# NZ mathematics education reports

This section currently contains the Annual Evaluation Reports and Compendium Papers on the the Numeracy Development Projects, and other references from books and journals. Content will be updated to include other reports on New Zealand maths education before term two of 2018.

### Annual Evaluation Reports

Annual evaluation reports and compendium papers have been written on each section of the Numeracy Development Projects.

Pāngarau/Mathematics: Best Evidence Synthesis

This file summarises the history of the development of the New Zealand mathematics curriculum (PDF, 99KB) from 1990 to 2000.

### Other References

The following references have relevance to the Numeracy Project. Click on the summary link for a description of the main findings contained in the reference.

Anghileri, J. (1999). Issues in teaching multiplication and division. In I.Thompson (Ed.). *Issues in teaching numeracy in primary schools *(pp.184-194). Buckingham, UK: Open University Press. (__summary__)

Anghileri, Julia. (2001). Contrasting approaches that challenge tradition. In J. Anghileri (Ed.)(2001) *Principles and practices in arithmetic teaching* (pp.4-14). Buckingham: Open University Press. (summary)

Anthony, Glenda & Walshaw, Margaret. (2002). Swaps and Switches: Students’ understandings of Commutativity. In B. Barton, K. Irwin, M. Pfannkuch, & M. Thomas (Eds.)(2002). *Mathematics Education in the South Pacific*: Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia,(pp.91-99). Sydney: MERGA (summary)

Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. *The Elementary School Journal,* 93, (4), 373-97. (__summary__)

Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In J. Mulligan& M. Mitchelmore (Eds). *Children’s number learning*. Adelaide: The Australian Association of Mathematics Teachers, 1996, pp. 17-33. (__summary__)

Boulton-Lewis, G., Wilss, L. & Mutch, S. (1996). Representations and Strategies for subtraction used by primary school children. Mathematics Education Research Journal, 8 (2), 137-152. (__summary__)

Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction, *The Elementary School Journal*, 97 (1), 3-20. (__summary__)

Clark, F. B., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. *Journal for Research in Mathematics Education*, 27 (1), 41-51. (__summary__)

Clements, D. H. (1999). Subitizing: What is it? Why teach it? *Teaching Children Mathematics*, March, 400-405. (__summary__)

Fuson, K. C. & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. *Journal for Research in Mathematics Education*, 21 (3), 180-206. (__summary__)

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

Irwin, K.C. (1996). Children’s understanding of the principles of covariation and compensation in part-whole relationships, *Journal for Research in Mathematics Education*, 27 (1), 25-40. (__summary__)

Irwin, Kathryn & Ell, Fiona. (2002). Visualising and the move from informal to formal linear measurement. In B. Barton, K. Irwin, M. Pfannkuch, & M. Thomas (Eds.)(2002). *Mathematics Education in the South Pacific*: Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, (pp.358-365). Sydney: MERGA (summary)

Irwin, Kathryn, (2003). Multiplicative Strategies of New Zealand Secondary School Students. In Pateman, N. A., Dougherty, B. J., & Zilliox, J. T. (Eds.)(2003). *Proceedings of the 2003 Joint Meeting of PME and PMENA*, CRDG, College of Education, University of Hawai‘i (summary)

Lamon, S. J. (1996). The Development of unitizing: Its role in children’s partitioning strategies. *Journal for Research in Mathematics Education*, 27 (2), 170-93. (__summary__)

Lampert, M. (1989). Choosing and using mathematical tools in classroom discourse. *Advances in Research on Teaching*, 1, 223-64. (__summary__)

Maclellan, E. (1997). The importance of counting. In I. Thompson (Ed.). *Teaching and learning early number *(pp.33-40). Buckingham, UK: Open University Press. (__summary__)

McIntosh, A. (1996). Mental computation and number sense of Western Australian students. In J. Mulligan & M. Mitchelmore, (Eds). *Children’s Number Learning* (pp.259-276). Adelaide: Australian Association of Mathematics Teachers. (__summary__)

Mulligan, J. T. and Mitchelmore, M. C. (1997). Young children’s intuitive models of multiplication and division. *Journal for Research in Mathematical Education*, 28 (3), 309-330. (__summary__)

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

Ritchie, G. (1991). Does mathematics equipment help? Interviews with children using equipment. *SAMEPapers,* 79-101 (__summary__)

Sowder, J. (1997). Place value as the key to teaching decimal operations. *Teaching Children Mathematics*, 448-53, April. (__summary__)

Steffe, Leslie. (1994). Children’s multiplying schemes. In G. Harel & J. Confrey (Eds.)* The development of multiplicative reasoning in the learning of mathematics (*pp. 3-39). Albany,NY: SUNY. (summary)

Thomas, N. (1996). Understanding the number system. In J. Mulligan & M. Mitchelmore (Eds.). *Children’s Number Learning*, (pp. 89-106). Adelaide, South Australia: MERGA/AAMT. (__summary__)

Thomas, Gill, Tagg, Andrew, & Ward, Jenny. (2002). Making a difference: The Early Numeracy Project. In B. Barton, K. Irwin, M. Pfannkuch, & M. Thomas (Eds.)(2002). *Mathematics Education in the South Pacific*: Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, (pp.49-57). Sydney: MERGA. (summary)

Thompson, I. (1997). Developing young children’s counting skills. In I. Thompson (Ed.) *Teaching and learning early number *(pp.123-132). Buckingham, UK: Open University Press. (__summary__)

Vance, J. H. (1998). Number operations from an algebraic perspective. *Teaching Children Mathematics*, pp. 282-5, January 1998. (__summary__)

Yackel, Erna (2001). Perspectives on arithmetic from classroom-based research in the United States of America. In J. Anghileri (Ed.)(2001) *Principles and practices in arithmetic teaching* (pp. 15-31). Buckingham: Open University Press. (summary)

Young-Loveridge, J. (1999). The acquisition of numeracy. *set,*Research Information for Teachers, 1. (__summary__)

Young-Loveridge, Jenny & Wright, Vince. (2002).Validation of the New Zealand Number Framework. In B. Barton, K. Irwin, M. Pfannkuch, & M. Thomas (Eds.)(2002). *Mathematics Education in the South Pacific*: Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, (pp.722-729). Sydney: MERGA (summary)