Papers by David Leigh-Lancaster
Following the recent review of the Victorian Certificate of Education the mathematics schoolbased... more Following the recent review of the Victorian Certificate of Education the mathematics schoolbased Common Assessment Task (CAT) has been removed due to perceived problems with the authentication of students' work & excessive student and teacher workloads. The CAT has been replaced with more a flexible assessment format to address these concerns, however, the tasks are to be smaller in scope and undertaken mainly during school hours. This paper presents the preliminary results of a survey of VCE mathematics teachers on the first year of implementation of this new assessment format. In this survey teachers have indicated that high workloads remain a significant issue in the VCE but issues concerning high student workload and authentication have been diminished. Broader issues were also explored and in this paper we present preliminary findings on the perceived impact on the quality of students' learning outcomes and the types of tasks chosen by teachers in the school-based asse...
One way of summarising some of the relationships that exist between certain functions, and their ... more One way of summarising some of the relationships that exist between certain functions, and their inverse, derivative and anti-derivative functions is to use a 'concept map' or a 'mind map'. Concept maps can be used to assist students in critically reviewing their understanding of such relationships, and hopefully avoid erroneous recall of 'facts' involving functions and relationships between them and their corresponding inverse, derivative and anti-derivative functions. This 'concept map' could be elaborated by the inclusion of relevant graphs, and used as a reference, in conjunction with a suitable summary on transformations of functions and their graphs, when students practice questions from past VCE examination papers for revision.
Review(s) of: The Myth of Ability Nurturing Mathematical Talent in Every Child, by John Mighton, ... more Review(s) of: The Myth of Ability Nurturing Mathematical Talent in Every Child, by John Mighton, Text Publishing, Melbourne, 2005, ISBN: 9781920885496. Includes references.
Review(s) of: Hal Hellman, Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever, John W... more Review(s) of: Hal Hellman, Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever, John Wiley and Sons, New Jersey, 2006, ISBN 9780471648772. Includes references.
This article discusses the power set of a given set and the related partial order defined in term... more This article discusses the power set of a given set and the related partial order defined in terms of the subset relation. A collection of illustrative examples is used, and referenced to the relevant sections of the Mathematics 'Victorian Essential Learning Standards' (VELS).
Mathematics
The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra S... more The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by change...
examinations in Victoria, in particular with respect to common items with the standard course, we... more examinations in Victoria, in particular with respect to common items with the standard course, were reported at the 2002 and 2003 MERGA conferences. This paper extends analysis to student performance on aspects of the 2004 examinations, with consideration of some emerging trends over the three years. Several possible areas for a broader research agenda with respect to implementation of a CAS enabled senior mathematics curriculum are proposed. Mathematical Methods (CAS) Units 1- 4 is an accredited pilot study of the Victorian
In November 2007 around 14 000 Mathematical Methods students and around 1 500 Mathematical Method... more In November 2007 around 14 000 Mathematical Methods students and around 1 500 Mathematical Methods (CAS) students sat a common one hour technology-free examination. The examination covered the same function, algebra, calculus and probability content with corresponding expectations for key knowledge and key skills for both studies. This paper provides some analysis of the examination and items and student performance with respect to both cohorts.
The relationship between socio-economic background and completion of senior secondary mathematics... more The relationship between socio-economic background and completion of senior secondary mathematics study leading to various post-schooling pathways has been an area of keen interest to researchers, school systems and policy makers for some time. This paper briefly considers some aspects of this relationship using recent Victorian data relating to the index of relative socio-economic disadvantage (IRSD), enrolments and study scores for Victorian senior secondary mathematics students and On Track destination data. Background A distinctive feature of senior secondary mathematics curricula in countries around the world and also in Australia is the common use of a hierarchy of three to four distinctive mathematics subjects typically characterised in terms of a combination of: depth, breadth and directness of application to practical problem solving in real life; the level and scope of complexity and demand in ‘pure ’ and ‘applied ’ mathematical concepts, skills and processes; expectations...
Most teachers and students will be familiar with Venn diagrams involving two or three intersectin... more Most teachers and students will be familiar with Venn diagrams involving two or three intersecting circles and their use in solving sorting, combinatorial, logic or probability problems. They appear in the Structure dimension of the VELS Levels 4, 5 and 6. They are also frequently used as a representational tool in business. The English logician John Venn discussed and illustrated their application to solving problems in logic in his work Symbolic Logic (1881).
This section provides an insight into the study of simple functional equations for conceptualizin... more This section provides an insight into the study of simple functional equations for conceptualizing and understanding key aspects of functions and algebra. It also provides examples of two simple functional equations and emphasizes the two important principles of mathematical reasoning - proof and disproof of a general mathematical statement.
2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mat... more 2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key knowledge and key skills. There was also separate technology-assumed examinations comprising common and different multiple choice and extended response questions. In 2009 the two cohorts were of similar size, comprising 7000-8000 students each. This paper analyses student performance for both cohorts with respect to these common items.
The evaluation of certain definite integrals that provides a measure of the difference between va... more The evaluation of certain definite integrals that provides a measure of the difference between various rational numbers and Pi drawing on ideas and material outlined in the brief technical paper 'More on Pi' by Michael Hirschhorn, are considered. It is suggested that these and related ideas could be used as the basis for a short activity and/or an assessment task suitable for students of Specialist Mathematics that involves the integration of rational functions.
Australian Senior Mathematics Journal, 1996
Mathematics Education Research Group of Australasia, Jul 1, 2010
The relationship between socioeconomic background and completion of senior secondary mathematics ... more The relationship between socioeconomic background and completion of senior secondary mathematics study leading to various post-schooling pathways has been an area of keen interest to researchers, school systems and policy makers for some time. This paper briefly considers some aspects of this relationship using recent Victorian data relating to the index of relative socioeconomic disadvantage (IRSD), enrolments and study scores for Victorian senior secondary mathematics students and On Track destination data.
Insights into aspects of teachers' planning reported here were gathered as part of a broader proj... more Insights into aspects of teachers' planning reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics. In particular, responses of teachers to a survey of various aspects of decisions that inform their planning are discussed. While there is diversity in processes teachers use for planning, a consistent theme was that teachers make active decisions at all stages in the planning process. There were slight differences in the ways that primary and secondary teachers plan. There are important implications from our findings for those who support teachers in the transition to the Australian Curriculum: Mathematics.
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Papers by David Leigh-Lancaster