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| Courtney is in Year 8 and she is trying to interpret decimals in terms of fraction notation. She sees the decimal part as the denominator of a fraction, with larger denominators creating smaller fractions. This misconception is revealed when she chooses 0.3 as the larger of 0.3 and 0.4 (as 1/3 is larger than 1/4). Reciprocal thinking is one of the shorter-is-larger misconceptions. |  |
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Look at Courtney's answers to the Decimal Comparison Test. (You can double-click on the yellow notes for her reasons) | ||||||||||||
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Interviews with Courtney
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See how Courtney would count from 1 to 2 with decimals and compare with other students. | ||||||||||||
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Attempt a short decimal comparison test to check your understanding of Courtney's thinking. This will help you learn to diagnose this error. |
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Lesson ideas appropriate for students like Courtney. |
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Research
on our Australian sample shows that 5% of students* use reciprocal
thinking, but at one school, 27% of the Grade 6 students were
diagnosed this way. (* This percent includes both reciprocal and negative thinking, because the basic decimal comparison test does not separate these groups. Courtney's interview shows she is a reciprocal thinker. See full descriptions of reciprocal thinking and negative thinking. ) |