This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then discussed.

ABSTRACT. The study was conducted to explore performance on a variety of mental computation tasks using two presentation formats (visual and oral). Students at four grade levels between grades 2 and 9 in three countries (Australia, Japan, United States) were given a group administered mental computation test consisting of two parts (oral presentation format, visual presentation format).The sample of nearly 2000 students represents 6 classes at each of four grade levels in each country. Results indicate a wide variation in performance within the sample of each country at each grade level. Differences in performance between countries are also apparent and may reflect variations in instructional focus on mental computation. In particular, Japanese students perform at a higher level at the early grades than do students in either of the other countries sampled. However, by grade 8 this difference narrows in the American sample, and vanishes for the Australian sample. Differences in performance related to presentation format were dramatic for particular items and non-existent for other items. The most consistent effect was found in the Japanese sample where the visual presentation format resulted in higher performance levels on most items.It is hypothesised that superior results on visually presented items are attributable to a greater reliance on use of the standard written algorithm, while superior results on orally presented items indicate a greater tendency to use invented mental algorithms.

At the primary-grades level, the benefits of developing and using mental strategies for computing have been well articulated (see, e.g., Beberman (1959); Brownell [1972); Cobb and Merkel [1989]: Kamii [1989]; Reys and Barger [1994): Shuard [1987); Trafton [1978)), and many primary-grades teachers are now encouraging students to invent and use thinking strategies as a way to facilitate their development of number sense. They are also dealing with the practical implications of implementing this approach to computation, which is very different from the traditional. rule-oriented, procedural approach to computation. At the middle-grades level, however, comparatively Little discussion related to the same issue has occurred. At this level, should students be encouraged to invent mental strategies for computing? Should standard written algorithms for computing continue to be taught? How does an emphasis on thinking strategies relate to the current emphasis on using the calculator as an efficient tool for computation?

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