Towards an inclusive education for all

Chapter 1: Presents international perspectives and understandings of what inclusion means, and explains why it is necessary for teachers to develop their own deep understanding of the beliefs and values that inform teaching. The chapter introduces the construct of an inclusive school community, which is an important focus of inclusive schooling, and explains how the theoretical framework for inclusion informs our thinking, and the ongoing processes of review and development. This framework also informs the stance we take on preparing teachers to work in more inclusive ways in schools. The chapter aims to encourage an appreciation of what it means to be included and excluded, and invites the reader to consider the challenges ahead.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

Real, complex, and binary semantic vectors

This paper presents a combined structure for using real, complex, and binary valued vectors for semantic representation. The theory, implementation, and application of this structure are all significant. For the theory underlying quantum interaction, it is important to develop a core set of mathematical operators that describe systems of information, just as core mathematical operators in quantum mechanics are used to describe the behavior of physical systems. The system described in this paper enables us to compare more traditional quantum mechanical models (which use complex state vectors), alongside more generalized quantum models that use real and binary vectors. The implementation of such a system presents fundamental computational challenges. For large and sometimes sparse datasets, the demands on time and space are different for real, complex, and binary vectors. To accommodate these demands, the Semantic Vectors package has been carefully adapted and can now switch between different number types comparatively seamlessly. This paper describes the key abstract operations in our semantic vector models, and describes the implementations for real, complex, and binary vectors. We also discuss some of the key questions that arise in the field of quantum interaction and informatics, explaining how the wide availability of modelling options for different number fields will help to investigate some of these questions.

Short answer versus multiple choice examination questions for first year chemistry

Multiple choice (MC) examinations are frequently used for the summative assessment of large classes because of their ease of marking and their perceived objectivity. However, traditional MC formats usually lead to a surface approach to learning, and do not allow students to demonstrate the depth of their knowledge or understanding. For these reasons, we have trialled the incorporation of short answer (SA) questions into the final examination of two first year chemistry units, alongside MC questions. Students’ overall marks were expected to improve, because they were able to obtain partial marks for the SA questions. Although large differences in some individual students’ performance in the two sections of their examinations were observed, most students received a similar percentage mark for their MC as for their SA sections and the overall mean scores were unchanged. In-depth analysis of all responses to a specific question, which was used previously as a MC question and in a subsequent semester in SA format, indicates that the SA format can have weaknesses due to marking inconsistencies that are absent for MC questions. However, inclusion of SA questions improved student scores on the MC section in one examination, indicating that their inclusion may lead to different study habits and deeper learning. We conclude that questions asked in SA format must be carefully chosen in order to optimise the use of marking resources, both financial and human, and questions asked in MC format should be very carefully checked by people trained in writing MC questions. These results, in conjunction with an analysis of the different examination formats used in first year chemistry units, have shaped a recommendation on how to reliably and cost-effectively assess first year chemistry, while encouraging higher order learning outcomes.

Comparison and modification of car following models toward a more accurate microscopic simulation parameters reproduction

Traffic safety studies demand more than what current micro-simulation models can provide as they presume that all drivers of motor vehicles exhibit safe behaviours. Several car-following models are used in various micro-simulation models. This research compares the mainstream car following models’ capabilities of emulating precise driver behaviour parameters such as headways and Time to Collisions. The comparison firstly illustrates which model is more robust in the metric reproduction. Secondly, the study conducted a series of sensitivity tests to further explore the behaviour of each model. Based on the outcome of these two steps exploration of the models, a modified structure and parameters adjustment for each car-following model is proposed to simulate more realistic vehicle movements, particularly headways and Time to Collision, below a certain critical threshold. NGSIM vehicle trajectory data is used to evaluate the modified models performance to assess critical safety events within traffic flow. The simulation tests outcomes indicate that the proposed modified models produce better frequency of critical Time to Collision than the generic models, while the improvement on the headway is not significant. The outcome of this paper facilitates traffic safety assessment using microscopic simulation.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.

The future of Australian e-learning : it’s all about access

This article clarifies the interdependence between high-speed broadband and e-Learning. It does this by identifying the importance of the internet for Australia’s education future and the importance of education for the future of the internet. It concludes by confirming the role the NBN will play as an enabler of both; and the need to ensure access for all to appropriate skills, as well as to services.

Teacher aides and their pedagogical contributions in the underachieving Indigenous mathematics classroom

This study examines the pedagogical contributions made by teacher aides in underperforming Indigenous mathematics secondary classrooms. Three teaching teams, each consisting of a teacher and their teacher aide, responded to semi-structured interviews. Their mathematics classrooms were observed for details of pedagogical contributions to the mathematics lessons. It was found that the pedagogical contributions of the teacher aides varied from co-teaching contributions, to the provision of menial support and behaviour management. The techniques used by the teacher aides to provide student feedback, to support behaviour management and to undertake questioning vary greatly, and this variance is also evident in the classroom atmosphere. Teacher aides are providing pedagogical contributions, and are engaged in instructional interactions, and are in a sense “teaching”.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Curriculum, assessment teaching and learning for all

This chapter explores how the culture of classrooms and schools can acknowledge diversity and meet all learning needs. Classroom and school culture can and should enhance the belonging and learning of all students. Understanding of learning, curriculum, pedagogy and assessment influences the ways teachers consider their expectations of student achievement and participation in school. We revisit the theory of social constructionism to emphasise the development of shared and valued curriculum, which meets all learner needs. Decisions about what to teach, how to teach and assess, and what supports student needs are important considerations discussed in this chapter. Key messages drawn from the Australian and New Zealand curriculum reinforce the need to ensure education responds to the diversity of students in classrooms. A range of models of pedagogy that have influenced education in Australia and New Zealand are presented, with a particular focus on meeting the needs of students who have disabilities. In addition, the issues related to student and teacher identity, the importance of respectful partnerships that acknowledge family knowledge, and respectful collaboration are discussed. Belonging to a community of learners is made possible through teachers forming authentic relationships with students and their families. In turn, these relationships support teachers to understand how the students in their classrooms learn, and to know their students’ strengths and interests.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Combinatorial design of key distribution mechanisms for wireless sensor networks

Secure communications in wireless sensor networks operating under adversarial conditions require providing pairwise (symmetric) keys to sensor nodes. In large scale deployment scenarios, there is no prior knowledge of post deployment network configuration since nodes may be randomly scattered over a hostile territory. Thus, shared keys must be distributed before deployment to provide each node a key-chain. For large sensor networks it is infeasible to store a unique key for all other nodes in the key-chain of a sensor node. Consequently, for secure communication either two nodes have a key in common in their key-chains and they have a wireless link between them, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path have a key in common. Length of the key-path is the key factor for efficiency of the design. This paper presents novel deterministic and hybrid approaches based on Combinatorial Design for deciding how many and which keys to assign to each key-chain before the sensor network deployment. In particular, Balanced Incomplete Block Designs (BIBD) and Generalized Quadrangles (GQ) are mapped to obtain efficient key distribution schemes. Performance and security properties of the proposed schemes are studied both analytically and computationally. Comparison to related work shows that the combinatorial approach produces better connectivity with smaller key-chain sizes.