Number Words & NumeralsCounting

Number Words and NumeralsNumbers: ideas or concepts (idea of ‘six-ness’)Number words: Names for numbers

(distinguish between names that are spoken or heard and names that are written or read)

Digits: Ten basic symbols in the numerations system (system of symbolizing numbers). Are 0,1, 2,….9

Numerals: Written symbols for numbers; the ten digits also can be referred to as numerals

Number Words and NumeralsDevelop at the same time as counting is

developingSeveral components:

Forward (backward) number word sequencesNumber word after (before)Numeral identificationNumeral recognitionSequencing numeralsOrdering numeralsLocating numbers in range 1-100

Number Words and NumeralsDevelop at the same time as counting is

developingSeveral components:

Forward (backward) number word sequences

Number word after (before)Numeral identificationNumeral recognitionSequencing numeralsOrdering numeralsLocating numbers in range 1-100

Teacher’ CommentsWe have done a lot more counting from a

specific number, up to a specific number. For example, I ask the children to count from say 8 up to 15, rather than always to start counting from one. I also do this when counting backwards, for example, count from 19 to 12.

Teacher’s CommentsGenerally, we do a lot more counting

backwards. Children need to be as fluent in counting backwards as they are at counting forwards. This applies to counting in ones, but also in twos, threes etc.

Number Words and NumeralsDevelop at the same time as counting is

developingSeveral components:

Forward (backward) number word sequencesNumber word after (before)Numeral identificationNumeral recognitionSequencing numeralsOrdering numeralsLocating numbers in range 1-100

Number Words and NumeralsNumeral identification

Set of numeral cards 1-10 or 11-20 or selected in range 21-100 [about 15-20 cards]

Display the cards in turn “Tell me the number on the card”

Numeral recognition Set of five or more numeral cards (e.g., 1-10) Arrange cards randomly on the desk “Which number is six? Three? And so on.

Number Words and Numerals Numeral identification

“Tell me the number on the card”

Numeral recognition “Which number is six? Three? And so on.

Children might be able to recognize numerals they cannot identify. For example, a child cannot identify the numeral 12 (when an individual card with the numeral 12 is displayed) but can successfully respond to which number is the 12 (e.g., using a set of cards for the numbers from 11 to 20). These children have difficulty generating the sound image for the word ‘twelve.’

Why might this be important to know?

CountingCounting is an extremely important aspect of

early number instruction.There are two main approaches to describing

children’s development of counting strategies.

Knowing these stages helps teachers better able to develop instruction approaches focused on developing more sophisticated strategies.

Counting: Less In-Depth Approach

Three distinct stages of counting that can be observed among young students.

Each stage represents progressively more refined counting skills.

Rote CountingThis is when students say a string of number

names, and this string is very stable.Students at this stage appear to be counting

but are not able to come to the correct amount of ‘how many’ objects in a collection.

Point CountingWhen given a collection of objects to count,

students will make gestures of counting by touching objects in the collection, but cannot tell how many (will begin again at 1 to count objects).

Students at this stage have trouble keeping track of what they have counted and may double, triple, etc. count objects.

Rational CountingStudents are deemed rational counters when

they demonstrate an understanding of the following counting principles (Fuson, 1988):

1. Each item to be counted is assigned one (and only one) number name. (one-to-one correspondence – students can match a count with an object)

Rational Counting2. The order in which the items are counted

must be undertaken in specific and appropriate number order (i.e., 1, 2, 3, …)

3. The order in which the items are counted is irrelevant – it is possible to start at either end of a collection.

4. The last number counted represents the number in a collection

Counting: More In-Depth ApproachSix stages:

Stage 0: Emergent countingStage 1: Perceptual countingStage 2: Figurative countingStage 3: Initial number sequenceStage 4: Intermediate number sequenceStage 5: Facile number sequence(See chart: Model for stages of early arthimetic

learning)

ReferencesWright, Stanger, Stafford, and Martland.

(2006). Teaching Number in the Classroom with 4-8 year-olds. Paul Chapman Publishing.