College aantekeningen
samenvatting hoorcolleges mathematics
samenvatting hoorcolleges mathematics (dus geen language)
[Meer zien]Voorbeeld 4 van de 51 pagina's
Voorbeeld 4 van de 51 pagina's
In winkelwagen
Voorbeeld van de inhoud
Inhoudsopgave1 What is mathematics?................................................................................................................................. 5
1.1 Nature of mathematics..................................................................................................................................5
1.2 Where does mathematics come from and what is a mathematical truth?...................................................5
1.3 Epistemological beliefs about mathematics..................................................................................................5
2 Why should it be taught?............................................................................................................................ 6
3 How to learn and teach mathematics?........................................................................................................ 6
3.1 General educational psychology perspective.................................................................................................6
3.2 Mathematics education perspective..............................................................................................................6
3.2.1 Mechanistic or skills approach...............................................................................................................7
3.2.2 Structuralistic approach..........................................................................................................................7
3.2.3 Realistic approach...................................................................................................................................7
1 Early numberical abilities and number sense...............................................................................................9
1.1 Preverbal number sense: Stanislas Dehaene – Brian Butterworth................................................................9
1.2 Foundational number sense (FONS).............................................................................................................10
1.3 Applied number sense..................................................................................................................................11
2 Conceptual analysis of components of early numerical abilities.................................................................11
2.1 Number recognition.....................................................................................................................................12
2.2 Systematic counting.....................................................................................................................................12
2.3 Awareness of the relationship between number and quantity....................................................................13
2.4 Quantity discrimination................................................................................................................................14
2.5 Understanding of different representations of number...............................................................................15
2.6 Estimation....................................................................................................................................................16
2.7 Simple arithmetic competence.....................................................................................................................16
2.8 Awareness of number patterns....................................................................................................................17
2.9 Conclusion of FONS......................................................................................................................................18
3 Emperical analysis of early numerical abilities...........................................................................................18
1 Adaptive routine expertise....................................................................................................................... 19
2 Strategy development in domain of single-digit arithmetic........................................................................19
2.1 Addition and substraction (<10)...................................................................................................................19
2.2 Addition and substraction (>10)...................................................................................................................19
2.2.1 Some major findings and issues...........................................................................................................19
2.2.2 Overlapping waves theory (Siegler)......................................................................................................20
2.3 Multiplication and division...........................................................................................................................20
2.3.1 Multiplication by the mechanistic approach........................................................................................21
2.3.2 Multiplication by the realistic approach...............................................................................................21
3 Strategy development in domain of multi-digit arithmetic.........................................................................21
1
, 3.1 Standard written algorithms........................................................................................................................22
3.2 3 algorithms for written substraction..........................................................................................................22
3.3 Mental computation....................................................................................................................................22
3.3.1 Mental computation strategies............................................................................................................22
3.3.2 Teaching for routine expertise in multi-digit mental arithmetic..........................................................23
1 Model of strategy change.......................................................................................................................... 23
1.1 Choice/no-choice method............................................................................................................................23
1.1.1 Choice method......................................................................................................................................23
1.1.2 Subject-based measure of flexibility....................................................................................................24
1.1.3 Previous studies with children..............................................................................................................24
1.2 Design...........................................................................................................................................................25
1.3 Flemish pupils’ educational background......................................................................................................25
1.4 Conditions.....................................................................................................................................................25
1.5 Analysis.........................................................................................................................................................26
1.6 Results: repertoire and frequency................................................................................................................26
1.6.1 Flexibility...............................................................................................................................................26
1.7 Conclusion....................................................................................................................................................26
1 Introduction.............................................................................................................................................. 28
1.1 Mathematical focusing tendencies..............................................................................................................28
1.2 Basic claims..................................................................................................................................................28
1.3 Mechanism of self-initiated practice............................................................................................................28
1.4 Different tendencies.....................................................................................................................................29
2 SFON......................................................................................................................................................... 29
2.1 Methodological criteria for SFON measures................................................................................................29
2.2 SFON measures............................................................................................................................................30
2.3 What do we know about SFON?..................................................................................................................30
3 SFONS....................................................................................................................................................... 31
3.1 SFONS picture task.......................................................................................................................................31
3.2 Research questions.......................................................................................................................................32
4 SFOR......................................................................................................................................................... 32
4.1 Tasks go messure SFOR................................................................................................................................32
5 SFOP......................................................................................................................................................... 33
5.1 Measures......................................................................................................................................................34
6 Conclusion and discussion......................................................................................................................... 35
6.1 Conceptual issues.........................................................................................................................................35
6.2 Measurement issues.....................................................................................................................................36
6.3 Developmental issues...................................................................................................................................36
6.3.1 Sequence..............................................................................................................................................36
6.3.2 Influencing factors................................................................................................................................36
2
, 6.3.3 Impact on general math development.................................................................................................37
6.4 Educational issues........................................................................................................................................37
1 Introduction.............................................................................................................................................. 38
2 Basic notions............................................................................................................................................. 38
2.1 Word problems.............................................................................................................................................38
2.2 Functions......................................................................................................................................................39
2.3 Word problem solving..................................................................................................................................39
3 Some research results............................................................................................................................... 40
3.1 Lacks in the content-specific knowledge......................................................................................................40
3.2 No use of valuable heuristics........................................................................................................................40
3.3 No use of valuable metacognitive skills.......................................................................................................40
3.4 Inadequate conceptions and beliefs.............................................................................................................41
4 Causes...................................................................................................................................................... 41
4.1 Nature of problems......................................................................................................................................42
4.2 Ways in which problems are conceived.......................................................................................................42
5 Remedies.................................................................................................................................................. 43
5.1 Goals.............................................................................................................................................................43
5.2 Major pillars.................................................................................................................................................44
5.3 Structure of lesson series..............................................................................................................................44
5.4 Research design (not important)..................................................................................................................45
5.5 Results..........................................................................................................................................................45
5.6 Important barriers........................................................................................................................................45
6 Mathematical modelling........................................................................................................................... 45
6.1 More extended model..................................................................................................................................46
1 Definitions & concepts.............................................................................................................................. 47
1.1 Numbers: changes in meaning.....................................................................................................................47
2 Rational numbers in the curriculum........................................................................................................... 48
2.1 Curriculum in primary school (Flemish)........................................................................................................48
2.2 Curriculum in secondary school (Flemish)....................................................................................................48
2.3 How do children do?.....................................................................................................................................48
3 Transition from natural to rational numbers.............................................................................................. 48
3.1 Meaning of operations.................................................................................................................................48
4 Theory about knowledge and learning (conceptual change theory)............................................................49
4.1 Continuous discontinuous...........................................................................................................................49
4.2 Naïve conceptions (=conceptual change theory).........................................................................................49
3
, 5 Exemplary elaboration in research about rational numbers.......................................................................50
5.1 Conceptual change in math.........................................................................................................................50
5.2 Early number knowledge..............................................................................................................................50
5.3 Initial instruction..........................................................................................................................................50
5.4 Consequence................................................................................................................................................50
5.5 From a discrete to a dense number line.......................................................................................................50
4
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
√ Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, Bancontact of creditcard voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper samenvattingenpw. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €6,49. Je zit daarna nergens aan vast.
Is Stuvia te vertrouwen?
4,6 sterren op Google & Trustpilot (+1000 reviews)
Afgelopen 30 dagen zijn er 53022 samenvattingen verkocht
Opgericht in 2010, al 14 jaar dé plek om samenvattingen te kopen