Summary of Reference
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
This paper describes a model for teaching numeracy strategies. A model for knowledge teaching would be quite different from this and would be more closely aligned with teachers’ current models of teaching. It outlines various research such as that of Wright and Young-Loveridge that underpin the strategy teaching model. The first part of the paper provides a discussion of the distinction between knowledge and strategy from its origins in the work of Wright. The author examines the arbitrary nature of the relationship and illustrates this with examples. Drawing on the work of Young-Loveridge and Wright he suggests that it is best thought of as a blurred distinction and concludes that the maintenance of this dichotomy is for purely pedagogical reasons. The paper goes on to discuss the complexities of assessing strategy as compared to the more straightforward task of assessing knowledge. Part of this complexity arises from children’s use of multiple counting types to solve problems and the fact that the size of the number is no guide to the degree of sophistication of the students’ thinking.
The main part of the paper discusses the model for teaching numeracy strategies. This is prefaced with an overview of Pirie and Kieren’s dynamical theory for the growth of student understanding that highlights the stages and idea of “folding back” that influenced the development of the strategy teaching model for Steffe’s counting types and their extensions. The key features of the model are existing knowledge and strategies on which student understanding develops. The levels of understanding comprise “using materials”, “using imaging”, and “using number properties”. “Using materials” is part of the traditional approach used by teachers of young children. “Using imaging” is less familiar to teachers and aims to help children connect the use of materials to abstract mathematical ideas. The manipulatives selected for this stage are ones that can readily be imagined when they are screened or shielded from the child. The author explains that “the strategy teaching model suggests that when children do not make connections at the “Using Imaging” stage in the model that they fold back to using materials”.
The “Using number properties” stage incorporates Pirie and Kieren’s ideas of “property noticing” and “formalising”. The feature of this stage is that children are able to reason mathematically “directly with numbers and their properties”. If children are able to do this then the author contends that they have reached the next stage of the model in having “new current knowledge and strategies” and that “the model may now be reused from the beginning”. The paper concludes by detailing restrictions on the use of the model.