Connect with Maths Early Years Learning in Mathematics Webinar series - Mathematical Thinking in the Early Years ( Part 2) Supporting children as mindful mathematicians presented by Louise Hodgson. This presentation is focused on key mathematical processes - problem solving, reasoning and proof, communication and connections and habits of mind such as curiosity, imagination and persistence which together are as important as mathematical content in a high quality early childhood mathematics program. Practical strategies will be discussed to support young children to develop reasoning which is central to learning about mathematics.

1. Early mathematical thinking
Louise Hodgson 2014

2. Outline of presentation
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Background
Mathematical processes
Role of the Early Childhood Educator
Mathematising
Mathematising in a play based curriculum

3. Pre school children’s knowledge of
mathematics predicts their later school
success…it predicts later reading
achievement…and predicts College science
achievement across subjects.
The quantitative , spatial, and logical
reasoning competencies of mathematics may
form a cognitive foundation for thinking and
learning across subjects.
Clements and Sarama 2011.

4. All children need robust knowledge of
mathematics in their earliest years, however
not all children have opportunities …
Some 6 yr olds have not acquired the
mathematical knowledge that other children
acquire at 3 years of age
Children from low income families less able to
explain mathematical ideas and processes.
Clements and Sarama 2011

5. • Mathematical processes - problem
solving, reasoning and
proof, communication and connections
and habits of mind such as
curiosity, imagination and
persistence, collectively are as important
as mathematical content in a high quality
early childhood mathematics program.
Clements and Sarama 2009

7. EYLF Outcome 4: Children are
confident and involved learners.
Children develop dispositions for learning such
as
curiosity, cooperation, confidence, creativity…,
enthusiasm, persistence, ...
Children develop a range of skills and
processes such as problem solving, inquiry,…
hypothesising, researching and investigating”.
(EYLF, 2009)

8. EYLF Outcome 5: Children are
effective communicators.
Spatial sense, structure and pattern,
number, measurement, data,
argumentation, connections
and exploring the world
mathematically are the
powerful mathematical ideas children
need to become numerate.
(EYLF, 2009 p38)

9. Early childhood teachers often believe
they are “doing mathematics” when they
provide puzzles, blocks and counting
songs. Even when they teach
mathematics, the content is not the main
focus but usually embedded in a fine
motor or reading activity…Such an
approach is ineffective, owing to lack of
explicit attention to mathematical
concepts.
Clements and Sarama 2011; Chen and McCray 2014

10. Early Childhood Teachers need:
To understand
1. What to teach (content)
2. Whom to teach (developmental
pathways)
3. How to teach (strategies for supporting
thinking about the content)
Teachers need integrated knowledge of all
three components.
Clements and Sarama 2011; Chen and McCray 2014

11. The notion of play
• Important to be clear about the notion of
play, the relationship between the playing
and learning and position of adults
towards play.
• What is your understanding of play in a
play based curriculum?

12. Play based curriculums
• Play is not some Laissez-faire event
• The teacher constructs the curriculum in
close interaction with the
children, informed by children’s interests
and the teachers mandatory goals.

13. Intentional pedagogy in mathematics permeates all
areas in a classroom throughout the day. The term
“mathematising” describes this approach.
“Mathematising” refers to the process of taking an
everyday situation or problem in daily life and
framing it in mathematical terms.
“Mathematising involves children in the construction
and re-construction processes of mathematical
reasoning, problem solving, … and communication”
Chen and McCray, 2014

14. Mathematising
• “Mathematising is the basis of
mathematical thinking that underlies both
operational-procedural thinking and
mathematical problem solving. Helping
young children to appropriate strategies of
mathematising is a core element of the
stimulation of their mathematical literacy”
Van Oers 2013

15. Mathematising
• Children must learn to mathematise their
informal experiences by abstracting,
representing and elaborating them
mathematically. If they do not, they miss
the opportunity to learn the language of
mathematics in all its multifaceted forms.
Clements and Sarama 2011

16. In other words…
As educators, we support young children’s
mathematical thinking and development
when we purposefully and intentionally
organise children’s playful experiences for
mathematical purposes.
This process is called“mathematising.”

17. Mathematical thinking
“Playful activity for young children is the
interactional niche for the development of
mathematical thinking”
• “Mathematical thinking should start out as
mathematics in play (rather than direct
instruction on elementary maths
operations) and then be fostered into
mathematics as play”
Van Oer, 2013

18. Mathematising in a play based
curriculum
In a genuine play based curriculum;
• mathematising is provoked and
encouraged as a way of dealing
(collaboratively) with the quantitative and
spatial dimensions of reality
• Play is the format for all student activities
• Children work out solutions to problems
collaboratively under the guidance of a
teacher or more knowledgable peer
• Van Oers, 2013

19. Mathematising in a play based
curriculum
Effective teachers:
• Ask questions that encourage children to
reflect on their actions
• Ask for arguments that explain their ideas
“Are you sure?”
“Can you convince us”
…contributes to the sense of the questions and
enhances children’s ability to participate more
successfully with others.
Van Oers 2013

20. Mathematising in a play based
curriculum
• To support children develop mathematical
reasoning and a mathematical space for
focussed communication, the following
mediums are helpful
• Picture books
• Gestures
• Schematic representations

21. Schematic representations
• Children produce
more sophisticated
schematic
representations of
quantities and their
relationships as long
as it is meaningful to
the children and in the
context of their play.
• Van Oers, 2013

22. Picture books in mathematics
learning
Picture books in mathematics teaching
enable children to encounter problematic
situations, ask questions, search for
answers, consider different points of view,
exchange views with others and guide them
toward higher levels of proficiency.
Van den Heuvel-Panhuizen, 2013

23. Picture books can have a dual function…
1.An informal and spontaneous activity that
children engage in
1.An intentional activity organised and
directed by the teacher

24. Mathematising story books
Draw the people
in your family
from the shortest
to the tallest.
What if some teddies fell out?
Draw a picture to show how
many teddies were in the bed
and how many fell out. Can
you find all the ways?

25. What will
happen after 7
more sleeps?

29. “What would it be like if
there weren’t any
numbers in our world?”
A four year olds response

30. How can we foster a culture of
mathematising in our early
childhood classrooms?

31. Role of the early childhood
educator
• Model mathematical language.
• Ask probing questions.
• Build on children’s interests and
natural curiosity.
• Provide meaningful experiences.
• Scaffold opportunities for learning &
model strategies.
• Monitor children’s progress and plan
for learning.

32. Role of the early childhood
educator
• “It is important in a play based curriculum
that the teacher has the curriculum
requirements for mathematics learning
always in mind, when collaborating in
children’s projects. With this content in
mind he/she should decide in advance
which of these should be explored and
practiced with children in the context of
their play”
FIJMA 2012

33. Mathematise teachable
moments as they occur
“I wonder if we’ll have enough cupcakes for
everyone to share”

34. Bobby Bear NCTM Illuminations
Can you find all the different ways to
dress the teddies Charlotte”?
“

35. Mathematics in play
“How many cups would you need to make a
triangle building with four levels?”

36. Play spaces
Role play (home, shoe
shop, bank, post
office, doctor, restaurant, superm
arket)
Construction
(blocks, tracks, linking materials)
Display area (peg
line, pinboards, magnet board)
Play trays (sand, water, multiple
objects e.g.
buttons, pasta, shells, leaves)
Mini-worlds (story/drama,
cloth or sand tray

37. Play spaces
Modelling & painting
Graphics (drawing,
writing, recording,
shapes)
Reading and listening
areas (story-telling,
picture books, rhymes,
songs, CDs, music &
percussion

38. “How many milk cartons do we
have to build our reading igloo?”
(ACMNA002)

39. Challenges
• The elaboration of play as a context for
meaningful mathematics learning
• The tension between instruction and
construction

40. Mathematics as Play
My friend Louise has an apple stall at the market.
She sells her apples in bags of ten. The other day
she had a box of thirty four apples. How many bags
of apples could she put on her stall?
(ACMNA014)

41. Somebody told me the calculator can count
for us. Lets investigate what happens when
we press 1+1===

42. Mathematics as Play
“Your job at the factory is to put
chocolates into bags and send
them to the shops. Each bag
has exactly ten chocolates in it.
At the end of the day you have
to draw a picture to show how
many chocolates you have
packed”.
(ACMNA014)

43. “The future of mathematical thinking in
young children strongly depends on the
quality of early years teachers to recognise
mathematical actions in children, to see the
potential of play activities and play objects
and to guide children into the future where
they can participate creatively and
autonomously in mathematical
communications”
Van Oers, 2013

44. References
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Chen, J. Q., & McCray, J. (2014). Intentional Teaching: Integrating the
Processes of Instruction and Construction to Promote Quality Early
Mathematics Education. In Early Mathematics Learning (pp. 257-274). Springer
New York.
Clements, D. H., & Sarama, J. (2011). Early childhood mathematics
intervention. Science, 333(6045), 968-970.
Fijma, N. (2012). Learning to communicate about number. In Developmental
Education for Young Children (pp. 253-269). Springer Netherlands.
Rudd, L. C., Lambert, M. C., Satterwhite, M., & Zaier, A. (2008). Mathematical
language in early childhood settings: What really counts? Early Childhood
Education Journal, 36(1), 75-80
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education
research: Learning trajectories for young children. Routledge.
Van den Heuvel-Panhuizen, M., & Elia, I. (2013)The role of picture books in
young children’s mathematics learning. In Reconceptualizing Early
Mathematics Learning (pp. 183-203). Springer Netherlands.
Van Oers, B. (2013). Communicating about number: Fostering young children’s
mathematical orientation in the world. In Reconceptualizing Early Mathematics
Learning (pp. 183-203). Springer Netherlands.
Van Oers, B. (2013). Challenges in the innovation of mathematics education for
young children. Educational Studies in Mathematics, 84(2), 267-272.