A Further investigation of decimal misconceptions held by primary and secondary students

Thesis (M.Ed.)--University of Melbourne, Dept. of Science and Mathematics Education,(Incorporating IT in Education and Health & Physical Education), 2005This 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