While the emphasis and content of school mathematics differ little between Japan and America, by the time students reach junior high school, performance as measured by international studies differs greatly. This report provides a profile of the attitudes toward, strategies used, and performance on mental computation of Japanese students in grades 2, 4, 6, and 8, in order to identify factors that may contribute to this difference. Students in two randomly selected classes in each of grades 2, 4, and 6, and six randomly selected classes in grade 8 were selected from three elementary and one junior high school in Tshuchiura, Japan. Data were collected using a preference survey of numerical computation methods used, an attitude survey, a mental computation test, and interviews of selected students in grac'es 4 and 8. The major findings were that: (1) Japanese students thought both mental computation and written computation were important; (2) teacher attitudes toward mental computation varied; (3) students across all grades preferred mental computations; (4) a wide range of performance on mental computation was found; (5) performance levels on items presented visually was significantly higher than those presented orally; (6) performance on common items increased as schooling increased; (7) the range of mental computation strategies was very narrow; and (8) few students in the interview were able to express alternative strategies for mentally computing an item. Six appendices contain copies of the instruments and the categorization of anticipated strategies.

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This study assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. A sample of students in grades 4 and 8 scoring in the upper and middle quintiles on the mental computation test was interviewed to identify strategies used to mentally compute. All data were collected during the last month of the school year. A wide range of performance on mental computation was found with respect to all types of numbers (whole numbers, decimals, and fractions) and operations at every grade level; the mode of presentation (visual or oral) significantly affected performance levels, with visual items generally producing higher performance; and the range of strategies (initial and alternative) used to do mental computation was narrow, with the most popular approach reflecting a mental version of a learned “paper/pencil” algorithm.

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.

Four hundred and sixty-six fifth- and eighth-grade Japanese students were administered a computational estimation test. The fifth-grade mean was 7.39 and the eighth-grade mean was 11.15 on the 39-item open-ended test. Interviews with 21 students who had scored in the top 5% revealed that the Japanese students employed the three general cognitive processes outlined in a theoretical model based on interviews with United States students: reformulation, translation, and compensation. They also used many of the same strategies (front-end, compatible numbers, flexible rounding) utilized by American students. Few of the Japanese students could recall being taught to estimate in school. Japanese students demonstrated a greater degree of mental computation ability than American students, less frequently made order-of-magnitude errors, and were more reluctant to accept error. Japanese students tended to apply algorithmic computational procedures. Their tendency to use paper-and-pencil procedures mentally often interfered with the estimation process.