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# Mathematics

Alton-Lee, A. (2003). * Quality teaching for diverse students in schooling best evidence synthesis.* Ministry of Education: Wellington.

Askew, M., Brown, M., Rhodes, V., William, D. & Johnson, D. (1997). * Effective Teachers of Numeracy.* King’s College, University of London: London.

Bishop, R., Berryman, M., Richardson, C., & Tiakiwai, S. (2003). *Te Kotahitanga: The experiences of year 9 and 10 Māori students in mainstream classes.* Wellington: Ministry of Education.

Bobis, J. (1996). * Visualisation and the development of number sense with kindergarten children.* In J. Mulligan & M. Mitchelmore (Eds.) Children’s number learning, a research monograph of MERGA/AAMT. Adelaide: AAMT.

Behr,M.,Harel,G.,Post,T., & Lesh,R. (1994). * Units of Quantity: A conceptual basis common to additive and multiplicative structures.* In: Harel, G., & Confrey, J. (Eds)

*The Development of Multiplicative Reasoning in the Learning of Mathematics*. NY:State University of New York Press.

Brophy, J.,& Good, T. (1986). * Teacher behaviour and student achievement.* In M.C. Wittrock (Ed.), handbook of research on teaching, 3rd ed. (pp. 328-375). New York: MacMillan.

Clarke, D., & Hoon, S.L. (2005) * Studying the Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai.* In Chick, H. & Vincent, J. (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education July 10-15, 2005, PME: Melbourne

Cobb, P., McClain, K, & Whitenack, J. (1995) * Supporting Young Children’s Development of Mathematical Power,* In Richards, A (Ed.),

*FLAIR: Forging Links and Integrating Resources, Proceedings of the 15th Biennial Conference of the Australian Association of Mathematics Teachers*, Darwin., AAMT: Adelaide, Australia.

Cobb, P. (2009) * Designing Schools and Districts as Learning Organisations for Instructional Improvement in Mathematics.* Key note address the National Numeracy Conference. February 2009. www.nzmaths.co.nz

Ellerton, N., & Clements, M. (2005). * A Mathematics Education Ghost Story: Herbartianism and School Mathematics*. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, A. Roche, (Eds.).

*Building connections: theory, research and practice*(Proceedings of the annual conference of the Mathematics Education Group of Australasia, Melbourne, pp.313-321.) Sydney: Mathematics Education Research Group of Australasia.

Fuson, K.C., Wearne, D., Hiebert, J., Murray, H., Human, P., Oliver, A., Carpenter, T., Fennema, E. (1997). * Children’s conceptual structures for multidigit numbers and methods of multi-digit addition and subtraction.* Journal for Research in Mathematics Education, 28(2), 130-162.

Hart, K. (1989). * A lecture on bridging. First New Zealand Association of Mathematics Teachers (NZAMT) Conference.* Waikato University.

Hattie, J (2002). * What are the attributes of excellent teachers?* In: New Zealand Council for Educational Research Annual Conference. NZCER:Wellington

Hughes, P. (2002). * A model for teaching numeracy strategies.* In B. Barton B., K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas, (Eds.). Mathematics Education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Group of Australasia, Auckland, 350-357.) Sydney: Mathematics Education Research Group of Australasia.

Irwin, K. C, & Britt, M. S. (2005). * The algebraic nature of students’ numerical manipulation in the New Zealand Numeracy Project.* Educational Studies in Mathematics, 58, 169-188.

Jones, G., Thornton, C., Putt, I., Hill, K., Mogill, A., Rich, B., & Van Zoest, L. (1996). * Multi-digit number sense: A framework for instruction and assessment. *Journal for Research in Mathematics Education, 27 (3), 310-336.

Lamon, S. (1994). * Ratio and proportion: Cognitive foundations in unitising and norming.* In: Harel, G., & Confrey, J. (Eds.)

*The Development of Multiplicative Reasoning in the Learning of Mathematics*. NY:State University of New York Press.

Ministry of Education (2005 d). * Book 5 teaching addition, subtraction, and place value.* Wellington: Ministry of Education.

Mulligan, J. (1999). * “Seeing is Learning”: Promoting Mathematical Thinking Through Awareness of Pattern and Structure.* Key note address the National Numeracy Conference. February 2009. www.nzmaths.co.nz

New South Wales Department of Education and Training (1999). * Count me in too professional development package.* Ryde: NSW Department of Education and Training.

Pirie, S., & Kieren, T. (1989). *A recursive theory of mathematical understanding.**For the Learning of Mathematics*, 9(3).

Pirie, S., & Kieren, T. (1994). *Beyond metaphor: Formalising in mathematical understanding within constructivist environments.**For the Learning of Mathematics*, 14(1).

Pirie, S., & Martin, L. (2000). * The role of collecting in the growth of mathematical understanding.* Mathematics Education Research Journal, 12(2), 127-146.

Pitkethly, A. & Hunting, R. (1996) *A review of recent research in the area of initial fraction concepts.**Educational Studies in Mathematics* 30: 5-38. Belgium: Kluwer Academic.

Ross, S. (1989). * Parts, wholes and place value: a developmental view.* Arithmetic Teacher, 36(60), 41-51.

Slavin, R.E. (1996). * Research on co-operative learning and achievement: What we know and what we need to know.* Contemporary Educational Psychology, 21, 43-69.

Shulman, L. S. (1987). * Knowledge and Teaching: Foundations of the New Reform.* Harvard Educational Review, 57(1), 1-22.

Steffe, L. (1994). * Children’s Multiplying Schemes.* In: Harel, G., & Confrey, J. (Eds.)

*The Development of Multiplicative Reasoning in the Learning of Mathematics*. NY: State University of New York Press.

Steffe, L., von Glasersfeld, E., Richards, J. & Cobb, P. (1983). * Children’s counting types: philosophy theory and application.* New York: Paeder.

Steffe, L., & Cobb, P. with von Glasersfeld, E. (1988). * Construction of arithmetical meanings and strategies.* New York: Springer-Verlag.

Steffe, L., Kieren, T. (1994). * Radical Constructivism and Mathematics Education.* Journal for research in mathematics education, 25(6), 711 - 733.

Steffe, L. (1994). * Children’s Multiplying Schemes.* In: Harel, G., & Confrey, J. (Eds.)

*The Development of Multiplicative Reasoning in the Learning of Mathematics*. NY: State University of New York Press.

Stigler, J., & Hiebert, J. (1997). * Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study, In Raising Australian Standards in Mathematics and Science: Insights from TIMSS*, ACER:Melbourne.

Sweller, J. (1994). * Cognitive Load Theory, Learning Difficulty, and Instructional Design. Learning and Instruction,* 4: 295-312.

von Glasersfeld, E. (1992). * Aspects of radical constructivism and its educational recommendations.* Paper presented at the ICME-7, Draft to Working Group #4, Montreal. Retrieved March 18, 2003 from http://www.umass.edu/srri/vonGlasersfeld/onlinePapers/html/195.html

Vygotsky, L.S. (1978). *Mind and society: The development of higher mental processes.* Cambridge, MA: Harvard University Press.

Wright, R. (1991a). * An application of the epistemology of radical constructivism to the study of learning.* The Australian Educational Researcher, 18(1), 75-95.

Wright, R. (1991b). * The role of counting in children's numerical development.* The Australian Journal of Early Childhood, 16(2), 43-48

Wright, R. (1991c). * What number knowledge is possessed by children entering the kindergarten year of school?* The Mathematics Education Research Journal, 3(1), 1-16.

Wright, R. J. (1998). * An overview of a research-based framework for assessing and teaching early number.* In C. Kanes, M. Goos & E. Warren (Eds.),

*Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia*, Vol. 2, 701-708. Brisbane: Griffith University.

Wright, R. J. (1998). * Children’s beginning knowledge of numerals and its relationship to their knowledge of number words: An exploratory, observational study.* In A. Olivier & K. Newstead (Eds.),

*Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education*, Vol. 4, 201-208. Stellenbosh, South Africa: University of Stellenbosh.

Wright, R. (1991a). * An application of the epistemology of radical constructivism to the study of learning.* The Australian Educational Researcher, 18(1), 75-95.

Wright, R. (1991b). * The role of counting in children's numerical development.* The Australian Journal of Early Childhood, 16(2), 43-48

Wright, R. (1991c). * What number knowledge is possessed by children entering the kindergarten year of school?* The Mathematics Education Research Journal, 3(1), 1-16.

[Wright, R. J. (1998). * An overview of a research-based framework for assessing and teaching early number.* In C. Kanes, M. Goos & E. Warren (Eds.),

*Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia*, Vol. 2, 701-708. Brisbane: Griffith University.

Wright, R. J. (1998). * Children’s beginning knowledge of numerals and its relationship to their knowledge of number words: An exploratory, observational study.* In A. Olivier & K. Newstead (Eds.),

*Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education*, Vol. 4, 201-208. Stellenbosh, South Africa: University of Stellenbosh.

Young-Loveridge, J. & Wright, V. (2002) *Data from the Numeracy development project and the New Zealand Number Framework.* Paper presented at the 2nd Biennial Conference of the Teacher Education Forum of Aotearoa New Zealand (TEFANZ), 28-31 August, 2002.

Young-Loveridge, J. (2004). * Patterns of performance and progress on the Numeracy Projects: further analysis of the Numeracy Project data.* Hamilton: University of Waikato.