Faculty of Education - Theses
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ItemThe evolution of concepts of decimals in primary and secondary students( 1994)This thesis studies children's conceptions about ordering decimals. It builds upon previous work which established three commonly used systematic errors in children's understanding as they encounter decimal notation. Students were categorised according to erroneous rule usage. This work includes a small longitudinal study which showed little change over twelve months in rule usage by an Australian sample of 50 secondary students. The categorising tests were redeveloped to make them suitable for primary students and to have increased reliability. The main study traced the use of rules from Year Four to Year Ten in a sample of 379 students and showed how students with different rules performed on other decimal tasks. It was found that one of the rules, called the whole number rule (in comparing two decimals that with more decimal places is chosen as the larger) was important in earlier years but disappeared with time. The second rule, called the fraction rule (the decimal with fewer decimal places is chosen as the larger), persisted in worrying proportions well into the secondary years and it was shown that significant gaps in knowledge of decimal notation existed which had not corrected themselves with time. The third rule was shown to be not important. Further investigation of a longitudinal nature to examine how individuals actually make the transition to mastery of decimal notation is encouraged by this study.
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ItemA Further investigation of decimal misconceptions held by primary and secondary students( 2005)This study investigates Australian students' thinking about decimals. A Decimal Comparison Test was used to diagnose thousands of Victorian primary and secondary students' misconceptions of decimal notation. Data from 1998 to 1999 were extracted (from a study funded by the Australian Research Council) and analysed. These data were analysed with the use of cross-sectional and longitudinal approaches. The cross-sectional approach adopted in this study focuses on the tests while the longitudinal approach focuses on the students. Analysis of students' decimal misconceptions was conducted at both the coarse level (4 behaviours) and fine level (12 ways of thinking). Firstly, the variability of the prevalence of expertise by class was investigated, as well as the various misconceptions. It was determined that there were large variations especially in the prevalence of expertise by class, in particular Grade 6 (anywhere between 5% and 95%). The second analysis involved tests that do not match any predicted pattern of correct and incorrect responses (referred to as unclass feeds). From the results, there were Grade 6 students who answered the test inconsistently and have a tendency towards choosing the decimal with the most digits as the largest number. Also, there were Grade 10 students who answered the test inconsistently and have a tendency towards choosing the decimal with the fewest digits as the largest number. The third analysis involved 122 students who completed their first test as experts but made more errors in their second test approximately 6 months later. The analysis of responses to individual test items indicated some of these students were consistent in using various incomplete algorithms to choose correctly on many of the decimal comparisons. However, when the incomplete algorithm failed to give a definite answer, they might guess or revert to a latent misconception.