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The concept of counting: theory and teaching materials
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Presentatie titel
Rotterdam, 00 januari 2007
Counting and calculating;
The concept of counting
Okahandja, October 2013
Before counting starts
Sorting – making groups Cardinal numbers
Ordering – making seriesOrdinal numbers
Conservation of numberStill the same number?
Making pairsLess-equal-more?
All kind of numbers
Cardinal numberOrdinal/Order numberMeasure numberLabel numberCalculation number
The teaching-learning trajectory of counting
Context-based counting and calculating
Object-based counting and calculating
Pure counting and calculating
CountingContext-based counting and calculating
StoriesDaily life situations
CountingObject-based counting and calculating
Counting the objects in the classroomCounting objects/people in daily life
Resultative countingcounting and slipping one-by-onesynchronic counting
Short countingStart counting with a known quantity
Structured countingCounting in two’s
Structured counting,Counting in fives
Structured countingCounting in tens
CountingPure counting and calculating
Representing numbers
Dots patterns, • 10-frames and dices
Tallies, Digits, Fingers,
SubitizingResultative countingShort countingStructured counting
Teaching materials1 Buttons, bottle tops, beans, strings, sticks, stones,
all kind of counting materials
1 2
3 4 5
76
8 9
10
Unstructured counting materials
Sorting – making groups Cardinal numbersOrdering – making seriesOrdinal numbers
Making pairsLess-equal-more?Conservation of numberStill the same number?
Counting: Resultative – Short – StructuredNumber bonds…..
Number bonds 8
53
Teaching materials2 Flashcards with number images 1 to 10
Flashcards with number images of fingers, dices, 10-frames and tallies
‘Pairs’ and ‘rows’
SubitizingCompleting to 10/friends of 10Pairs – even and odd numbers…..
home made ten frames
Which number?
Which number?
Which number?
Teaching materials3 Classroom number line 1 - 20 with 5- and 10-structure
Counting 1 – 10, 1 – 20Counting back 10 – 1, 20 – 1Counting in two’sEven and odd numbersCounting in fives,Neighbours Number bonds…..
Teaching materials4 Dices and number games - Rikash
Start
Finish
The race course, from home to school, ….
Subitizing Counting one-by-oneCounting and calculating?
Teaching materials5 Number cards 1 -20
Ordering numbersEven and odd numbersMultiples of 5 Friends of 10Number bondsNeighbours More/lessNumber lineNumber games……
Please make and collect the materials yourself.
Use the materials and discover the possibilities to teach mathematics with these ‘easy to make’ teaching materials!
Jaap Griffioen – j.griffioen@hr.nl Jaap de Waard – j.de.waard@hr.nl
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