Assessing Young Children's Arithmetical Strategies and Knowledge: Providing Learning Opportunities for Teachers

Abstract

Two interrelated initiatives in early numeracy are briefly described—the Count Me In Too Project in New South Wales, and Mathematics Recovery. The article then focuses on an approach to student assessment which is used in both initiatives. This approach enables teachers to better understand young children's early arithmetical strategies and knowledge. The approach is described in three parts: Part A focuses on initial strategies for addition or subtraction; for example, counting-from-one, counting-on, using finger patterns, and using strategies other than counting by ones. Part B focuses on strategies to solve two-digit subtraction and strategies for incrementing by tens and ones. And Part C focuses on strategies for early multiplication and division. Following this, the strategies which have been described in each part are discussed in terms of their relative sophistication. The discussion includes links to relevant literature and issues relevant to the teaching of early numbers. The conclusion lists six important points about early number teaching and learning.

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References

Beishuizen

, & Anghileri

(1998). Which mental strategies in the early number curriculum? A comparison of British Ideas and Dutch Views. British Education Research Journal, 24, 519–538.

Bobis

, & Gould

(1998). The impact of an early number project on the professional development of teachers. In Kanes

, Goos

& Warren

(Eds.), Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia, 2, 107–113. Brisbane: Griffith University.

Bobis

, & Gould

(1999). The mathematical achievement of children in the Count Me In Too Program. In Truran

& Truran

, K. (Eds.), Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia, 84–90. Sydney: MERGA.

Bobis

, & Gould

(2000). Changing the professional knowledge of teachers. In Bana

& Chapman

(Eds.), Proceedings of the 23rd Annual Conference of the Mathematics Education Research Group of Australasia, 1, 47–54. Perth: Edith Cowan University.

Clay

M. M.

(1993). Reading recovery: A guide book to teachers in training. Portsmouth, NH: Heinemann.

Deford

E. D

, Lyons

C. A

, & Pinnell

G. S.

(1991). Bridges to literacy: Learning from reading recovery. Portsmouth, NH: Heinemann.

Gray

E. M.

(1991). An analysis of diverging approaches to simple arithmetic: Preference and its consequences. Educational Studies in Mathematics, 22, 551–74.

Gray

E. M.

, & Tall

D. O.

(1994). Duality, ambiguity, and flexibility: A ‘proceptual’ view of simple arithmetic. Journal for Research in Mathematics Education, 25, 116–140.

Mulligan

J. T.

, (1998). A research-based framework for assessing early multiplication and division. In Kanes

, Goos

& Warren

(Eds.), Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia, 2, 404–411. Brisbane: Griffith University.

10.

Mulligan

J. T.

& Mitchelmore

M. C.

(1997). Young children's intuitive models of multiplication and division. Journal for Research in Mathematics Education, 25, 309–331.

11.

NSW Department of Education and Training. (2000). Count Me In Too Professional Development Package. Sydney: NSWDET.

12.

Steffe

L. P.

(1991). The constructivist teaching experiment: Illustrations and implications. In von Glasersfeld

(Ed). Radical constructivism in mathematics Education 177–194. Dordrecht: Kluwer.

13.

Thomas

, & Ward

(2001). An evaluation of the Count Me In Too pilot project. Wellington, New Zealand: Ministry of Education. [Available from Learning Media Customer Services, Box 3293 Wellington, New Zealand (quote item #10211)].

14.

Thompson

(1995). The role of counting in the idiosyncratic mental calculation algorithms of young children. European Early Childhood Education Research Journal, 3, 5–16.

15.

Wright

R. J.

(2000). Professional development in recovery education. In Steffe

L. P.

& Thompson

P. W.

(Eds.), Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld 134–151. London: Falmer.

16.

Wright

R. J.

, Martland

, & Stafford

(2000). Early numeracy: Assessment for teaching and intervention. London: Sage.

17.

Wright

R. J.

, Martland

, Stafford

, & Stanger

(2002). Teaching number: Advancing children's skills and strategies. London: Sage.

18.

Wright

R. J.

, Stanger

, Cowper

, & Dyson

(1996). First-graders’ progress in an experimental mathematics recovery program. In Mulligan

& Mitchelmore

(Eds), Research in early number learning: An Australian perspective (p. 55–72). Adelaide: AAMT.