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Samenvatting Taal- en Wiskundedidactiek
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Taal- en Wiskundedidactiek - Pedagogische wetenschappen - Onderwijskunde - schakelprogramma of derde fase - KU Leuven en Kulak
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Taal- en wiskundedidactiekTaal- en wiskundedidactiek
1 Visies op en benaderingen van wiskundeonderwijs ............................................................................................................................................................................................ 4
1.1 Wat is wiskunde?..................................................................................................................................................................................................................................................... 4
De aard van wiskunde...................................................................................................................................................................................................................................... 4
Waar komt wiskunde vandaan en wat betekent ‘waarheid’ in wiskunde.....................................................................................................................................5
Epistemologische opvattingen over wiskunde....................................................................................................................................................................................5
1.2 Waarom moet het onderwezen worden? .........................................................................................................................................................................................................6
Wiskunde is al heel lang een kernonderdeel van het curriculum .................................................................................................................................................6
Er zijn tal van argumenten te geven voor het onderwijzen van de wiskunde ...........................................................................................................................6
De (prominente) plaats ervan wordt ook in vraag gesteld ............................................................................................................................................................6
1.3 Hoe moet het geleerd en onderwezen worden? ............................................................................................................................................................................................6
Mechanistische visie ..................................................................................................................................................................................................................................6
Structuralistische visie ............................................................................................................................................................................................................................ 7
Realistische visie (zie ook Van den Heuvel-Panhuizen & Drijvers, 2014).................................................................................................................................... 7
1.4 Onderzoek over het wiskundeonderwijs ..........................................................................................................................................................................................................8
2 Vroege wiskundige vaardigheden.............................................................................................................................................................................................................................9
2.1 Vroege wiskundige vaardigheden en “number sense”.................................................................................................................................................................................9
2.2 Een conceptuele analyse van de onderdelen van “early numerical abilities”: Andrews & Saeyers (2015) ..................................................................................11
2.3 Een empirische analyse van de “early numerical abilities”: Cirino (2011) ............................................................................................................................................ 13
3 Vroege neiging tot wiskundig focussen ................................................................................................................................................................................................................ 13
3.1 Spontaneous focusing on (Exact) numerosities (SFON) .............................................................................................................................................................................14
3.2 Spontaneous focusing on Arabic numerical symbols (SFONS) ............................................................................................................................................................... 15
3.3 Spontaneous focusing on Quantitative relations (SFOR) .................................................................................................................................................................... 16
3.4 Spontaneous focusing on Mathematical patterns (SFOP) ......................................................................................................................................................................... 16
3.5 Besluit .................................................................................................................................................................................................................................................................17
Conceptuele kwesties ............................................................................................................................................................................................................................... 17
Methodologische kwesties ......................................................................................................................................................................................................................17
Ontwikkelingspsychologische kwesties .............................................................................................................................................................................................. 18
Onderwijs kwesties .................................................................................................................................................................................................................................. 18
4 Mentaal en schriftelijk rekenen............................................................................................................................................................................................................................... 18
4.1 Strategie-competenties in het domein van de natuurlijke getallen: inleiding ..................................................................................................................................... 18
Adaptieve vs routine expertise ............................................................................................................................................................................................................. 18
Theoretisch en methodologisch kader (zie deel 2) ......................................................................................................................................................................... 18
Strategieontwikkeling in het domein rekenen met eencijferige natuurlijke getallen............................................................................................................ 18
Strategieontwikkeling in het domein rekenen met meercijferige natuurlijke getallen ....................................................................................................... 20
4.2 Subtraction-by-addition (indirecte optelstrategie).....................................................................................................................................................................................21
5 Vraagstukken en wiskundig modelleren .............................................................................................................................................................................................................. 22
Astrid De Brabandere 1
, Taal- en wiskundedidactiek
5.1 Eindtermen en leerplandoelenn ....................................................................................................................................................................................................................... 22
5.2 Basisbegrippen ..................................................................................................................................................................................................................................................... 22
5.3 Moeilijkheden ................................................................................................................................................................................................................................................... 23
5.4 Oorzaken? .............................................................................................................................................................................................................................................................. 24
5.5 Interventieonderzoek.......................................................................................................................................................................................................................................... 24
5.6 Afrondende beschouwingen........................................................................................................................................................................................................................ 25
6 Rationale getallen ...................................................................................................................................................................................................................................................... 25
6.1 Definitie, begrippen ............................................................................................................................................................................................................................................. 25
6.2 Rationale getallen in de eindtermen............................................................................................................................................................................................................... 26
6.3 De overgang van natuurlijke naar rationale getallen .......................................................................................................................................................................... 26
6.4 Een theorie over kennis en leren (conceptual change theory) ...............................................................................................................................................................27
6.5 Exemplarische uitwerking in onderzoek over rationale getallen ......................................................................................................................................................27
6.6 Rol van instructie? ........................................................................................................................................................................................................................................ 28
7 Ontluikende geletterdheid ....................................................................................................................................................................................................................................... 29
7.1 Introductie en definitie ....................................................................................................................................................................................................................................... 29
7.2 Methodologie ......................................................................................................................................................................................................................................................... 29
7.3 Aspecten van geletterdheid .............................................................................................................................................................................................................................. 30
Awareness of print.................................................................................................................................................................................................................................. 30
Relationship of print to speech............................................................................................................................................................................................................ 30
Text structure........................................................................................................................................................................................................................................... 30
Phonological awareness ......................................................................................................................................................................................................................... 31
Letter naming and writing ...................................................................................................................................................................................................................... 31
7.4 Domeinen van geletterdheidservaring .......................................................................................................................................................................................................... 32
De ruimere culturele context............................................................................................................................................................................................................... 32
Thuis-, peuter- en kleuterklas omgevingen ..................................................................................................................................................................................... 32
Interacties rond prentenboeken ......................................................................................................................................................................................................... 32
8 Lezen .............................................................................................................................................................................................................................................................................. 33
“Alphabetics” ............................................................................................................................................................................................................................................ 34
Vlotheid ....................................................................................................................................................................................................................................................... 36
Begrijpend lezen [zie andere tekst van hoofdstuk 2].................................................................................................................................................................... 36
Lerarenopleiding en leesinstructie .................................................................................................................................................................................................... 38
ICT en leesinstructie ............................................................................................................................................................................................................................... 38
8.2 Explicit reading comprehension instruction volgens Andreassen, R.................................................................................................................................................... 38
Achtergond ................................................................................................................................................................................................................................................ 38
Onderzoeksvragen................................................................................................................................................................................................................................... 38
Methode ...................................................................................................................................................................................................................................................... 38
Resultaten and conclusies .................................................................................................................................................................................................................... 38
9 Schrijven....................................................................................................................................................................................................................................................................... 39
Astrid De Brabandere 2
, Taal- en wiskundedidactiek
9.1 Nieuwe contexten................................................................................................................................................................................................................................................. 39
9.2 Schrijfprocessen.................................................................................................................................................................................................................................................. 40
9.3 Leren schrijven............................................................................................................................................................................................................................................... 42
Schrijfonderwijs in actie: Klassieke benaderingen ........................................................................................................................................................................ 42
Meta-analyses over effectiviteit van schrijfinstructie ................................................................................................................................................................. 42
Onderwijs aan moeilijk schrijvenden.................................................................................................................................................................................................. 43
Een dubbele uitdaging............................................................................................................................................................................................................................. 43
De rol van leerlingkenmerken .............................................................................................................................................................................................................. 43
9.4 Schrijven om te leren ......................................................................................................................................................................................................................................... 43
Wat?............................................................................................................................................................................................................................................................. 43
Mechanismen .............................................................................................................................................................................................................................................44
Knowledge Forum als voorbeeld ..........................................................................................................................................................................................................44
Empirische resultaten over impact .....................................................................................................................................................................................................44
9.5 Meten van schrijfvaardigheden ..................................................................................................................................................................................................................44
9.6 Onderzoek naar schrijven: issues..............................................................................................................................................................................................................44
10 Literatuuronderwijs .................................................................................................................................................................................................................................................. 45
10.1 Begrippen ......................................................................................................................................................................................................................................................... 45
10.2 Doelen en methodes...................................................................................................................................................................................................................................... 46
Waarom lezen/literatuur? .................................................................................................................................................................................................................... 46
Spontaan lezen stimuleren ....................................................................................................................................................................................................................47
Leeservaringen en -competenties ontwikkelen ...............................................................................................................................................................................47
11 Vreemde talen onderwijs ......................................................................................................................................................................................................................................... 49
11.1 Hoe leert men een tweede taal?...................................................................................................................................................................................................................... 49
11.2 Leertheorieën in Second language acquisition ........................................................................................................................................................................................... 50
11.3 Learner differences ............................................................................................................................................................................................................................................. 51
Cognitive variables................................................................................................................................................................................................................................... 51
Affective and social-psychological variables .................................................................................................................................................................................. 52
SLA research and language pedagogy .............................................................................................................................................................................................. 52
11.4 Task complexity, student perceptions of vocabulary learning in EFL and task performance ....................................................................................................... 53
Self-efficacy .............................................................................................................................................................................................................................................. 53
Astrid De Brabandere 3
, Taal- en wiskundedidactiek
Wiskundedidactiek
1 Visies op en benaderingen van wiskundeonderwijs
1.1 Wat is wiskunde?
De aard van wiskunde
Definities van wiskunde
The science of quantity (Aristoteles, 4de eeuw BC) Focus op hoeveelheden
Mathematics is the science that draws necessary conclusions. (Benjamin Peirce, 1870) Logisch en deductief karakter van de wiskunde
Mathematics is the art of giving the same name to different things. (Henri Poincaré, 1850-1912) Bv. 2 + 2 = 4; twee namen geven aan hetzelfde, gesloten
systeem om bepaalde dezelfde zaken te definiëren
Mathematics is the classification and study of all possible patterns. (Walter Warwick Sawyer, 1955) Studie van patronen
The study of the measurement, properties, and relationships of quantities and sets, using numbers Focus op het gebruik van cijfers en symbolen
and symbols. (http://www.thefreedictionary.com/mathematics)
The abstract science which investigates deductively the conclusions implicit in the elementary Geen empirische wetenschap, maar deductieve
conceptions of spatial and numerical relations, and which includes as its main divisions geometry, wetenschap. Verwijzing naar verschillende onderdelen
arithmetic, and algebra. (Oxford English Dictionary, 1933) van wiskunde (meetkunde, rekenkunde, algebra…)
The science of structure, order, and relation that has evolved from elemental practices of counting, Verwijst naar waar wiskunde vandaan komt
measuring, and describing the shapes of objects. (Encyclopaedia Britannica)
Mathematics is a broad-ranging field of study in which the properties and interactions of idealized Gaat om concrete praktijken die gesitueerd zijn in
objects are examined. (Wolfram MathWorld) dagelijkse activiteiten. Idealisering van situaties
Wiskunde is de studie van onderwerpen als kwantiteit, structuur, ruimte en verandering. Er is een scala aan opvattingen onder wiskundigen en filosofen over de exacte
reikwijdte en definitie van wiskunde. Wiskundigen zoeken naar patronen, en gebruiken die om nieuwe vermoedens te formuleren. Wiskundigen lossen de waarheid of
onwaarheid van vermoedens op door wiskundig bewijs. Als wiskundige structuren goede modellen zijn van echte fenomenen, dan kan wiskundig redeneren inzicht of
voorspellingen over de natuur geven. Door het gebruik van abstractie en logica ontwikkelde de wiskunde zich van tellen, rekenen, meten en de systematische studie van
de vormen en bewegingen van fysieke objecten. Praktische wiskunde is al een menselijke activiteit zolang er geschreven gegevens bestaan. Het onderzoek dat nodig is
om wiskundige problemen op te lossen, kan jaren of zelfs eeuwen van aanhoudend onderzoek vergen.
Wiskunde Lange tijd werd wiskunde gedefinieerd als "de wetenschap van de hoeveelheid" (Aristoteles) en deze definitie werd ruim gebruikt tot de
18e eeuw
Latere definities benadrukken vooral het deductieve karakter van de wiskunde; andere benadrukken haar abstract karakter; haar
aandacht voor structuren en patronen; haar probleemoplossend karakter
Basiskenmerken van wiskunde
Dual nature of mathematics
- Zuivere wiskunde: wiskunde om de wiskunde (in al haar onderdelen zoals analyse, algebra, meetkunde, logica, getaltheorie, numerieke wiskunde,
topologie…), blijft binnen systeem
- Toegepaste wiskunde: het inzetten van wiskunde in allerlei dagelijkse situaties en in andere wetenschappen (fysica, economie, informatica,
statistiek, biowetenschappen, mens en maatschappijwetenschappen…), praktische toepassingen van zuivere wiskunde
- De scheiding is niet scherp te maken
o Praktische activiteiten → zuivere wiskunde
o Zuivere wiskunde → praktische toepassingen
Intrinsic inaccessibility of mathematical (thinking) objects
- Wiskundige objecten zijn niet rechtstreeks toegankelijk (via de zintuigen), maar enkel via één of andere representatiewijze (symbool, woord,
tekening, beweging, enz.), altijd objecten nodig
- De ontwikkeling en toepassing van wiskunde is onlosmakelijk verweven met het gehanteerde symboolsysteem
Astrid De Brabandere 4
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