Math 412 Math 412 Number ReadinessNumber Readiness

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Developing Number ConceptsDeveloping Number Concepts

What type of pre-number activities must children engage in to develop understanding of number concepts?

What type of counting abilities are necessary for children to develop?

What are several of the ways that children must be able to represent numbers?

What types of number relationships are essential for children to understand?

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Number ReadinessNumber Readiness

Ages 3 to 6Preoperational thought according to PiagetUnderstand best when they can invent

meaning

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Pre-number ConceptsPre-number Concepts

ClassificationClass inclusionSeriationNumber conservationEquivalence of sets

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ClassificationClassification

Child must make a decision about certain attributes of objects and sort them based on the classification

Earliest stage of logical thinking

Sample ActivitySample Activity Grades Pre-K-1Grades Pre-K-1

Identifying Attributes Materials: Classroom objects or toys Directions: Hold up an object and ask the children to

describe it. The scenario may go something like this:

What can you tell me about this?What properties does it have?

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Sample Activity Sample Activity Grades Pre-K-2Grades Pre-K-2

Sorting ObjectsMaterials: Attribute blocks or other objects

that may be sorted Directions: Ask students to sort by color Ask students to sort by shape Ask students to sort by size or thickness Ask students what types of objects are sorted at home: Toys, mail, groceries, laundry

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Class InclusionClass Inclusion

The ability for a child to see relationships between different groups at different levels in the classification system

For example, one group can be part of another group at the same time

For example, the group of girls in a classroom can also be part of the total group(Ms. Smith first grade class)

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Class InclusionClass Inclusion

Show the child a box of twenty red beads and ten yellow beads.

If you ask the child if there are more red beads or more plastic beads, a young child would say more red beads.

It is difficult for a young child to see the relationship between the two classes

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Number InclusionNumber Inclusion

This concept is directly related to the addition principle.

Because addition is putting two sets together and naming it as a single number, this concept is difficult for a young child ….

The child is not ready to add until they this skill is developed with practice

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Sample ActivitySample Activity Grades Pre-K-1 Grades Pre-K-1

Concept of Number InclusionMaterials: various objects Directions: Ask a child to count a number of objects, say 5, then add 3

more. Then ask how many things there are now. Most children will start counting the entire group

beginning at 1, rather than starting at 5 They do not think of the relationship between five and the

adjacent numbers

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Sample ActivitiesSample Activities

Whole to part and back to the whole activities will give children experience of putting sets together

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SeriationSeriation

This involves the ordering of objects and events

The child at this stage must be able to make comparisons and make decisions about differences

Sample ActivitySample Activity

Concept of SeriationMaterials: different size objectsDirections:Order the smallest block to the largest blockOrder the largest rock to the smallest rock What do you do first in the morning?

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Number ConservationNumber Conservation

How the child perceives number invariance and the degree that the child is tied to perceptual cues

Can the arrangement of a constant number of objects be changed without changing the number?

Sample ActivitySample ActivityGrades K-2Grades K-2

Concept of Conservation Materials: Five red blocks and five blue blocks Teacher statement: On the table I have a row of red blocks and a row

of blue blocks. Raise your hand if you think there are more red blocks than blue ones. Raise your hand if you think there are more blue blocks. Raise your hand if you think there are as many red blocks as blue

blocks. What about now? (spread out the row of blue blocks) Then ask the same questions again…..

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ConservationConservation

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Number ConservationNumber Conservation

Conservers do not see changes in configurations and counter suggestions

This is developmentalPiaget claims that without reversibility of

thought and number conservation, addition cannot be understood – first operation

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Equivalence of SetsEquivalence of Sets

A task associated with understanding numbers is equivalence of sets

Perceptual cues may interfere with a young child’s understanding of number

Sample ActivitySample ActivityGrades Pre-K-1Grades Pre-K-1

Concept of Equivalence of Sets Materials: Two glasses, one short, one tall filled

with the same size and same number of beads Teacher statement: Are there the same number of

beads in each glass?

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Developing Meaning for Developing Meaning for NumbersNumbers

Once children become aware that the quantity in a set is named by a specific name, they begin to associate meaning to numbers

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Building the Concept of Building the Concept of NumberNumber

Patterns Number relationships

– One to one correspondence– More, less, same– Rote counting– Rational counting (counting with meaning)– Counting sets– Numeral Set association (number, the number name,

written symbol) three 3

Cardinal NumbersCardinal Numbers

“Cardinal” numbers are used to designate the quantity of a set

For example: If a child is asked to count the pieces of chalk in the chalk tray and counts to seven, then he is using the cardinal aspect of the number

When a set is counted the last number named is the total number of objects in the set

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Ordinal NumbersOrdinal Numbers

“Ordinal” means order. Ordinal numbers are used to denote the

order of an objectFor example: “ Michelle finished her test

first”

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Nominal NumbersNominal Numbers

“Nominal” means name.Numbers are used to name objectsExamples: a social security number, a

postal code, a license plate, a house address

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Readiness for OperationsReadiness for Operationsin this Orderin this Order

AdditionSubtractionMultiplicationDivision