Mental computation performance in Australia, Japan and the United States

Abstract

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.

Computational Estimation Performance on Whole‐Number Multiplication by Third‐ and Fifth‐Grade Chinese Students

“…See LeFevre et al (1993)), some researchers focused on the effect of mode of presentation, i.e., whether a task is presented visually or orally, on participants' performance. McIntosh et al (1995) found that while it affected American and Australian students' mental computation only marginally, the visual mode produced dramatically better success rates for Japanese students than the oral mode. Reys et al (1995) found that mode of presentation drastically affected their Japanese participants' mental computation, with visually presented items generally producing higher performance.…”

“…Research on computational estimation and its related areas has been conducted on participants from other countries as well, such as Australia, Britain, Canada, France, Japan, Mexico, and Taiwan (Dowker, 1997; Lemaire, LeCacheur, & Farioli, 2000; McIntosh, Nohda, Reys, & Reys, 1995; Reys, 1991; Reys et al, 1991; Reys, Reys, Nohda, & Emori, 1995; Shimizu & Ishida, 1994; Yang, 2005, 2007). In general terms, it was recognized that estimation ability is not independent of exact calculation ability, and that many students are, in fact, highly dependent on standard written algorithms in their estimation.…”

An Overview of Mental Calculation Strategies and the Frequency of Their Application

“…For the purpose of the research, a test and an interview were conducted with each respondent, with mental calculation tasks modeled on a study about mental calculation by McIntosh et. al.…”

“…A method (Greek μέϑοδος: research path, mode, procedure) is a planned or premeditated procedure for achieving a certain theoretical or practical goal (Hrvatska enciklopedija, 2013). As with calculation methods, numerical tasks can be solved with three methods: using mental calculation, or written calculation (paper and pencil), or using a calculator (McIntosh et al, 1995;Selter, 2000). In this paper, we will focus on mental calculation (known also as mental computation).…”

“…Mental calculation is based on understanding the structure of numbers; it increases the comprehension of the number system and is closely related to the concept of number sense (Bruinsma, 1961;Lemonidis, 2016;Sowder 1992). Number sense refers to a person's general understanding of numbers and operations and the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful and efficient strategies for managing numerical situations (McIntosh et al, 1997b).…”