Academic journal article Australian Journal of Early Childhood

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

Academic journal article Australian Journal of Early Childhood

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

Article excerpt

Count Me In Too (CMIT) (Bobis & Gould, 1998, 1999, 2000; NSW Department of Education and Training, 2000) is a systemic initiative operating in NSW government schools since 1996, which aims to enhance teachers' understandings of young children's arithmetical strategies. CMIT was judged to be successful in its initial trial (Bobis & Gould, 1998) and since 1996 has received increased government funding each year. By July 2001, CMIT had been fully implemented in more than 1000 schools, and by 2003 will be available in all primary and central schools (approx. 1800). As well, CMIT has been implemented in other Australian school systems and in 2000 was implemented on a large scale in New Zealand (81 schools and 581 teachers) (Thomas & Ward, 2001).

Mathematics Recovery (Wright, 2000; Wright, Martland, Stafford & Stanger, 2002; Wright, Stanger, Cowper & Dyson, 1996) is a specialised professional development program for teachers and a recovery program (Clay, 1993; Deford, Lyons & Pinnell, 1991) for students in the second year of school, which was developed in northern New South Wales during 1992-95. Since 1995, Mathematics Recovery has been adopted by school systems in 15 states in the US, in nine Local Education Authorities in the north of England, and in the Bahamas and Scotland.

Development of CMIT drew extensively on the theory and methods that had been developed for Mathematics Recovery and the programs have several commonalities--their research base, learning framework (Wright, Martland & Stafford, 2000), approach to assessment, and approaches to teachers' learning. The Learning Framework in Number (LFIN) (NSW Department of Education and Training, 2000; Wright et al., 2000) is the central guiding framework for assessment and teaching. A distinctive feature of both programs is their focus on providing for teachers a rich mosaic of children's arithmetical knowledge and strategies. This is in accordance with the increasing focus on teaching that takes account of and accords with children's strategies and thinking in mathematics (Beishuizen & Anghileri, 1998).

This paper does not focus on describing LFIN because this is already available (Wright et al., 2000, p. 24). Rather, the paper provides an introduction to an approach to assessment which is central to both programs. This approach provides a basis for teachers coming to learn more about young children's arithmetical thinking. The approach is illustrated in the following three parts: A) Assessing Early Arithmetical Strategies; B) Assessing Base-Ten and two-digit Addition and Subtraction Strategies; and C) Assessing Early Multiplication and Division Strategies.

Part A--Assessing early arithmetical strategies

This aspect of the assessment focuses on the early strategies used by students in arithmetical situations which are problematic for them, and typically involve counting, addition or subtraction. The assessment tasks involve activities such as counting the items in a collection of counters, working out how many counters in two screened collections, and various kinds of subtractive tasks presented with screened collections of counters. Verbal and written tasks might also be presented. The strategies evoked by these tasks relate to a central aspect of LFIN known as Stages of Early Arithmetical Learning (SEAL). This section provides four examples of assessment of these strategies.

Counting-from-one on additive tasks involving two collections

Shirley, a first-grader who participated in the first year of Mathematics Recovery in NSW, was taught individually, in sessions of 25 minutes duration, four days per week. She made major progress in the course of about four weeks. Early in her teaching cycle Shirley was presented with three additive tasks (3+2, 5+3, 10+3) using two collections of counters, one or both of which were screened. …

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