Transcript Number Readiness

Math 412
Number Readiness
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Developing 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 Readiness
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Ages 3 to 6
 Preoperational thought according to Piaget
 Understand best when they can invent
meaning
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Pre-number Concepts

Classification
 Class inclusion
 Seriation
 Number conservation
 Equivalence of sets
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Classification

Child must make a decision about certain
attributes of objects and sort them based on
the classification
 Earliest stage of logical thinking
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Sample Activity
Grades Pre-K-1
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Identifying Attributes
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Materials: Classroom objects or toys
Directions: Hold up an object and ask the children to
describe it.
The scenario may go something like this:
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What can you tell me about this?
 What properties does it have?
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Sample Activity
Grades Pre-K-2
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Sorting Objects
 Materials: Attribute blocks or other objects
that may be sorted
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Directions:
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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 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 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 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 Activity
Grades Pre-K-1

Concept of Number Inclusion
 Materials: various objects
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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 Activities

Whole to part and back to the whole
activities will give children experience of
putting sets together
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Seriation
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This involves the ordering of objects and
events
 The child at this stage must be able to make
comparisons and make decisions about
differences
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Sample Activity

Concept of Seriation
 Materials: different size objects
 Directions:
 Order the smallest block to the largest block
 Order the largest rock to the smallest rock
 What do you do first in the morning?
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Number Conservation

How the child perceives number invariance and
the degree that the child is tied to perceptual cues
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Can the arrangement of a constant number of
objects be changed without changing the number?
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Sample Activity
Grades K-2
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Concept of Conservation
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Materials: Five red blocks and five blue blocks
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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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Conservation
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Number Conservation
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Conservers do not see changes in
configurations and counter suggestions
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This is developmental
 Piaget claims that without reversibility of
thought and number conservation, addition
cannot be understood – first operation
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Equivalence of Sets

A task associated with understanding numbers is
equivalence of sets
 Perceptual cues may interfere with a young child’s
understanding of number
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Sample Activity
Grades Pre-K-1
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Concept of Equivalence of Sets
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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
Numbers

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
Number
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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
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Cardinal 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 Numbers
“Ordinal” means order.
 Ordinal numbers are used to denote the
order of an object
 For example: “ Michelle finished her test
first”
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Nominal Numbers
“Nominal” means name.
 Numbers are used to name objects
 Examples: a social security number, a postal
code, a license plate, a house address
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Readiness for Operations
in this Order

Addition
 Subtraction
 Multiplication
 Division
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