Mathematical Literacy and Understanding

1
?????????Mathematical Literacy and Understanding
2
????????

• ???????????????
• ????????? ????????????
• ??????????????, ??, ??????
• ????????,??? ??????????????
• ????????? ????????????

3
Humans are born with a fundamental sense of
quantity?
Same number of marbles?
4/5 years old Left, yes Right, no. they can
answer correctly until 7-8 years.
4
Younger children do not posses a conceptual
understanding of numbers and that any number
re-related activities are learned by rote?
5
2 1/2 years to 4 1/2 years olds
Take the row you want to eat, and eat all the
MMs in that row.
Children understand more than and less than.
6
Numerical Competencies

• Numerosity (???) ??????
• Ordinality(???) ??????
• Arithmetic ??????

7
????

• ???????????????? ????, ?????????????
• ??????????(Innate)??????????
• ??????????, ??????????????????????

8
Numerosity

• Habituation procedure dishabituation means
  notificaiton of number of presented dots changed.
• 4 months to 7 1/2 months discriminate 2 from 3
  items but not 4 from 6 itms.
• 10 - 12 months 2 from 3, not 4 from 5
• infants look longer when 2 dots presented with 2
  drum bits, (abstracts codes for numerosities up
  to 3 or 4 items)

9
Infants abilities in numerosity

• Not dependent on a specific modality
• not influenced by factors such as
• whether dots or household items are presented,
• whether the presented items are static or moving,
• density of the displays

10
Ordinality
????

• Infants sensitive to numerosity implies they
  understand larger than or less than?
• Ordinality before or after numerosity? Why?

11
Ordinality

• Infants represent numerosity do not imply they
  can rank the representations.
• Developed during the first 1 1/2 years of life.

12
????

• ??????????, ????????
• ???????????????, ????????

13
Arithmetic

• Infants have a preliminary sense of addition and
  subtraction at 5 months of age.

Objects take out or add in
Infant looks in this direction
14
????

• ?????????????

15
Development of Early Numerical Abilities

• Subitizing
• Counting
• Estimating

16
Reaction Time Patters for Making Numerosity
Judgments
17
????

• ??????????

18
Error Rates

• Rare for arrays with 4 or fewer items
• gt50 for arrays with more than 7 items

19
????

• ????????? ?????????
• ????????
• ?????? ??????? ??????????????
• ???????????, ??????????,???????????

20
Properties of Number System

• Each number word is unique and represent a unique
  quantity
• numbers are serially ordered
• each number reflects a group of smaller numbers.

21
Counting basic skills involved

• One-to-one correspondence between number names
  and the counted items
• order the number names in the correct sequence
• the last number named in the count (the cardinal
  number) represents the total number of counted
  items.

22
Cardinality and Ordinality

• Cardinality number word assigned to the last
  counted object can be used to represent the total
  number of the counted objects
• Ordinality successive number words represent
  successively larger quantities.

23
Cardinality and Last-word Rule

• Test of cardinality
• A child is asked to count his or her fingers
• asked, How many fingers do you have?
• understand the concept of cardinality or just use
  the Last-word Rule?
• Cardinality is always confused by how the items
  are arranged.

24
Ordinality

• Refers mostly to the childs knowledge of
  equivalence and greater than and less than.
• Children as young as 2 1/2 years of age have an
  understanding of ordinal relationships.

25
Developmental Mechanisms for Counting and Number
Knowledge

• Most researchers agree that a sensitivity to
  numerical information is, at least in part,
  inborn, there is considerable disagreement over
  the relative importance of this innate
  sensitivity.
• Tow general positions
• principals-first innate principles guide the
  development,
• procedures-first first count by rote and
  gradually induce counting concepts.

26
Principles-First

• Behavior of young children guided by 5
  principles
• one-one correspondence one number word one
  counted object
• stable order same sequence of number words for
  counting
• cardinality the number word associated with the
  last counted item has a special meaning.
• Abstraction awareness of what is countable
  (skill at counting mixed sets too)
• order irrelevance

27

• The principles guide and structure the childs
  counting behavior, serve as a reference against
  which the child can evaluate this actual counting
  behavior, and motivate that behavior.

28
Procedure First

• Children first learn to count largely by rote
  through the imitation of parents or siblings, for
  example.
• Induces basic principles by noticing regularities
  in the outcome of counting.