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This study reports how the difficulty of simple worded percentage problems is affected by the problem structure and the complexity of the numbers involved. We also investigate which methods students know. Results from 677 Year 8 and 9 students are reported. Overall the results indicate that more attention needs to be given to this important topic. Simple unit fraction equivalents seem to be emphasised, at the expense of fundamental definition ("out of a hundred") and apparently easy percentages such as 30%. The draft National Curriculum gives better guidance on the variation amongst percentage problems. (Contains 1 table and 3 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

Most successful Bayesian network (BN) applications to datehave been built through knowledge elicitation from experts.This is difficult and time consuming, which has lead to recentinterest in automated methods for learning BNs from data. We present a case study in the construction of a BN in anintelligent tutoring application, specifically decimal misconceptions. Wedescribe the BN construction using expert elicitation and then investigate how certainexisting automated knowledge discovery methods might support the BN knowledge engineering process., Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001)

A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on how students' ideas changed across the grades, which ways of thinking were most prevalent, the most persistent and which were most likely to lead to expertise. Interestingly the answers were different for primary and secondary students. Estimates are also given of the proportion of students affected by particular ways of thinking during schooling. The conclusion shows how a careful mapping can be useful and draws out features of the learning environment that affect learning. (Contains 7 figures and 3 tables.) [For complete proceedings, see ED496845.]

Students who learn mathematics with CAS calculators are likely to develop new practices for doing and recording mathematics. Students discussed in this paper were able to use CAS calculators in examinations, making their own decisions about what to document as written records for solutions to problems. A comparison of some features of written records produced by these students, with an achievement matched random sample of students with only graphics calculators, gives insight into the new practice which is emerging. Students who had learned with CAS wrote generally shorter answers, used more ordinary words and used function notation more frequently but they did not over-use non-standard calculator syntax. [For complete proceedings, see ED489632.]

This paper describes features of a group of misconceptions about decimal notation that lead to students selecting as larger, decimals that look smaller. A longitudinal study identified approximately 900 students from a variety of schools who exhibited these misconceptions and whose subsequent progress could be traced. The data demonstrates that the progress that students makes depends to a certain extent both on the nature of their misconceptions and the grade at which the misconception is held. Such phenomena could be expected to hold for misconceptions in other topics. (Contains 1 table and 2 figures.) [For complete proceedings, see ED489597.]

This paper reports on the experiences of students who were learning mathematics with CAS for a second consecutive school year. Evidence presented shows that nearly all students managed the challenging task of mastering the technical aspects of using CAS well. It also shows that the level of technical difficulty and the degree to which it presents an obstacle to mathematical learning is not predictable from conventional mathematical ability. There is a complex interaction between cognitive and affective factors. Planning appropriate teaching for developing the effective use of CAS will require awareness and understanding of these individual differences. (Contains 1 table and 3 figures.) [For complete proceedings, see ED489597.]

Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation. Analysis of the longitudinal data demonstrates that different misconceptions persist among students to different degrees and in different patterns across the grades. Estimating the prevalence of misconceptions is complex due to the nature of longitudinal data. Best estimates are provided of grade prevalences and the proportions of students affected during schooling. (Contains 1 footnote, 4 figures and 3 tables.) [For complete proceedings, see ED500860.]

The ability to recognize equivalent algebraic expressions quickly and confidently is important for doing mathematics in an intelligent partnership with computer algebra. It is also a key aspect of algebraic expectation, the algebraic skill that parallels numeric estimation. The progress in this ability of 50 students learning mathematics with CAS over two school years was monitored using a novel instrument called the Algebraic Expectation Quiz. Students began with very low facility and confidence and made moderate progress, confirming the importance of addressing this obstacle to using CAS explicitly in the curriculum. We offer conclusions about test items, students' strengths and weaknesses and suggest possible teaching actions. The results demonstrate that recognizing equivalence, even in simple cases, is a significant obstacle for students. (Contains 1 figure and 1 table.) [For complete proceedings, see ED500860.]

There are many sources of professional development for K-6 teachers that help them learn how to use computers, but much less is available on how to use computers in classrooms to enhance learning. Members of the Department of Science and Mathematics Education at the University of Melbourne (Australia) have developed CLICK! (Computers and Learning in Classrooms: K-6), a professional development CD-ROM resource for teachers about effective uses of computer in the K-6 classroom. CLICK! comprises 36 professional development modules, 30 associated case studies, and video and multimedia materials illustrating how computers can be used to enhance learning. This project involved teachers and academics involved in teacher education from Australia and the United States and has resulted in a powerful resource to support K-6 teachers in integrating computers into their classrooms. (Author/AEF)

Members of the Department of Science and Mathematics Education at the University of Melbourne, Australia have developed a range of multimedia resources for undergraduate education students that allow the students to participate in authentic tasks that would otherwise be difficult or impossible to arrange for large numbers of students. The multimedia resources are designed to project students into their future role as classroom teachers as it has been observed that those students who do this tend to perform better as they can see the relevance of learning opportunities presented in their studies. Observation of student work using these resources shows deeper thinking and enhanced reflective practices in considering how children think and how classrooms can be managed. The first section of this paper describes three recently developed multimedia resources: "Computers and the K-6 Classroom: Kids Can Do!,""Teaching and Learning about Decimals," and "Teaching and Learning about Whole Numbers." Modes of interactivity are discussed in the second section, including analyzing classroom interactions and classroom management, as well as the advantages of multimedia for making children's thinking an object of study. (Author/AEF)