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ERIC Number: ED308962
Record Type: Non-Journal
Publication Date: 1989-Apr
Pages: 7
Abstractor: N/A
Reference Count: N/A
Developmental Changes in the Use of Logical Principles in Mental Arithmetic.
Bisanz, Jeffrey; And Others
Because little is presently known about changes in children's knowledge of the logical principles of arithmetic and, more specifically, about how children's developing knowledge is reflected in the use of solution procedures, two types of three-term arithmetic problems were presented for solution to 6-, 7-, 9-, 11-, and 20-year-olds. Problems were to be solved mentally. One type could be solved only by calculating sums and differences. The other type could also be solved without computation by using a procedural shortcut based on the logical principle of inversion, i.e., a + b - b must be equal to a. Analyses of latencies and verbal reports revealed that: (1) some children as young as 6 years of age used inversion-based shortcuts spontaneously; (2) there were marked individual differences among elementary school children in the use of inversion-based shortcuts; (3) the use of procedural shortcuts based on knowledge of logical principles increased markedly between 9 and 20 years but changed little from 6 to 9 years; and (4) some 6-year-olds used a functional shortcut, the negation procedure, that may be a precursor to inversion-based procedures. It is concluded that the results indicate that early improvements in arithmetic may reflect changes in computational skill rather than in knowledge and use of the logical principles that characterize the domain of arithmetic. (Author/RH)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A