An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Small acts of resistance : the role of intergenerational collaborative drawing in early childhood teaching and learning

This chapter focuses on ‘intergenerational collaborative drawing’, a particular process of drawing whereby adults and children draw at the same time on a blank paper space. Such drawings can be produced for a range of purposes, and based on different curriculum or stimulus subjects. Children of all ages, and with a range of physical and intellectual abilities are able to draw with parents, carers and teachers. Intergenerational collaborative drawing is a highly potent method for drawing in early childhood contexts because it brings adults and children together in the process of thinking and theorizing in order to create visual imagery and this exposes in deep ways to adults and children, the ideas and concepts being learned about. For adults, this exposure to a child’s thinking is a far more effective assessment tool than when they are presented with a finished drawing they know little about. This chapter focuses on drawings to examine wider issues of learning independence and how in drawing, preferred schema in the form of hand-out worksheets, the suggestive drawings provided by adults, and visual material seen in everyday life all serve to co-opt a young child into making particular schematic choices. I suggest that intergenerational collaborative drawing therefore serves to work as a small act of resistance to that co-opting, in that it helps adults and children to collectively challenge popular creativity and learning discourses.

A threshold concepts focus to curriculum design: supporting student learning through application of variation theory

This project develops and evaluates a model of curriculum design that aims to assist student learning of foundational disciplinary ‘Threshold Concepts’. The project uses phenomenographic action research, cross-institutional peer collaboration and the Variation Theory of Learning to develop and trial the model. Two contrasting disciplines (Physics and Law) and four institutions (two research-intensive and two universities of technology) were involved in the project, to ensure broad applicability of the model across different disciplines and contexts. The Threshold Concepts that were selected for curriculum design attention were measurement uncertainty in Physics and legal reasoning in Law. Threshold Concepts are key disciplinary concepts that are inherently troublesome, transformative and integrative in nature. Once understood, such concepts transform students’ views of the discipline because they enable students to coherently integrate what were previously seen as unrelated aspects of the subject, providing new ways of thinking about it (Meyer & Land 2003, 2005, 2006; Land et al. 2008). However, the integrative and transformative nature of such threshold concepts make them inherently difficult for students to learn, with resulting misunderstandings of concepts being prevalent...

Perceptions of online learning in an Australian university : Malaysian students’ perspectives-usability of the online learning tools

This study set out to investigate the kinds of learning difficulties encountered by the Malaysian students and how they actually coped with online learning. The modified Online Learning Environment Survey (OLES) instrument was used to collect data from the sample of 40 Malaysian students at a university in Brisbane, Australia. A controlled group of 35 Australian students was also included for comparison purposes. Contrary to assumptions from previous researches, the findings revealed that there were only a few differences between the international Asian and Australian students with regards to their perceptions of online learning. Recommendations based on the findings of this research study were applicable for Australian universities which have Asian international students enrolled to study online.

Perceptions of online learning in an Australian university: an international students’ (Asian Region) perspective – enjoyment

Several researchers have reported that cultural and language differences can affect online interactions and communications between students from different cultural backgrounds. Other researchers have asserted that online learning is a tool that can improve teaching and learning skills, but its effectiveness depends on how the tool is used. To delve into these aspects further, this study set out to investigate the kinds of learning difficulties encountered by the international students and how they actually coped with online learning. The modified Online Learning Environment Survey (OLES) instrument was used to collect data from the sample of 109 international students at a university in Brisbane. A smaller group of 35 domestic students was also included for comparison purposes. Contrary to assumptions from previous research, the findings revealed that there were only few differences between the international Asian and Australian students with regards to their perceptions of online learning. Recommendations based on the findings of this research study were made for Australian universities where Asian international students study online. Specifically the recommendations highlighted the importance of upskilling of lecturers’ ability to structure their teaching online and to apply strong theoretical underpinnings when designing learning activities such as discussion forums, and for the university to establish a degree of consistency with regards to how content is located and displayed in a learning management system like Blackboard.

Crypto topics and applications II

In this chapter we continue the exposition of crypto topics that was begun in the previous chapter. This chapter covers secret sharing, threshold cryptography, signature schemes, and finally quantum key distribution and quantum cryptography. As in the previous chapter, we have focused only on the essentials of each topic. We have selected in the bibliography a list of representative items, which can be consulted for further details. First we give a synopsis of the topics that are discussed in this chapter. Secret sharing is concerned with the problem of how to distribute a secret among a group of participating individuals, or entities, so that only predesignated collections of individuals are able to recreate the secret by collectively combining the parts of the secret that were allocated to them. There are numerous applications of secret-sharing schemes in practice. One example of secret sharing occurs in banking. For instance, the combination to a vault may be distributed in such a way that only specified collections of employees can open the vault by pooling their portions of the combination. In this way the authority to initiate an action, e.g., the opening of a bank vault, is divided for the purposes of providing security and for added functionality, such as auditing, if required. Threshold cryptography is a relatively recently studied area of cryptography. It deals with situations where the authority to initiate or perform cryptographic operations is distributed among a group of individuals. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Signature schemes deal with the problem of generating and verifying electronic) signatures for documents.Asubclass of signature schemes is concerned with the shared-generation and the sharedverification of signatures, where a collaborating group of individuals are required to perform these actions. A new paradigm of security has recently been introduced into cryptography with the emergence of the ideas of quantum key distribution and quantum cryptography. While classical cryptography employs various mathematical techniques to restrict eavesdroppers from learning the contents of encrypted messages, in quantum cryptography the information is protected by the laws of physics.

Setting water quality objectives for the health of freshwater fish

An important responsibility of the Environment Protection Authority, Victoria, is to set objectives for levels of environmental contaminants. To support the development of environmental objectives for water quality, a need has been identified to understand the dual impacts of concentration and duration of a contaminant on biota in freshwater streams. For suspended solids contamination, information reported by Newcombe and Jensen [ North American Journal of Fisheries Management , 16(4):693--727, 1996] study of freshwater fish and the daily suspended solids data from the United States Geological Survey stream monitoring network is utilised. The study group was requested to examine both the utility of the Newcombe and Jensen and the USA data, as well as the formulation of a procedure for use by the Environment Protection Authority Victoria that takes concentration and duration of harmful episodes into account when assessing water quality. The extent to which the impact of a toxic event on fish health could be modelled deterministically was also considered. It was found that concentration and exposure duration were the main compounding factors on the severity of effects of suspended solids on freshwater fish. A protocol for assessing the cumulative effect on fish health and a simple deterministic model, based on the biology of gill harm and recovery, was proposed. References D. W. T. Au, C. A. Pollino, R. S. S Wu, P. K. S. Shin, S. T. F. Lau, and J. Y. M. Tang. Chronic effects of suspended solids on gill structure, osmoregulation, growth, and triiodothyronine in juvenile green grouper epinephelus coioides . Marine Ecology Press Series , 266:255--264, 2004. J.C. Bezdek, S.K. Chuah, and D. Leep. Generalized k-nearest neighbor rules. Fuzzy Sets and Systems , 18:237--26, 1986. E. T. Champagne, K. L. Bett-Garber, A. M. McClung, and C. Bergman. {Sensory characteristics of diverse rice cultivars as influenced by genetic and environmental factors}. Cereal Chem. , {81}:{237--243}, {2004}. S. G. Cheung and P. K. S. Shin. Size effects of suspended particles on gill damage in green-lipped mussel perna viridis. Marine Pollution Bulletin , 51(8--12):801--810, 2005. D. H. Evans. The fish gill: site of action and model for toxic effects of environmental pollutants. Environmental Health Perspectives , 71:44--58, 1987. G. C. Grigg. The failure of oxygen transport in a fish at low levels of ambient oxygen. Comp. Biochem. Physiol. , 29:1253--1257, 1969. G. Holmes, A. Donkin, and I.H. Witten. {Weka: A machine learning workbench}. In Proceedings of the Second Australia and New Zealand Conference on Intelligent Information Systems , volume {24}, pages {357--361}, {Brisbane, Australia}, {1994}. {IEEE Computer Society}. D. D. Macdonald and C. P. Newcombe. Utility of the stress index for predicting suspended sediment effects: response to comments. North American Journal of Fisheries Management , 13:873--876, 1993. C. P. Newcombe. Suspended sediment in aquatic ecosystems: ill effects as a function of concentration and duration of exposure. Technical report, British Columbia Ministry of Environment, Lands and Parks, Habitat Protection branch, Victoria, 1994. C. P. Newcombe and J. O. T. Jensen. Channel suspended sediment and fisheries: A synthesis for quantitative assessment of risk and impact. North American Journal of Fisheries Management , 16(4):693--727, 1996. C. P. Newcombe and D. D. Macdonald. Effects of suspended sediments on aquatic ecosystems. North American Journal of Fisheries Management , 11(1):72--82, 1991. K. Schmidt-Nielsen. Scaling. Why is animal size so important? Cambridge University Press, NY, 1984. J. S. Schwartz, A. Simon, and L. Klimetz. Use of fish functional traits to associate in-stream suspended sediment transport metrics with biological impairment. Environmental Monitoring and Assessment , 179(1--4):347--369, 2011. E. Al Shaw and J. S. Richardson. Direct and indirect effects of sediment pulse duration on stream invertebrate assemb ages and rainbow trout ( Oncorhynchus mykiss ) growth and survival. Canadian Journal of Fish and Aquatic Science , 58:2213--2221, 2001. P. Tiwari and H. Hasegawa. {Demand for housing in Tokyo: A discrete choice analysis}. Regional Studies , {38}:{27--42}, {2004}. Y. Tramblay, A. Saint-Hilaire, T. B. M. J. Ouarda, F. Moatar, and B Hecht. Estimation of local extreme suspended sediment concentrations in california rivers. Science of the Total Environment , 408:4221--

Teacher understandings of orientation and transition programs from action research in five schools

Discontinuity between prior-to-school and school sectors in Australia reflects an historical, philosophical and pedagogical schism. This is most evident as children transition from one sector to the other. However, contemporary international research, alongside an intensive focus on policy and practice in early years education has challenged many of the taken-for-granted assumptions that perpetuate this rift. Drawing on data collected in a recent action research project, we present evidence of how a group of primary school kindergarten teachers define differences between orientation and transition programs, understand the importance of transition and how they position themselves in this process. The absence of Australian policy mandating and guiding the work of teachers across sectors is a significant factor perpetuating discontinuity in transition practices between prior–to-school and school sectors.

Teaching fractions to adult learners enrolled in a civil construction course : knowledge, action and materials action in tandem

This paper investigates the teaching and learning of fractions to Indigenous adult learners in a Civil Construction Certificate Course. More specifically it explores why the use of materials is critical to building knowledge and understanding. This focus is important for two reasons. First, it allows for considerations of a trainer’s approach for teaching fractions and, second it provides insights into how adult learners can be supported with representing their practical experiences of fractions to make generalisation thus building on their knowledge and learning experiences. The paper draws on teaching episodes from an Australian Research Council funded Linkage project that investigates how mathematics is taught and learned in Certificate Courses, here, Certificate 11 in Civil Construction. Action research and decolonising methods (Smith, 1999) were used to conduct the research. Video excerpts which feature one trainer and three students are analysed and described. Findings from the data indicate that adult learners need to be supported with materials to assist with building their capacity to know and apply understandings of fractions in a range of contexts, besides construction. Without materials and where fractions are taught via pen and paper tasks, students are less likely to retain and apply fraction ideas to their Certificate Course. Further they are less likely to understand decimals because of limited understanding of fractions.

Applying threshold learning theory to teach sustainable business practice in post-graduate engineering education

This paper presents the results of a qualitative action-research inquiry into how a highly diverse cohort of post-graduate students could develop significant capacity in sustainable development within a single unit (course), in this case a compulsory component of four built environment masters programs. The method comprised applying threshold learning theory within the technical discipline of sustainable development, to transform student understanding of sustainable business practice in the built environment. This involved identifying a number of key threshold concepts, which once learned would provide a pathway to having a transformational learning experience. Curriculum was then revised, to focus on stepping through these targeted concepts using a scaffolded, problem-based-learning approach. Challenges included a large class size of 120 students, a majority of international students, and a wide span of disciplinary backgrounds across the spectrum of built environment professionals. Five ‘key’ threshold learning concepts were identified and the renewed curriculum was piloted in Semester 2 of 2011. The paper presents details of the study and findings from a mixed-method evaluation approach through the semester. The outcomes of this study will be used to inform further review of the course in 2012, including further consideration of the threshold concepts. In future, it is anticipated that this case study will inform a framework for rapidly embedding sustainability within curriculum.

Shaping lecturers’ beliefs about teaching and learning in higher education in the Pacific

The aim of this study was to describe the educational experiences shaping the teaching and learning beliefs held by a group of beginning lecturers in higher education at various tertiary institutions in the Pacific Island Countries (PICs). A total of sixty three essays written by participants in an online course on teaching in higher education comprised the data for the study. A modified version of narrative analysis was used. This is a powerful methodology in qualitative research that can provide remarkable insights into individuals’ beliefs. The critical experiences that were thought to shape their beliefs in teaching and learning were identified and discussed in the light of relevant literature. The participants described a range of influences that shaped their beliefs about teaching and learning including realisation about the need to work harder and know more, the importance of independence, support systems, curriculum, qualities of a teacher, teaching and learning process, teaching and learning strategies, and learning environments. This information was useful in teaching these students and for further courses.

Dictionary learning and sparse coding on Grassmann manifolds : an extrinsic solution

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

Peer assisted learning and generation Y : a case study

In recent years Australian Law Schools have implemented various forms of peer assisted learning or mentoring, including career mentoring by former students of final year students and orientation mentoring or tutoring by later year students of incoming first year students. The focus of these programs therefore is on the transition into or out of law school. There is not always as great an emphasis however, as part of this transition, on the use of law students belonging to the same unit cohort as a learning resource for each other within their degree. This is despite the claimed preference of Generation Y students for collaborative learning environments, authentic learning experiences and the development of marketable workplace skills. In the workplace, be it professional legal practice or otherwise, colleagues rely heavily on each other for information, support and guidance. In the undergraduate law degree at the Queensland University of Technology (‘QUT’) the Torts Student Peer Mentor Program aims to supplement a student’s understanding of the substantive law of torts with the development of life-long skills. As such it has the primary objective, albeit through discussion facilitated by more senior students, of encouraging first year students to develop for themselves the skills they need to be successful both as law students and as legal practitioners. Examples of such skills include those relevant to: preparation for assessment tasks; group work; problem solving, cognition and critical thinking; independent learning; and communication. Significantly, in this way, not only do the mentees benefit from involvement in the program, but the peer mentors, or program facilitators, themselves also benefit from their participation in the real world learning environment the program provides. This paper outlines the development and implementation of the above program, the pedagogy which influenced it, and its impact on student learning experiences

Informed systems approach : new directions for organizational learning

The Informed Systems Approach offers models for advancing workplace learning within collaboratively designed systems that promote using information to learn through collegial exchange and reflective dialogue. This systemic approach integrates theoretical antecedents and process models, including the learning theories of Peter Checkland (Soft Systems Methodology), which advance systems design and informed action, and Christine Bruce (informed learning), which generate information experiences and professional practices. Ikujiro Nonaka’s systems ideas (SECI model) and Mary Crossan’s learning framework (4i framework) further animate workplace knowledge creation through learning relationships engaging individuals with ideas.