This Presentation will help in understanding of development of Numeracy at foundational stage.

1. Understanding foundational
Numeracy : Paradigm Shift

2. 2
What is “Numeracy?”
“Numeracy is the ability to use some mathematics for a purpose in
a context”
[Susan McDonald ]
“Foundational Numeracy means the ability to reason and to apply
simple numerical concepts in daily life problem solving.”
[NIPUN BHARAT]
Numeracy encompasses the knowledge, skills, behaviours and
dispositions that students need to use mathematics in a wide range of
situations. It involves students recognizing and understanding the role of
mathematics in the world and having the dispositions and capacities to
use mathematical knowledge and skills purposefully
[The Australian Curriculum]

3. “
Number Sense
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It includes the ability to
i. Make an understanding of quantities.
ii. Develop concepts like more and less, and larger and smaller.
iii. Establish relationships between single items and groups of items
(seven means one group of seven items which is one more than a
group of six items).
iv. Use symbols that represent quantities (7 means the same thing as
seven).
v. Compare numbers (10 is greater than 8, and three is half of six).
vi. Arrange numbers in a list in order: 1st, 2nd, 3rd, etc.
vii.Visualize shapes and space around them.

4. “
Major aspects and components of Numeracy
(NIPUN BHARAT)
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1.Pre-Number concepts
2.Numbers and operations on numbers
3.Shapes and Spatial Understanding
4. Measurement
5.Patterns
6.Data Handling
7.Mathematical Communication

5. Let’s look at one example
Gungun, aged 6 years, had no problems with questions like 2+3= and
even8+ =9. Her teacher said that she thought Gungun had a good
understanding of the equals sign. But then the teacher asked Gungun
how she did 2+4= 6. Gungun replied, "I said to myself, two (then
counting on her fingers), three, four, five, six, and so the answer is six.
Sometimes I do them the other way round, but it doesn’t make any
difference' She pointed to 1+ =10 'For this one I did ten and one, and
that's eleven.“

6. Learning of procedures for
manipulating symbols in order to
answer various types of questions is not
the basis of understanding in
mathematics.

7. Challenge for a teacher
Identifying most significant ways of promoting understanding of
learning of Numeracy
Cognitive Processes of learning
Creating Connections between formal mathematical language and
everyday language, concrete or real life situations, pictures, etc?

8. A paradigm Shift
Learning of a collection of RECIPES / PROCEDURES and RULES
Vs
Development of understanding of mathematical concepts, principles and
processes

9. Focus should be on understanding the
ways of learning of children.
Shift in Direction of Pedagogies
Pedagogical processes
to promote
understanding that helps
children to make
connections with
Concepts of Numeracy
Facilitator should be
equipped with the
processes of the ways of
learning (Cognitive
processes)

10. Concrete materials, symbols, language and picture
refer to any kind of real, physical
materials, structured or unstructured,
that children might use to enable them
to construct mathematical concepts.
numbering the questions, breaking up
numbers into tens and units; writing
numerals in boxes, underlining the
answer, pressing buttons on their
calculator,
reading instructions from work cards
or text- books making sentences
incorporating specific mathematical
words, processing the teacher's
instructions,
language picture
Concrete materials symbols
drawing various kinds of
number strips and num-
ber lines, set diagrams,
arrow pictures and graphs.
04
02
03
01

11. ELPS Approach
He sees, feels, tastes, holds,
rolls and drops his ball. He has
‘fun’, and learns about many
of its properties,.
He associates the sound of the
word ‘ball’ with his toy. This is
useful. If he says the word, he
may be given the ball to play
with. He will soon associate
‘ball’ with other objects that
have the same rolling
property as his ball.
E - Experience with
physical objects,
Spoken language that describes that
experience,
02
01

12. He recognizes a picture of a
ball. The picture is very
different from the ball itself.
The picture does not roll, or feel
like a ball. But the child sees
that it has enough in common
with his own ball to be called
‘ball’.
P - Pictures that
represent the experience,
S - Written symbols that generalize
the experience.
Much later, he learns the
symbol that we write to
represent the sound ‘ball’.
This is sophisticated. The
symbol has no properties at
all in common with a real
ball, and it is only artificially
associated with the sounds
that we utter in saying the
word ‘ball’.
04
03

13. Connection between
real object, symbols,
language and pictures
More strongly connected the
experience, the greater and more
secure is our understanding.

14. Rote Learning
Learning without making
connections is what we would call
learning by rote.

15. What are mathematical
symbols?

16. Mathematical symbols are
not just abbreviations?
● What is
4+2=6
A symbol represents a network of
connections

17. Transformation and Equivalence
What is different?
What is same?

18. What is different about two things?
What has something become?.
What is same?
What remains unchanged?,
Transformation Equivalence

19. Two and four makes SIX
The Equal Sign
2+4 = 6

20. Two add four is the same as SIX
The Equal Sign
2+4 = 6

21. SIX is the same as Two add something
The Equal Sign
6 = 2+

22. Two and four makes SIX
The Equal Sign
2+4 = 6
Transformation

23. Two add four is the same as SIX
The Equal Sign
2+4 = 6
Equivalence

24. What is a number?

25. What is three?

26. Numbers Numerals Digits

27. Three is adjective
or noun?
Adjective to Noun

28. What are the
functions of a
number?

29. Functions
Three sets of things
Three on a clock face
My house number is 3
Page number 3 of a book
Mark of a 3 degree on a thermometer
Nominal
Ordinal
Cardinal

30. What is Number?
Symbol used a label to identify things
Labels putting things in order
How many there are in a set of things
Nominal
Cardinal
Ordinal

31. Number Strip
Number Line

32. The between Game
Bottle Game

33. How many pages have you read?
What page are you on?
There are three children in
a class four who are five
Cardinal or Ordinal

34. Prepare questions /activities on
manipulations of numbers.
Group Activity

35. Close your eyes and think about zero
ZERO
Birthdays in my class

36. Zero
‘0’ Bag
Nothing in a or absence
of something
Ordinal Zero is very definitely something
Ordinal
Cardinal

37. Overemphasis on the Cardinal Aspect
NEGATIVE NUMBERS?

38. Prepared by
Ranajit R Kondhare,
TA (Primary), ZIET
Chandigarh