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Summary of Reference

Author:
Young-Loveridge, Jenny & Wright, Vince

Title:
Validation of the New Zealand Number Framework

Bibliographic data:
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 ofAustralasia, (pp.722-729). Sydney: MERGA

Summary:
This paper presents the research-base in the development of the New Zealand Number Framework by examining patterns of performance among Year 4 to 6 students. The two interdependent components of the Framework are strategy and knowledge “with Strategy creating new knowledge through use, and Knowledge providing the foundation upon which new strategies are built”.

The lower stages of the framework focus on counting and were informed by the Count Me In Too (CMIT) pilot project based on Bob Wright and Les Steffe’s work. The upper stages of the framework focus on part-whole thinking and these were informed by the work of several internationally recognised mathematics educators such as Confrey and Harel, Lamon, and Pitkethly and Hunting. The authors stress that while the lower (counting) stages have been validated empirically, the upper (part-whole) stages have not. This paper presents an analysis of data gathered as part of the Advanced Numeracy Project in which teachers interviewed children in their classes at the beginning and end of the project using a diagnostic interview. The analysis examined interrelationships among different aspects of the framework. The authors conclude that “the complexity of unit structures involved in number problems is the most significant indication of difficulty” and that “students appear to acquire strong control of additive unit structures before getting strong control of multiplicative structures then, in turn, proportional structures”. They argue that their findings provide support for the hierarchical organisation of frameworks and that “some minimal level of knowledge about numbers is a prerequisite for the development of part-whole strategies”.