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Interventions Proposal
Nicole Barber
The effectiveness of multiple
representations in developing
pre-primary students’
understanding of numbers
one to ten.
Research Title:
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.
The Literature
 Early Childhood Counting (Gelman & Gallistal, 1978)
 One-to-one Correspondence
 Stable-order
 Cardinality
 Abstraction
 Order irrelevance
The Literature
“No way. The hundred is there.”
(Malaguzzi, as cited in Edwards, Gandini, & Forman, 1993, p.vi)
Research Question
“How effective are multiple
representations in developing pre-
primary students’ understanding of
numbers one to ten?”
Participants
 Three pre-primary students (one girl, two boys) from a
local primary school in Perth (selected by teacher).
 Students’ teacher.
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
Data Collection
 Pre- & post- tests
 Observations & notes
 Photographs
 Audio recordings
Data Analysis
 Pre- & post- tests comparisons
 Synthesis of all data collected
Ethics
 Information and Consent Forms
 Both parent and child
 Teacher
 School representatives
 Work samples/photographs authorised
 Research confidentiality
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.
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.

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Interventions proposal

  • 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
  • 9. Data Collection  Pre- & post- tests  Observations & notes  Photographs  Audio recordings
  • 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

  • #5: 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
  • #6: 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.
  • #9: 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.
  • #10: 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.
  • #12: Also they can pull out at any time.