically to learn”
Staat in VS of school mathematics
Mathematische vaardigheden (profiency)
- Conceptual understanding
- Procedural understanding
- Strategic competence
- Adaptive reasoning
- Productive disposition
Kennisontwikkeling
- Gehele getallen (whole numbers)
- Rational numbers
- Ontwikkelen van een vaardigheid die
ontelbaar is
Aanleren van mathematische vaardigheid
- Effective teaching (enactment)
- kwaliteit van instructie hangt af van
o cognitief veeleisende oefening
1
, Mathematics and language education AJ 21-22 Anke Van der Schoot
o Wiskunde dmv taken leren
uitwerken
o Tijd
à reactie llng bepaalt hoe lkr
zichzelf ziet
o Ook hoe llng zich met
leertaken bezig houden
(voorkennis en automatisatie)
Ontwikkelen van vaardigheden in het aanleren
van mathematics
Hoofdstuk 2: Early numerical abilities
Andrew and Sayers Foundational number sense (FONS)
- Wat is het
- Number sense als predictor voor later
3 perspectieven:
- Preverbal number sense
- FONS
- Applied number sense
Characteristics of FONS
- Number recognition
- Systematic counting
- Awareness of the relationship between
number and quantity
- Quantity discrimination
- Understanding of different
representations of number
- Estimation (schatting)
- Simple arithmetic (rekenkundig)
competence
- Awareness of number patterns
Torbeys and Verschaffel Number sense
- Lower-order characterization
- Higher order characterization
o 3 areas voor higher order
o Kritiek door Verschaffel
Numerical magnitude understanding
Counting skills
- Verbal counting
o 2 overlappende fases
- Object counting
o 5 counting principes
§ One-one principe
§ Stable order
§ Cardinal principe
§ Order irrelevance
§ Abstraction
- Simultanious or synchronic counting
- Resultative counting
Cirino Pathways model (LeFevre)
3 types precursors
- Quantity precursors
o Nonsymbolic comparison
2
Hoofdstuk 1: views and approaches to math. Education
Verschaffel What is mathematics?
- The nature of math.
- Nature of mathematical objects and
truth
Views of the purposes of math. Teaching and
learning
Views on and approaches to learning and
teaching (elementary) math.
- Mechanistic
o Skills or drill (baroody)
- Structural
o New math
- Constructivistic/realisqtic
o Freudenthal
o 2 types of mathemazation
Mathematics education as a research field on
its own
Van den Heuvel What is RME
Freudenthals’s guiding ideas about math en
math education
Core teaching principles of RME
- Activity principe,
- Reality principe
- Leven principe
- Interactivity principe
- Guidance principe
What is recontextualization
- Social activity method (SAM)
What is reflective practice
- Reflective practitioner
- Knowing in action
- Reflection in action
Kilpatrick “ all young Americans must learn to think
mathematically and they must think
mathematically to learn”
Staat in VS of school mathematics
Mathematische vaardigheden (profiency)
- Conceptual understanding
- Procedural understanding
- Strategic competence
- Adaptive reasoning
- Productive disposition
Kennisontwikkeling
- Gehele getallen (whole numbers)
- Rational numbers
- Ontwikkelen van een vaardigheid die
ontelbaar is
Aanleren van mathematische vaardigheid
- Effective teaching (enactment)
- kwaliteit van instructie hangt af van
o cognitief veeleisende oefening
1
, Mathematics and language education AJ 21-22 Anke Van der Schoot
o Wiskunde dmv taken leren
uitwerken
o Tijd
à reactie llng bepaalt hoe lkr
zichzelf ziet
o Ook hoe llng zich met
leertaken bezig houden
(voorkennis en automatisatie)
Ontwikkelen van vaardigheden in het aanleren
van mathematics
Hoofdstuk 2: Early numerical abilities
Andrew and Sayers Foundational number sense (FONS)
- Wat is het
- Number sense als predictor voor later
3 perspectieven:
- Preverbal number sense
- FONS
- Applied number sense
Characteristics of FONS
- Number recognition
- Systematic counting
- Awareness of the relationship between
number and quantity
- Quantity discrimination
- Understanding of different
representations of number
- Estimation (schatting)
- Simple arithmetic (rekenkundig)
competence
- Awareness of number patterns
Torbeys and Verschaffel Number sense
- Lower-order characterization
- Higher order characterization
o 3 areas voor higher order
o Kritiek door Verschaffel
Numerical magnitude understanding
Counting skills
- Verbal counting
o 2 overlappende fases
- Object counting
o 5 counting principes
§ One-one principe
§ Stable order
§ Cardinal principe
§ Order irrelevance
§ Abstraction
- Simultanious or synchronic counting
- Resultative counting
Cirino Pathways model (LeFevre)
3 types precursors
- Quantity precursors
o Nonsymbolic comparison
2
