Samenvatting Wiskunde
Inhoud
Table of Contents
betekenisvolle situaties.........................................................................................................................4
concreet - schematisch – abstract.........................................................................................................4
concreet: concrete materialen en voorbeelden................................................................................4
schematisch: tekenen, schema, MAB in positietabel.........................................................................4
honderdveld..................................................................................................................................4
abstract: symbolen, tekens en getallen.............................................................................................4
Handelingsniveau van Galperin.............................................................................................................4
Materieel handelen...........................................................................................................................4
Perceptueel handelen........................................................................................................................4
Verbaal handelen...............................................................................................................................4
Mentaal handelen..............................................................................................................................4
Inzichtelijke aanpak...............................................................................................................................4
Belang van concreet wiskundig verwoorden.........................................................................................5
Automatiseren en memoriseren............................................................................................................5
Inductief werken....................................................................................................................................5
Gebruik van verhoudingstabellen..........................................................................................................5
functies van getallen..............................................................................................................................5
talstelsels...............................................................................................................................................5
10-delig talstelsel...............................................................................................................................5
andere talstelsels...............................................................................................................................7
Getalverzamelingen...............................................................................................................................7
Breuken.................................................................................................................................................7
inhoud................................................................................................................................................7
Didactiek............................................................................................................................................8
Soorten breuken................................................................................................................................9
Breuken vereenvoudigen.................................................................................................................10
Breuken vergelijken.........................................................................................................................10
breuken gelijknamig maken.............................................................................................................10
relatie breuken – kommagetallen – procenten................................................................................10
aanbreng basisbewerkingen................................................................................................................10
, vermenigvuldigen en delen.............................................................................................................10
Hoofdrekenen......................................................................................................................................13
Inhoud.............................................................................................................................................13
Didactiek..........................................................................................................................................14
Basisbegrippen.............................................................................................................................14
Hoofdrekenen..............................................................................................................................16
Eigenschappen van bewerkingen........................................................................................................16
Wisseleigenschap.............................................................................................................................17
Schakeleigenschap...........................................................................................................................17
Splitsen en verdelen........................................................................................................................17
Optellings- en vermenigvuldigingswip en aftrekkings-en delingshalter...........................................17
Evenredigheidseigenschap en omgekeerd evenredigheidseigenschap...........................................17
Handige methodes...........................................................................................................................17
Cijferen................................................................................................................................................18
Inleiding...........................................................................................................................................18
Optellen en aftrekking.....................................................................................................................19
Vermenigvuldigen............................................................................................................................20
Staartdeling.....................................................................................................................................21
Typische fouten bij cijferen..............................................................................................................22
Controlestrategieën.............................................................................................................................23
Schattend rekenen...............................................................................................................................23
Schatten door benaderen van termen of factoren..........................................................................23
Compenseren...................................................................................................................................23
Schattend omgrenzen......................................................................................................................23
Schatstrategieën..............................................................................................................................23
Getallen afronden............................................................................................................................23
De rekenmachine.................................................................................................................................24
Kommagetallen....................................................................................................................................24
Begrippen........................................................................................................................................24
Leerlijn.............................................................................................................................................25
Aanbreng.........................................................................................................................................25
Bewerkingen met kommagetallen...................................................................................................26
Tijd.......................................................................................................................................................27
Meten en metend rekenen..................................................................................................................27
Basisbegrippen................................................................................................................................27
Wat is meten en metend rekenen...............................................................................................27
Meetinstrumenten.......................................................................................................................28
Referentiematen – ijzeren maten................................................................................................28
, Herleiden.....................................................................................................................................28
Grootheden en eenheden...............................................................................................................29
Lengtematen................................................................................................................................29
Oppervlakte en landmaten..........................................................................................................29
Volume- en inhoudsmaten.........................................................................................................29
Gewicht/massa............................................................................................................................30
Inhoud
Table of Contents
betekenisvolle situaties.........................................................................................................................4
concreet - schematisch – abstract.........................................................................................................4
concreet: concrete materialen en voorbeelden................................................................................4
schematisch: tekenen, schema, MAB in positietabel.........................................................................4
honderdveld..................................................................................................................................4
abstract: symbolen, tekens en getallen.............................................................................................4
Handelingsniveau van Galperin.............................................................................................................4
Materieel handelen...........................................................................................................................4
Perceptueel handelen........................................................................................................................4
Verbaal handelen...............................................................................................................................4
Mentaal handelen..............................................................................................................................4
Inzichtelijke aanpak...............................................................................................................................4
Belang van concreet wiskundig verwoorden.........................................................................................5
Automatiseren en memoriseren............................................................................................................5
Inductief werken....................................................................................................................................5
Gebruik van verhoudingstabellen..........................................................................................................5
functies van getallen..............................................................................................................................5
talstelsels...............................................................................................................................................5
10-delig talstelsel...............................................................................................................................5
andere talstelsels...............................................................................................................................7
Getalverzamelingen...............................................................................................................................7
Breuken.................................................................................................................................................7
inhoud................................................................................................................................................7
Didactiek............................................................................................................................................8
Soorten breuken................................................................................................................................9
Breuken vereenvoudigen.................................................................................................................10
Breuken vergelijken.........................................................................................................................10
breuken gelijknamig maken.............................................................................................................10
relatie breuken – kommagetallen – procenten................................................................................10
aanbreng basisbewerkingen................................................................................................................10
, vermenigvuldigen en delen.............................................................................................................10
Hoofdrekenen......................................................................................................................................13
Inhoud.............................................................................................................................................13
Didactiek..........................................................................................................................................14
Basisbegrippen.............................................................................................................................14
Hoofdrekenen..............................................................................................................................16
Eigenschappen van bewerkingen........................................................................................................16
Wisseleigenschap.............................................................................................................................17
Schakeleigenschap...........................................................................................................................17
Splitsen en verdelen........................................................................................................................17
Optellings- en vermenigvuldigingswip en aftrekkings-en delingshalter...........................................17
Evenredigheidseigenschap en omgekeerd evenredigheidseigenschap...........................................17
Handige methodes...........................................................................................................................17
Cijferen................................................................................................................................................18
Inleiding...........................................................................................................................................18
Optellen en aftrekking.....................................................................................................................19
Vermenigvuldigen............................................................................................................................20
Staartdeling.....................................................................................................................................21
Typische fouten bij cijferen..............................................................................................................22
Controlestrategieën.............................................................................................................................23
Schattend rekenen...............................................................................................................................23
Schatten door benaderen van termen of factoren..........................................................................23
Compenseren...................................................................................................................................23
Schattend omgrenzen......................................................................................................................23
Schatstrategieën..............................................................................................................................23
Getallen afronden............................................................................................................................23
De rekenmachine.................................................................................................................................24
Kommagetallen....................................................................................................................................24
Begrippen........................................................................................................................................24
Leerlijn.............................................................................................................................................25
Aanbreng.........................................................................................................................................25
Bewerkingen met kommagetallen...................................................................................................26
Tijd.......................................................................................................................................................27
Meten en metend rekenen..................................................................................................................27
Basisbegrippen................................................................................................................................27
Wat is meten en metend rekenen...............................................................................................27
Meetinstrumenten.......................................................................................................................28
Referentiematen – ijzeren maten................................................................................................28
, Herleiden.....................................................................................................................................28
Grootheden en eenheden...............................................................................................................29
Lengtematen................................................................................................................................29
Oppervlakte en landmaten..........................................................................................................29
Volume- en inhoudsmaten.........................................................................................................29
Gewicht/massa............................................................................................................................30
