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# Mathematics In Early Childhood Education

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## Jacqueline Carter

on 20 November 2013

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#### Transcript of Mathematics In Early Childhood Education

Mathematics In Early Childhood Education
What Is Maths?
"Mathematics is the exploration and
use of patterns and relationships in
quantities, space and time"
- Te Whariki (Ministry of Education, 1996)
What else?
"Mathematics is the exploration and use of
patterns and relationships in quantities, space
and time... (Mathematics) equips students with effective means for investigating, interpreting, explaining, and making sense of the world in
which they live"
- The New Zealand Curriculum (Ministry of Education, 2007)
Te Whariki (Ministry of Education, 1996) defines curriculum as "the sum total of the experiences, activities and events... which occur within an environment designed to foster children's learning and development."

Therefore, "it is these experiences, activities and events that can contain rich mathematical activities and in turn form foundations of future mathematical skill" (Babbington, 2003)
- As cited in Lee, 2007
Math Concepts
Number strategies
Number knowledge
Equations and expressions
Patterns and relationships
Number:
Number involves calculating, estimating, using mental or written calculation methods.
Geometry and Measurement:
Measurement
Shape
Position and orientation
Transformation,

Geometry and measurement involves recognising and using the properties and symmetries of shapes, describing position and movement, and measuring using the appropriate units and instruments.
Statistics:
Statistical investigation
Statistical literacy
Probability
Statistics involves identifying what can be explored by the use of data, designing investigations, collecting data, solving problems, communicating findings, interpreting information, evaluating data.
Math Skills
“Students develop the ability to think creatively,
critically, strategically, and logically. They learn to structure and organise, to carry out procedures flexibly and accurately, to process and communicate information, and to enjoy intellectual challenge.”

“Students also develop other important thinking skills. They learn to create models, predict outcomes, to conjecture, to justify and verify, and to seek patterns and generalisations”

- The New Zealand Curriculum (Ministry of Education, 2007)
The New Zealand Curriculum (Ministry of Education, 2007)
The New Zealand Curriculum (Ministry of Education, 2007)
The New Zealand Curriculum (Ministry of Education, 2007)
The Importance Of Maths
Young-Loveridge (1991) found that children who "initially started ahead in mathematics, tended to stay ahead, while those who were behind tended to stay behind."

Wylie, Thompson and Lythe (1999) also found that "children who started school lacking in mathematics skills were unlikely to catch up." The gap between the least and more capable children continued to widen, not close, during the first three years at school. (As cited in Davies, 2003)
Young Loveridge (1991) identified 5 key mathematical concepts that predicted later success in mathematics:

Rote counting
Forming a group of objects of a specified number
Recognising numerals
Subitizing (instantly recognising how many objects are in a collection without having to count them)
Adding and subtracting imaginary objects up to 14
Teacher knowledge of maths is also crucial in the development of mathematical understanding in children (Aubrey as cited in Davies, 2003).

In order to provide support, teachers first need to have a sound grasp on the subject of maths, as what teachers know will affect the kinds of learning experiences they offer to children (Davies, 2003).

“Teachers who are confident about their subject knowledge are more likely to recognise and maximise potential learning in children’s play experiences” (Anning & Edwards as cited in Hedges & Cullen, 2005).

Teacher Knowledge
What Is Socio-Cultural Theory?
“Socio-cultural perspectives view children as capable and competent learners, learning as socially and culturally situated and mediated, and posit that active participation in learning experiences enables children to participate increasingly effectively in their communities” (Hedges & Cullen, 2005).

“The study of the development of psychological functions
through social participation in societally organized practices”
(Chaiklin, 2001).

Socio-Cultural Theories
• Zone of proximal development from Vygotsky

• Guided participation from Rogoff

• Scaffolding from Bruner

ZDP is the gap between what a child can achieve alone, their potential development determined by independent problems solving and what they can achieve through problem solving under adult guidance of in collaboration with more capable peers (Wood & Wood, 1966) as cited in Kristinsdottir, 2001).

Refers to a range of tasks that a child cannot yet handle alone, but can do with the help of a more skilled partner (Berk, 2001).

Adults can guide support, break tasks into manageable units, call the child’s attention to details (Berk, 2001)

Vygotsky and the Zone of Proximal Development
Bruner and Scaffolding
Scaffolding is used to describe the support structure that teachers, parents and whanau provide regularly for children during learning processes (MacNaughtons & Williams, 2009)

Learning is achieved when children build new ideas upon their current and previous knowledge (MacNaughtons & Williams, 2009)

Scaffolding can eventually help children to become independent and self-regulated learners (Saafi, n.d.)

Rogoff and Guided Participation
Not one particular strategy, as guided participation can take different forms in different contexts

Two main processes: mutual bridging of meanings and mutual structuring of participation.

Mutual bridging of meanings is when partners seek common perspective or language in order to communicate their ideas so they can work together (Rogoff, 2003) as cited in Arthur, Beecher, Death, Dockett, & Farmer, 2007)

Mutual structuring of participation is the structure of the situation in which children participate. The structuring occurs when teachers make choices over what the children have access to observe and engage in, as well as through conversations, recounting of narratives, and engagement in routines and play (Rogoff, 2003) as cited in Arthur et al., 2007)

It is also important for adults to give clues of what things mean and ask children open ended questions in order to guide their thinking (Arthur, Beecher, Death, Dockett, & Farmer, 2007)

Te Whariki and Socio-Cultural Theory
Davies (2003) states "Te Whariki purposefully avoids separation of knowledge into curriculum areas. It is suggested that learning within the early childhood centre will be holistic by nature and embedded within the social and physical experiences provided within the centre."

Haynes (2000) states that in accordance with theories of learning which emphasize the role of culture and social context in children's development and learning, teachers need to take an active role to support children on their learning journey." (As cited in Davies, 2003)
What Does Te Whariki Say About Maths?
Well-Being: "Children develop competence in mathematical concepts and enjoy using them in daily life," also, "children explore mathematical concepts that encourage creativity, perseverance, and self-confidence.

Belonging: "Children learn to use numbers in relation to family members, children in a group, and ordering the environment in patterns and relationships," also, "mathematical concepts are used in practical family and social contexts, such as remembering telephone numbers, street numbers and birth dates."
Contribution: "Children learn to use number to monitor fair division of resources and equitable sharing of effort towards a goal," also, "children develop mathematical problem-solving strategies in, for instances, sharing and dividing resources, turn taking and estimating times.

Communication: "Children have fun with numbers and begin to understand and respond to information presented in mathematical ways," also, "children develop mathematical vocabulary and concepts which help them to communicate complex ideas such as weight, volume and shape.

Exploration: "In exploring their world, children find reasons to calculate and estimate with increasing accuracy to use measuring instruments and mathematical concepts," also, "children develop and use mathematical concepts when they collect, organise, compare and interpret different objects and materials.
A Maths Experience For Infants: Block Building
Math Concepts Involved:
Counting
Measurement (height & width)
Shapes
Patterns
Size

Socio-Cultural Theories Involved:
Scaffolding
Guided participation
A Maths Experience For Toddlers: Threading
Math Concepts Involved:
Sequencing & patterning
Number knowledge (counting)
Measurement
Shape
Socio-Cultural Theories Involved:
Zone of Proximal Development
Scaffolding
A Maths Experience For Young Children: A Math Themed Game
Math Concepts Involved:
Counting
Statistics
Measurement (distance & height)
Data interpretation
Socio-Cultural Theories Involved:
Guided participation
Zone of Proximal Development
“Unless children’s play is viewed with a mathematical lens, the mathematics can go unnoticed and seem frivolous”

- (Pound, 1999) as cited in Lee (2007)
References:

Arthur, L., Beecher, B., Death, E., Dockett, S. & Farmer, S. (2008).
Programming and planning in
early childhood settings.
(4th ed.). South Melbourne, Australia: Thompson.

Berk, L. E. (2001).
Development through the lifespan.
(2nd ed.). Needham Heights, MA: Allyn & Bacon.

Chaiklin, S. (2003).
The zone of proximal development in Vygotsky’s analysis of learning and instruction.
Cambridge, Cambridge University Press.

Davies, N. (2003). Counting on early childhood educators.
Early Education, 32
, 29-35.

Hedges, H., & Cullen, J. (2005). Subject knowledge in early childhood curriculum and pedagogy: Beliefs and practices.
Contempry Issues in Early Childhood, 6
(1), 66-79.

Lee, S. (2007).
I think you are a hundred; Mathematics in early childhood.
Paper presented at 9th Early Childhood Convention, 2007, Rotorua.

MacNaughtons, G., & Williams, G. (2009).
Techniques for Teaching Young Children
(3 ed.). New South Wales, Australia: Perason Education Australia.

Ministry of Education. (2007).
The New Zealand Curriculum.
Wellington: Learning Media.

Ministry of Education. (1996).
Te Whāriki: He Whāriki Mātauranga mō ngā Mokopuna o Aotearoa: Early Childhood Education.
Wellington: Learning Media.

Saafi, A. (n.d.).
What Is Bruner's Theory of Scaffolding?