2. The effectiveness of multiple
representations in developing
pre-primary students’
understanding of numbers
one to ten.
Research Title:
3. The Issue
By the end of the year, children in pre-primary
need to count and use numbers up to 20 (ACARA).
Mid-way through the year, several children in a
pre-primary class are unable to count to, and
recognise numerals up to, ten.
4. The Literature
Early Childhood Counting (Gelman & Gallistal, 1978)
One-to-one Correspondence
Stable-order
Cardinality
Abstraction
Order irrelevance
5. The Literature
“No way. The hundred is there.”
(Malaguzzi, as cited in Edwards, Gandini, & Forman, 1993, p.vi)
6. Research Question
“How effective are multiple
representations in developing pre-
primary students’ understanding of
numbers one to ten?”
7. Participants
Three pre-primary students (one girl, two boys) from a
local primary school in Perth (selected by teacher).
Students’ teacher.
8. Intervention
Pre-test of students’ pre-counting skills and numeral
recognition
Intervention in two sessions of half-hour each day
Multiple forms of practice
Sensory
Physical
Musical
Technological
Traditional
Post-test of students’ pre-counting skills and numeral
recognition
10. Data Analysis
Pre- & post- tests comparisons
Synthesis of all data collected
11. Ethics
Information and Consent Forms
Both parent and child
Teacher
School representatives
Work samples/photographs authorised
Research confidentiality
12. References
ACARA. (2011). The Australian curriculum: Mathematics.
Retrieved from
http://www.australiancurriculum.edu.au/Mathematics/Cu
rriculum/F-10
Gelman, R. & Gallistel, C.R. (1978). The child’s
understanding of number. Cambridge, Massachusetts:
Harvard University Press.
Edwards, C., Gandini, L., & Forman, G. (Eds.) (1993).
The hundred languages of children: The Reggio Emilia
approach to early childhood education. Westport, CT:
Ablex Publishing Corporation.
13. Supporting References
Askew, M. (2012). Transforming primary mathematics. London: Taylor & Francis.
Cathcart, W.G., Pothier, Y.M., Vance, J.H., and Bezuk, N.S. (2011). Learning
mathematics in elementary and middle schools: A learner-centered approach (5th
ed). Boston, MA: Pearson.
Copley, J. V. (2000). The young child and mathematics. Washington, DC: National
Association for the Education of Young Children.
Gardner, H. (2011). Frames of mind: The theory of multiple intelligences. [Adobe
Digital Editions]. Retrieved from Ebook Library.
Kaur, B., Koay, P.L., Foong, P.Y., & Sudarshan, A. (2012). An exploratory study on low
attainers in primary mathematics (LAPM). In B. Kaur & M. Ghani (Eds.), Low
attainers in primary mathematics (pp. 1-18). Tuck Lick, Singapore: World Scientific.
Montague-Smith, A., & Price, A.J. (2012). Mathematics in early years education (3rd
ed.). New York: Routledge.
Pound, L. (2006). Supporting mathematical development in the early years (2nd ed.).
Berkshire, England: Open University Press.
Editor's Notes
one-to-one correspondence, that is, to counting each object in a set once and only once; stable-order refers to using the correct sequence of number labels (1,2,3,4,5,… in order); cardinality refers to recognising that the number label of the last object counted is the number of objects in the set; abstraction recognises that counting can be used on any set of items; and order-irrelevance indicates that objects in a set can be counted in any order with the same resulting number
In general terms, it is generally recognised thatteaching any concept using many different forms is beneficial to children’s learning. Research has shown specifically that teaching using many forms of representation assists mathematical development, and even self-esteem associated with maths as well. The current study therefore proposes to investigate developing the pre-counting principles using multiple representations.
Numeral recognition and writing will be developed through sensory activities such as drawing in sand and on sandpaper, physical activities such as hopscotch, and technological activities through the use of an iPad. In addition, more traditional methods such as manipulatives, books, rhymes, and songs will also be employed.
Pre- and post- tests will be conducted orally using props, with results recorded on paper by the researcher. Conversations with the children and the teacher will be audio recorded so that no information is lost. Notes and observations will be used extensively throughout the whole intervention to record the level of each child’s interest and enjoyment in the current activity, any particularly interesting anecdotes, and each child’s progress. Photographs will be particularly useful for capturing the children’s number formations in the sand, with other natural materials, and with their own bodies.
