Australian Government (2008).*National Numeracy Review Report*. Canberra: Commonwealth of Australia.

Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In J. T. Mulligan & M. C. Mitchelmore (Eds.),*Children’s number learning* (pp. 17–33). Adelaide: Australian Association of Mathematics Teachers/Mathematics Education Research Group of Australasia.

Bryant, D. P., Bryant, B. R., & Hammill, D. D. (2000). Characteristic behaviors of students with LD who have teacher-identified math weaknesses.

*Journal of Learning Disabilities, 33*, 168–177, 199.

CrossRefCarpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three.

*Journal for Research in Mathematics Education, 15*, 19–22.

CrossRefCobb, P. (1991). Reconstructing elementary school mathematics.*Focus on Learning Problems in Mathematics, 13*(3), 3–33.

Cobb, P. (2003). Investigating students’ reasoning about linear measurement as a paradigm case of design research. In M. Stephan, J. Bowers, P. Cobb, & K. Gravemeijer (Eds.),*Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context*, Journal for Research in Mathematics Education, Monograph No. 12, 1–16. Reston, VA: NCTM.

Denvir, B., & Brown, M. (1986). Understanding of number concepts in low attaining 7–9 year olds: Part 1. Development of descriptive framework and diagnostic instrument.

*Educational Studies in Mathematics, 17*, 15–36.

CrossRefEllemor-Collins, D., & Wright, R. J. (2008a). From counting by ones to facile higher decade addition: The case of Robyn. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepúlveda (Eds.),*Proceedings of the Joint Meeting of PME32 and PMENA XXX* (Vol. 2, pp. 439–446). México: Cinvestav-UMSNH.

Ellemor-Collins, D., & Wright, R. J. (2008b). Intervention instruction in Structuring Numbers 1 to 20: The case of Nate. In M. Goos, R. Brown & K. Makar (Eds.),*Navigating currents and charting directions* (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane, Vol. 1, pp. 179–186). Adelaide: MERGA.

Ellemor-Collins, D., Wright, R. J., & Lewis, G. (2007). Documenting the knowledge of low-attaining 3rd- and 4th- graders: Robyn’s and Bel’s sequential structure and multidigit addition and subtraction. In J. Watson & K. Beswick (Eds.),*Mathematics: Essential research, essential practice* (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart,Vol. 1, pp. 265–274). Adelaide: MERGA.

Freudenthal, H. (1983).*Didactical phenomenology of mathematical structures*. Dordrecht, The Netherlands: Reidel.

Freudenthal, H. (1991).*Revisiting mathematics education*. Dordrecht, The Netherlands: Kluwer.

Fuson, K. C. (1988).*Children’s counting and concepts of number*. New York: Springer.

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.),*Handbook of research on mathematics teaching and learning* (pp. 243–275). New York: Macmillan.

Gervasoni, A., Hadden, T., & Turkenburg, K. (2007). Exploring the number knowledge of children to inform the development of a professional learning plan for teachers in the Ballarat Diocese as a means of building community capacity. In J. Watson & K. Beswick (Eds.),*Mathematics: Essential Research, Essential Practice* (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, Vol. 1, pp. 317–326). Adeaide: MERGA.

Gravemeijer, K. P. E. (1991). An instruction-theoretical reflection on the use of manipulatives. In L. Streefland (Ed.),*Realistic mathematics education in primary school* (pp. 57–76). Utrecht, The Netherlands: Freudenthal Institute.

Gravemeijer, K. P. E. (1994). Instructional design as a learning process. In K. P. E. Gravemeijer (Ed.),*Developing Realistic Mathematics Education* (pp. 17–54). Utrecht, The Netherlands: Freudenthal Institute.

Gravemeijer, K. P. E., Cobb, P., Bowers, J. S., & Whitenack, J. W. (2000). Symbolizing, modeling and instructional design. In P. Cobb, E. Yackel, & K. J. McClain (Eds.),*Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design* (pp. 225–273). Hillsdale, NJ: Lawrence Erlbaum

Gray, E. (1991). An analysis of diverging approaches to simple arithmetic: Preference and its consequences.

*Educational Studies in Mathematics, 22*, 551–574.

CrossRefGreeno, J. G. (1991). Number sense as situated knowing in a conceptual domain.

*Journal for Research in Mathematics Education, 22*, 170–218.

CrossRefHeirdsfield, A. (2001). Integration, compensation and memory in mental addition and subtraction. In M. Van den Heuvel-Panhuizen (Ed.),*Proceedings of the 25th annual conference of the International Group for the Psychology of Mathematics Education* (Vol. 3, pp. 129–136). Utrecht, The Netherlands: Program Committee.

Hunting, R. P. (2003). Part-whole number knowledge in preschool children.

*Journal of Mathematical Behavior, 22*, 217–235.

CrossRef
*Mapping the territory: Primary students with learning difficulties*. (2000). Canberra: Department of Education Training and Youth Affairs.

McIntosh, A. J., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense.*For the Learning of Mathematics, 12*, 2–8.

Moon, B. (1986).*The ‘new maths’ curriculum controversy: An international story*. London: Falmer.

Moser Opitz, E. (2001). Mathematical knowledge and progress in the mathematical learning of children with special needs in their first year of school. In M. Van den Heuvel-Panhuizen (Ed.),*Proceedings of the 25th annual conference of the International Group for the Psychology of Mathematics Education* (Vol. 1, pp. 207–210). Utrecht, The Netherlands: Program Committee.

Mulligan, J., Mitchelmore, M., & Prescott, A. (2006). Integrating concepts and processes in early mathematics: The Australian pattern and structure mathematics awareness project (PASMAP). In J. Novotná, H. Moraová, M. Krátká, & N. StehlÍková (Eds.),*Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education* (Vol. 4, pp. 209–216). Prague: Program Committee.

Olive, J. (2001). Children’s number sequences: An explanation of Steffe’s constructs and an extrapolation to rational numbers of arithmetic.*The Mathematics Educator, 11*(1), 4–9.

Pearn, C. (1998). Is there a need for a mathematics intervention program in Grades 3 and 4? In C. Kanes, M. Goos, & E. Warren (Eds.),*Teaching mathematics in new times* (Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia, Gold Coast, Vol. 2, pp. 444–451). Adelaide: MERGA.

Pirie, S. E. B., & Kieren, T. E. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it?

*Educational Studies in Mathematics, 26*, 165–190.

CrossRef
*Principles and standards for school mathematics*. (2000). Reston, VA: National Council of Teachers of Mathematics.

Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.),*The development of mathematical thinking* (pp. 109–151). New York: Academic Press.

Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children’s problemsolving ability in arithmetic. In H. P. Ginsburg (Ed.),*The development of mathematical thinking* (pp. 153–196). New York: Academic Press.

Rivera, D. P. (1998). Mathematics education and students with learning disabilities. In D. P. Rivera (Ed.),*Mathematics education for students with learning disabilities* (pp. 1–31). Austin, TX: Pro-Ed.

Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin.

*Educational Studies in Mathematics, 22*, 1–36.

CrossRefSteffe, L. P., & Cobb, P. (1988).*Construction of arithmetic meanings and strategies*. New York: Springer.

Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. Kelly & R. Lesh (Eds.),*Handbook of research design in mathematics and science education* (pp. 267–306). Mahwah, NJ: Lawrence Erlbaum.

Sugarman, I. (1997). Teaching*for* strategies. In I. Thompson (Ed.),*Teaching and learning early number* (pp. 142–154). Milton Keynes, UK: Open University Press.

*The national numeracy project: An HMI evaluation*. (1998). London, UK: Office for Standards in Education.

Thompson, I. (1995). The role of counting in the idiosyncratic mental calculation algorithms of young children.

*European Early Childhood Education Research Journal, 3*(1), 5–16.

CrossRefThornton, C. A. (1978). Emphasising thinking strategies in basic fact instruction.

*Journal for Research in Mathematics Education, 9*, 214–227.

CrossRefThrelfall, J. (2002). Flexible mental calculation.

*Educational Studies in Mathematics, 50*, 29–47.

CrossRefTreffers, A. (1987).*Three dimensions: A model of goal and theory description in mathematics instruction-The Wiskobas Project*. Dordrecht: Reidel.

Treffers, A. (1991). Didactical background of a mathematics program for primary education. In L. Streefland (Ed.),*Realistic mathematics education in primary school* (pp. 21–56). Utrecht, The Netherlands: Freudenthal Institute.

Treffers, A. (2001). Grade 1 (and 2): Calculation up to 20. In M. van den Heuvel-Panhuizen (Ed.),*Children learn mathematics* (pp. 43–60). Utrecht, The Netherlands: Freudenthal Institute.

Treffers, A., & Beishuizen, M. (1999). Realistic mathematics education in the Netherlands. In I. Thompson (Ed.),*Issues in teaching numeracy in primary schools* (pp. 27–38). Milton Keynes, UK: Open University Press.

Verschaffel, L., Greer, B., & Torbeyns, J. (2006). Numerical thinking. In A. Gutiérrez & P. Boero (Eds.),*Handbook of research on the psychology of mathematics education*. Rotterdam: Sense Publishers.

van de Walle, J. A. (2004).*Elementary and middle school mathematics: Teaching developmentally* (5th ed.). Boston: Pearson.

van Hiele, P.M. (1973).*Begrip en inzicht* [Understanding and insight]. Purmerend, The Netherlands: Muusses.

Wright, R. J. (1994). A study of the numerical development of 5-year-olds and 6-year-olds.

*Educational Studies in Mathematics, 26*, 25–44.

CrossRefWright, R. J., & Ellemor-Collins, D. (2008).*Structuring numbers to 20: An important topic in early number learning*. Manuscript submitted for publication.

Wright, R. J., Ellemor-Collins, D., & Lewis, G. (2007). Developing pedagogical tools for intervention: Approach, methodology, and an experimental framework. In J. Watson & K. Beswick (Eds.),*Mathematics: Essential Research, Essential Practice* (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, Vol. 2, pp. 843–852). Adelaide: MERGA.

Wright, R. J., Martland, J., Stafford, A. K., & Stanger, G. (2006).*Teaching number: Advancing children’s skills and strategies* (2nd ed.). London: Chapman.

Wright, R. J., Stanger, G., Stafford, A. K., & Martland, J. (2006).*Teaching number in the classroom with 4-8 years-olds*. London: Chapman.

Young-Loveridge, J. (2002). Early childhood numeracy: Building an understanding of part-whole relationships.*Australian Journal of Early Childhood, 27*(4), 36–42.