Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

In search of the antecendents for risky driving at railway level crossings

This paper discusses human factors issues of low cost railway level crossings in Australia. Several issues are discussed in this paper including safety at passive level railway crossings, human factors considerations associated with unavailability of a warning device, and a conceptual model for how safety could be compromised at railway level crossings following prolonged or frequent unavailability. The research plans to quantify safety risk to motorists at level crossings using a Human Reliability Assessment (HRA) method, supported by data collected using an advanced driving simulator. This method aims to identify human error within tasks and task units identified as part of the task analysis process. It is anticipated that by modelling driver behaviour the current study will be able to quantify meaningful task variability including temporal parameters, between participants and within participants. The process of complex tasks such as driving through a level crossing is fundamentally context-bound. Therefore this study also aims to quantify those performance-shaping factors that contribute to vehicle train collisions by highlighting changes in the task units and driver physiology. Finally we will also consider a number of variables germane to ensuring external validity of our results. Without this inclusion, such an analysis could seriously underestimate the probabilistic risk assessment.

A human factors investigation into the unavailability of active warnings at railway level crossings

This paper discusses human factors issues of low cost railway level crossings in Australia. Several issues are discussed in this paper including safety at passive level railway crossings, human factors considerations associated with unavailability of a warning device, and a conceptual model for how safety could be compromised at railway level crossings following prolonged or frequent unavailability. The research plans to quantify safety risk to motorists at level crossings using a Human Reliability Assessment (HRA) method, supported by data collected using an advanced driving simulator. This method aims to identify human error within tasks and task units identified as part of the task analysis process. It is anticipated that by modelling driver behaviour the current study will be able to quantify meaningful task variability including temporal parameters, between participants and within participants. The process of complex tasks such as driving through a level crossing is fundamentally context-bound. Therefore this study also aims to quantify those performance-shaping factors that contribute to vehicle train collisions by highlighting changes in the task units and driver physiology. Finally we will also consider a number of variables germane to ensuring external validity of our results. Without this inclusion, such an analysis could seriously underestimate risk.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.

Charting the system : the integrated master schedule as a multi-level and poly-temporal boundary object in complex projects

This paper investigates the use of visual artifacts to represent a complex adaptive system (CAS). The integrated master schedule (IMS) is one of those visuals widely used in complex projects for scheduling, budgeting, and project management. In this paper, we discuss how the IMS outperforms the traditional timelines and acts as a ‘multi-level and poly-temporal boundary object’ that visually represents the CAS. We report the findings of a case study project on the way the IMS mapped interactions, interdependencies, constraints and fractal patterns in a complex project. Finally, we discuss how the IMS was utilised as a complex boundary object by eliciting commitment and development of shared mental models, and facilitating negotiation through the layers of multiple interpretations from stakeholders.

A multi-level model of leadership in complex project management

Management (or perceived mismanagement) of large-scale, complex projects poses special problems and often results in spectacular failures, cost overruns, time blowouts and stakeholder dissatisfaction. While traditional project management responds with increasingly administrative constraints, we argue that leaders of such projects also need to display adaptive and enabling behaviours to foster adaptive processes, such as opportunity recognition, which requires an interaction of cognitive and affective processes of individual, project, and team leader attributes and behaviours. At the core of this model we propose is an interaction of cognitive flexibility, affect and emotional intelligence. The result of this interaction is enhanced leader opportunity recognition that, in turn, facilitates multilevel outcomes.

Anonymity and one-way authentication in key exchange protocols

Key establishment is a crucial cryptographic primitive for building secure communication channels between two parties in a network. It has been studied extensively in theory and widely deployed in practice. In the research literature a typical protocol in the public-key setting aims for key secrecy and mutual authentication. However, there are many important practical scenarios where mutual authentication is undesirable, such as in anonymity networks like Tor, or is difficult to achieve due to insufficient public-key infrastructure at the user level, as is the case on the Internet today. In this work we are concerned with the scenario where two parties establish a private shared session key, but only one party authenticates to the other; in fact, the unauthenticated party may wish to have strong anonymity guarantees. We present a desirable set of security, authentication, and anonymity goals for this setting and develop a model which captures these properties. Our approach allows for clients to choose among different levels of authentication. We also describe an attack on a previous protocol of Øverlier and Syverson, and present a new, efficient key exchange protocol that provides one-way authentication and anonymity.

How do level of experience, purpose for riding, and preference for facilities affect location of riding?

Characteristics of the road infrastructure affect both the popularity of bicycling and its safety, but comparisons of the safety performance of infrastructure may be confounded by differences in the profiles of cyclists who use them. Data from a survey of 2,532 adult bicycle riders in Queensland, Australia, demonstrated that many riders rode reluctantly in particular locations and that preference for riding location was influenced by degree of experience and riding purpose. Most riders rode most often and furthest per week on urban roads, but approximately one-third of all riders (and more new riders) rode there reluctantly. Almost two-thirds of riders rode on bicycle paths, most by choice, not reluctantly. New riders rode proportionally more on bicycle paths, but continuing riders rode further in absolute terms. Utilitarian riders were more likely to ride on bicycle paths than social and fitness riders and almost all of this riding was by choice. Fitness riders were more reluctant in their use of bicycle paths, but still most of their use was by choice. One-third of the respondents reported riding on the sidewalk (legal in Queensland), with approximately two-thirds doing so reluctantly. The frequency and distance ridden on the sidewalk was less than for urban roads and bicycle paths. Sidewalks and bicycle paths were important facilities for both inexperienced and experienced riders and for utilitarian riding, especially when urban roads were considered a poor choice for cycling.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

The development of a conceptual framework for a district 4-Year Pavement Management Plan, implementation of network-level project screening process

The Texas Department of Transportation (TxDOT) is concerned about the widening gap between preservation needs and available funding. Funding levels are not adequate to meet the preservation needs of the roadway network; therefore projects listed in the 4-Year Pavement Management Plan must be ranked to determine which projects should be funded now and which can be postponed until a later year. Currently, each district uses locally developed methods to prioritize projects. These ranking methods have relied on less formal qualitative assessments based on engineers’ subjective judgment. It is important for TxDOT to have a 4-Year Pavement Management Plan that uses a transparent, rational project ranking process. The objective of this study is to develop a conceptual framework that describes the development of the 4-Year Pavement Management Plan. It can be largely divided into three Steps; 1) Network-Level project screening process, 2) Project-Level project ranking process, and 3) Economic Analysis. A rational pavement management procedure and a project ranking method accepted by districts and the TxDOT administration will maximize efficiency in budget allocations and will potentially help improve pavement condition. As a part of the implementation of the 4-Year Pavement Management Plan, the Network-Level Project Screening (NLPS) tool including the candidate project identification algorithm and the preliminary project ranking matrix was developed. The NLPS has been used by the Austin District Pavement Engineer (DPE) to evaluate PMIS (Pavement Management Information System) data and to prepare a preliminary list of candidate projects for further evaluation.

Understanding graphicacy : students’ making sense of graphics in mathematics assessment tasks

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed: 1) factors which contribute to success or hinder performance on tasks with various graphical representations; and 2) how the literacy and graphical demands of tasks influence the mathematical sense making of students. The outcomes of this study highlight the changing nature of assessment in school mathematics and identify the function and influence of graphics in the design of assessment tasks.