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Characteristics of unskilled, skilled and highly skilled mental calculators

University of British Columbia

This study was concerned with the identification of the processes and procedures which characterized unskilled, skilled, and highly skilled mental calculation performance of high-school students. Fifteen skilled and fifteen unskilled mental calculators were selected from 280 senior secondary mathematics students as a result of their performances on a mental multiplication test. One highly skilled 13-year-old was later added to the sample. These three skill groups were compared on a number of dimensions including the strategies used to determine the mental products of multi-digit factors, ability to recall numerical equivalents, and short-term memory capacity. The study identified twelve mental calculation strategies used by these students. The majority of unskilled subjects made extensive use of strategies more suited to written than mental calculation tasks. The more proficient subjects tended to employ strategies based upon properties suggested by the factors. There were statistically significant differences between the mean performance of each group on a multiplication basic fact recall test. A statistically significant but weak linear relationship between recall and mental multiplication performance existed. The proficient subjects retrieved significantly more large numerical equivalents during the solution of a mental calculation than did the unskilled subjects. The highly-skilled subject could recall quickly the majority of 2-digit squares and many 3-digit squares. Statistically significant differences between the performances of the skilled and unskilled groups on four measures of short-term memory capacity were found. Further analysis indicated that only a weak linear relationship between capacity and mental calculation performance existed. Certain aspects of the initially stated calculative task and the interim calculations were found to be particularly susceptible to forgetting by mental calculators. These suggestions for further research were made: studying the characteristics of subjects who differ in the ability to determine mental sums, differences, and quotients; evaluating the short-term memory demands imposed by different mental calculation strategies; determining which strategies can be used to improve the mental calculation abilities of lesser skilled subjects.

Text

2010-06-13

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http://hdl.handle.net/2429/25632

Mathematics Education

University of British Columbia

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