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This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

This paper investigates students' mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has been observed previously. Students concentrate on fitting mathematical objects such as functions to data, rather than using domain knowledge about the situation being modeled, mapping this to the data so as to capture the phenomenon as a whole. In other instances, students find functions that simply linearly interpolate the data and do not consider key features of the phenomenon, particularly when they have access to technological tools. The extent to which students' reasoning indicated awareness of their taking either approach was investigated in a qualitative study with Year 10/11 students. How the approach taken affected the processes students engage in whilst modeling was also investigated. The paper contributes to our currently limited literature on research into this issue and how it affects the outcome of students learning to model in classrooms at this level of schooling.

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker machine game and calculate the probability and payouts for four different winning outcomes. The second part of the paper describes how these calculations can then be used to configure a poker machine simulator written in the Python programming language. The code for the simulator is briefly explained and then results for several trials run in the simulator are presented. A discussion of how the student would be expected to present and interpret these results is then given. The next section of the paper explains how students can model their own more complex poker machine game and in turn how the simulator code can be extended to handle the more complex outcomes. Next, an extension to the investigation is described, in which students investigate how many coins need to be played on average before the player loses all their money. A task sheet, setup instructions, starting code and completed examples for teachers is available for free download on the Tes website at https://www.tes.com/en-au/teaching-resource/blow-up-thepokies-12308352 (Hemer, 2020).

Objective To assess the cost-effectiveness of the Quitline, a call-back counselling service for smoking cessation, in the states of Queensland, Western Australia and the Northern Territory. Methods A cost-effectiveness analysis using a deterministic Markov model, and cost per disability-adjusted life year (DALY) averted over a lifetime as the outcome measure. Population Current smokers, motivated to quit. Results Call-back counselling for smoking cessation provided by the Quitline is an intervention that both improves health with additional quitters, and achieves net cost savings due to the cost offsets being greater than the cost of the intervention. If cost offsets are excluded, the cost per quitter is $A773 (95% uncertainty interval $A769$-$A779), and the incremental cost-effectiveness ratio is $A294 per DALY (95% uncertainty interval $A293-$A298). Conclusions Call-back counselling is a cost-effective intervention for smoking cessation that can be provided by a centralised service for a large population, and to reach people in isolated communities. [ABSTRACT FROM AUTHOR]

In 2020, Year 12 students at John Curtin College of the Arts, were required to model COVID-19 data from five different countries in order to find correlations between daily infections and unemployment rates, in order to make future predictions. Work received from students demonstrated how the task successfully provided unique learning opportunities, which are otherwise not experienced in a classroom environment under the pressures of a curriculum that is highly exam-focused and based on mechanistic algorithms. The paper also discusses some challenges faced and how they were overcome.

Mathematical modelling is increasingly becoming an integral component of mathematical curricular in primary and secondary schools throughout the world. However, in Australia modelling skills are currently rarely found in university teacher preparation courses. Limited experience with modelling processes, as well as a lack of confidence and personal efficacy in the field of mathematics, limits the ability for prospective teachers of mathematics to develop into effective high school educators and thus concomitantly adversely affects student learning outcomes. To address the problems related to the lack of experience that prospective teachers have with mathematical modelling and the associated lack of confidence and personal efficacy that can result, this paper presents a case study of a strategy--the enhancement, learning, reflection (ELR) process--designed to improve prospective teachers' confidence and personal efficacy in teaching mathematics, with a focus on the modelling process as a teaching strategy.

This paper presents a study about using scientific simulations to enhance the process of mathematical modelling. The main component of the study is a lesson whose major objective is to have students mathematise a trajectory of a projected object and then apply the model to formulate other trajectories by using the properties of function transformations. It was hypothesised that situating the lesson in a modelling environment would enhance the meaning of transformations that are not often conceptualised in mathematics textbooks. The lesson is guided by inductive reasoning. As a medium of data gathering, a free simulation called "Projectile Motion" was used (available at http://phet. colorado.edu/sims/projectile-motion/projectile-motion_en.html). The inductively organised stages of the activity described in this paper were conducted with a group of (N = 22) mathematics students in a high school in Texas. The students' verbal reflections upon this type of novel learning environment supported the study hypothesis. Their perception of the process of studying function transformations has evolved into a meaningful and purposeful experience. Although, the unit was developed for high school math curriculum in the US, its objectives reflect the aims and scope of Australian math curriculum. The Victorian Certificate of Education Study Design (VCAA, 2010) states that students should model investigate and solve problems in unfamiliar situations. The proposed lesson supports this aim.

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second part goes on to address broader curriculum issues that a purely illustrative exercise in real world problem solving might not normally engage. The chosen example relates to a real world question that is located within the domain of Australian Rules Football, and it is recognized that while this provides a familiar, and often an emotionally engaged context in the majority of states, it may not do so for all. The specific mathematical and modelling issues raised in this particular problem have no essential connection with the discussion in the final part of the paper (other than in providing illustrations), where issues regarding the place of modelling and applications in curricula are considered. For that purpose, the football example can be replaced by any authentic modelling problem. (Contains 1 figure and 2 tables.)

In this article, the author clarifies the distinction between numeracy and mathematics and the implications of this distinction for teachers of mathematics. In doing so she has, of necessity, focused on one--albeit significant--high stakes assessment genre used on Australian students that purports to measure numeracy. It is essential that teachers understand the genre used in the National Assessment Program Literacy and Numeracy (NAPLAN) numeracy test in order for their students to be prepared for it. There does, of course, need to be some balance in how to do this: spending inordinate amounts of time "preparing for the test" creates another set of problems. However, if the preparation is embedded in the mathematics program of the school, where students are taught and required to clarify contexts and situations, make choices about the mathematical models, tools and strategies needed, and to critique their own mathematics choices as well as those of others, teachers will not only be improving students' numeracy capability but also their mathematics skills and understandings. The NAPLAN numeracy test is not perfect. However, the author believes that the way in which the results are used is more problematic than the test itself. Teachers can learn a lot from the test results if they analyse the data generated to inform their teaching and learning programs; i.e., if they were to use the information provided by the test data as assessment "for" learning, rather than as assessment "of" learning. Finally, teachers must ensure that they are teaching their students for numeracy attainment: mathematics skills and procedures alone are insufficient for students to have the capabilities needed to be numerate at school, home, at work, in the community and in civic life, let alone to be successful on an assessment genre designed to assess numeracy in a pen and paper test.

This paper explores the idea of thinking skills approaches as tools for pedagogical inquiry and in so doing seeks to develop the link between the promotion of inquiry-based learning, which is a central tenet of thinking skills, and inquiry-based teaching as an approach to professional development and school improvement. The first part of the paper examines the impact of teaching thinking skills on teachers by drawing upon a systematic review of research evidence. The second part of the paper sets the characteristics identified in the context of research into teachers' development and considers the contribution of a pedagogy based on thinking skills approaches to continuing professional development.

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results reported here are derived from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities requiring the creation of data models. The theme of "Looking after our Environment," a component of the children's science curriculum at the time, provided the context for the activities. Findings include children's abilities to focus their attention on qualities of items rather than the items themselves in identifying attributes, switch their attention from one item feature to another, and create a broad range of models in organising, structuring, and representing their data. Children's development of meta-representational knowledge facilitated their choice and nature of data representations. (Contains 2 figures.)

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Our research indicates that technologies that incorporate CAS capabilities have the potential to mediate collaborative approaches to mathematical enquiry within life-related mathematical tasks. (Contains 1 table and 4 figures.)

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved in developing a model and the differences between modelling and traditional problem solving. Two paper folding activities are used to demonstrate how mathematical modelling and technology can support mathematics learning.

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a "multi-method" technique developed to study student mathematical metacognition; to set out the structural elements and configuration of a coherent model of metacognition in the domain of mathematical problem solving; to report on the empirical utility (and validity) of this model; and, to report the insights into student mathematical metacognition arising from the research. Multi-Method Interview Tasks are appended. (Contains 4 figures.)

Background: Competent clinical reasoning forms the foundation for effective and efficient clinical swallowing examination (CSE) and consequent dysphagia management decisions. While the nature of initial CSEs has been evaluated, it remains unclear how new information gathered by speech–language therapists (SLTs) throughout a patient's acute‐care journey is integrated into their initial clinical reasoning and management processes and used to review and revise initial management recommendations. Aims: To understand how SLTs' clinical reasoning and decision‐making regarding dysphagia assessment and management evolve as patients transition through acute hospital care from referral to discharge. Methods & Procedures: A longitudinal, qualitative approach was employed to gather information from two SLTs who managed six patients at a metropolitan acute‐care hospital. A retrospective 'think‐aloud' protocol was utilized to prompt SLTs regarding their clinical reasoning and decision‐making processes during initial and subsequent CSEs and patient interactions. Three types of concept maps were created based on these interviews: a descriptive concept map, a reasoning map and a hypothesis map. All concept maps were evaluated regarding their overall structure, facts gathered, types of reasoning engaged in (inductive versus deductive), types of hypotheses generated, and the diagnosis and management recommendations made following initial CSE and during subsequent dysphagia management. Outcomes & Results: Initial CSEs involved a rich process of fact‐gathering, that was predominantly led by inductive reasoning (hypothesis generation) and some application of deductive reasoning (hypothesis testing), with the primary aims of determining the presence of dysphagia and identifying the safest diet and fluid recommendations. During follow‐up assessments, SLTs engaged in increasingly more deductive testing of initial hypotheses, including fact‐gathering aimed at determining the tolerance of current diet and fluid recommendations or the suitability for diet and/or fluid upgrade and less inductive reasoning. Consistent with this aim, SLTs' hypotheses were focused primarily on airway protection and medical status during the follow‐up phase. Overall, both initial and follow‐up swallowing assessments were targeted primarily at identifying suitable management recommendations, and less so on identifying and formulating diagnoses. None of the patients presented with adverse respiratory and/or swallowing outcomes during admission and following discharge from speech pathology. Conclusions & Implications: Swallowing assessment and management across the acute‐care journey was observed as a high‐quality, patient‐centred process characterized by iterative cycles of inductive and deductive reasoning. This approach appears to maximize efficiency without compromising the quality of care. The outcomes of this research encourage further investigation and translation to tertiary and post‐professional education contexts as a clear understanding of the processes involved in reaching diagnoses and management recommendations can inform career‐long refinement of clinical skills. WHAT THIS PAPER ADDS: What is already known on the subject: SLTs' clinical reasoning processes during initial CSE employ iterative cycles of inductive and deductive reasoning, reflecting a patient‐centred assessment process. To date it is unknown how SLTs engage in clinical reasoning during follow‐up assessments of swallowing function, how they assess the appropriateness of initial management recommendations and how this relates to patient outcomes. What this paper adds to the existing knowledge: Our longitudinal evaluation of clinical reasoning and decision‐making patterns related to swallowing management in acute care demonstrated that SLTs tailored their processes to each patient's presentation. There was an emphasis on monitoring the suitability of the initial management recommendations and the potential for upgrade of diet or compensatory swallowing strategies. The iterative cycles of inductive and deductive reasoning reflect efficient decision‐making processes that maintain high‐quality clinical care within the acute environment. What are the potential or actual clinical implications of this work?: Employing efficient and high‐quality clinical reasoning is a hallmark of good dysphagia practice in maximizing positive patient outcomes. Developing approaches to understanding and making explicit clinical reasoning processes of experienced clinicians may assist SLTs of all developmental stages to provide high standards of care. [ABSTRACT FROM AUTHOR]

Chronic low back pain is a leading cause of disability worldwide. A clinical model for its cause is lacking. Defining a cause based clinical model and a framework of understanding back pain in terms of peripheral structural and central functional pain is essential for optimal management. We describe the results of the largest published audit of 41 chronic low back pain patients, receiving outpatient sublingual ketamine therapy for defined central functional pain along with conventional peripheral structural pain management. Our clinical model assigns Movement Dysfunction as the primary cause for low back pain symptoms and restores it with Movement Therapy focused rehabilitation which is also defined. Patients were derived from a tertiary single neurosurgical specialist practice in Brisbane Australia over a three year period. Severe pain and disability measurements more than halved and only 13% of patients ceased ketamine prematurely due to predominantly non-sinister side effects common to all pharmaceutical therapies. All other surveyed metrics of utility were highly favourable in this challenging cohort of chronic back pain patients biased to poor outcomes. Outpatient ketamine maintains high efficacy and safety used in conjunction with a unique clinical model that describes chronic low back pain. This paper builds on our previous publications that describe the disease of movement dysfunction as an integral factor to the development of a cause based clinical model for the condition of chronic low back pain symptoms. Our clinical application of this model, applying the necessary dual approach of controlling symptoms arising from peripheral structural pain and central functional pain in conjunction with elimination of root causation has shown favourable outcomes in patients with high levels of pain and disability based on their tertiary referral origin and high Oswestry Disability Scores. Removing chronic low back pain from its position as one of the world's leading causes of pain and disability is more likely if the rehabilitation industry can replicate and test treatment algorithms based around established clinical models of disease which is the important subject of this paper. [ABSTRACT FROM AUTHOR]

Background: The implementation science literature acknowledges a need for engagement of key stakeholders when designing, delivering and evaluating implementation work. To date, the literature reports minimal or focused stakeholder engagement, where stakeholders are engaged in either barrier identification and/or barrier prioritisation. This paper begins to answer calls from the literature for the development of tools and guidance to support comprehensive stakeholder engagement in implementation research and practice. The paper describes the systematic development of the Implementation‐STakeholder Engagement Model (I‐STEM) in the context of an international, large‐scale empirical implementation study (ImpleMentAll) aimed at evaluating the effectiveness of a tailored implementation toolkit. The I‐STEM is a sensitising tool that defines key considerations and activities for undertaking stakeholder engagement activities across an implementation process. Methods: In‐depth, semistructured interviews and observations were conducted with implementers who were tailoring implementation strategies to integrate and embed internet‐based cognitive behavioural therapy (iCBT) services in 12 routine mental health care organisations in nine countries in Europe and Australia. The analytical process was informed by principles of first‐ and third‐generation Grounded Theory, including constant comparative method. Results: We conducted 55 interviews and observed 19 implementation‐related activities (e.g., team meetings and technical support calls). The final outcome of our analysis is expressed in an initial version of the I‐STEM, consisting of five interrelated concepts: engagement objectives, stakeholder mapping, engagement approaches, engagement qualities and engagement outcomes. Engagement objectives are goals that implementers plan to achieve by working with stakeholders in the implementation process. Stakeholder mapping involves identifying a range of organisations, groups or people who may be instrumental in achieving the engagement objectives. Engagement approaches define the type of work that is undertaken with stakeholders to achieve the engagement objectives. Engagement qualities define the logistics of the engagement approach. Lastly, every engagement activity may result in a range of engagement outcomes. Conclusion: The I‐STEM represents potential avenues for substantial stakeholder engagement activity across key phases of an implementation process. It provides a conceptual model for the planning, delivery, evaluation and reporting of stakeholder engagement activities. The I‐STEM is nonprescriptive and highlights the importance of a flexible, iterative approach to stakeholder engagement. It is developmental and will require application and validation across a range of implementation activities. Patient or Public Contribution: Patient contribution to ImpleMentAll trial was facilitated by GAMIAN‐Europe at all stages—from grant development to dissemination. GAMIAN‐Europe brings together a wide variety of patient representation organisations (local, regional and national) from almost all European countries. GAMIAN‐Europe was involved in pilot testing the ItFits‐toolkit and provided their views on the various aspects, including stakeholder engagement. Patients were also represented in the external advisory board providing support and advice on the design, conduct and interpretation of the wider project, including the development of the ItFits‐toolkit. Trial registration: ClinicalTrials.gov NCT03652883. Retrospectively registered on 29 August 2018. [ABSTRACT FROM AUTHOR]

Introduction: Telepractice service delivery of allied health interventions to people with disability can potentially reduce access barriers and improve service equity. However, questions remain regarding telepractice functionality for people with disability. This study addressed questions related to how allied health clinicians and managers perceive telepractice as functioning in the provision of therapy services to people with disability. Methods: Thirteen interviews of allied health clinicians and managers from across Australia were conducted between 21 November and 22 February via MS teams. Qualitative methodology and critical realist theoretical paradigm underpin the study. Data analysis was completed using a reflective thematic analysis method and five themes were generated and described utilising an analytic metaphor. Results: The study themes were described in relation to a shopping for shoes analytic metaphor and the five themes included (1) a shoe for every foot, (2) planned purchases, (3) shoe on the other foot, (4) you need both shoes and (5) help choosing their shoes. In summary, the function of telepractice fits differently for each individual, similar to pairs of shoes. Conclusions: Telepractice has its own strengths and weaknesses and isn't a direct substitute for in‐person sessions, much like left and right shoes are similar but not the same. The results support participant perceptions that telepractice functions best as an adjunct to in‐person sessions through a flexible hybrid delivery model in the provision of therapy services to people with a disability. A strategy for improving perceived usefulness may involve positioning telepractice as unique with strengths and weaknesses, not replacing in‐person care. Patient or Public Contribution: The paper forms part of a larger codesign process which included customer and carer participants throughout the design and planning of the project, inclusion of a peer researcher, and the selection of the analytic metaphor including in the findings of this article production. [ABSTRACT FROM AUTHOR]

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and graphical representations to determine the relationship. They also used a TI-84 calculator to investigate the relationship, and also modelled the scenario with the aid of "Geometer's Sketchpad" software. In this article, the author offers four reasons to use investigations and presents the first of three investigations posed to a group of preservice teachers in a geometry class for pre-service secondary school teachers in Texas, USA. (Contains 6 figures and 1 table.)

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design Polya's problem solving framework and a writing heuristic are used synergistically with group work to develop the mathematical skills and enhance the mathematical communication skills of novice students. Students' perceptions and performance indicate that this strategy has been a success and has facilitated the development of some metacognitive behaviours in the students. (Contains 4 figures and 2 tables.)

Background: Cross-sectoral collaborations are considered necessary to address detrimental health, social, educational and economic outcomes that impact marginalised and disadvantaged populations. There is a strong relationship between the health of children and their educational attainment; good health promotes positive learning. This paper reports cross-sectoral executive and senior management level systems changes required to enable the design of a collaborative primary healthcare service model for children and young people in rural Australia. Methods: A descriptive qualitative design was used. Data were collected from executive and senior managers from three organisations (Education, Health and a University Department of Rural Health [ n = 6]) through individual semi-structured interviews. Data were analysed using an inductive, thematic approach. The study draws on Lewin's Model of Change. Results: Three overarching themes were generated from the data: an embedded challenge and experimental solutions; building a shared language and understanding; and the role of relationships and trust. Despite the unique geographical and social context of the study area, strategies emerged from the data on how a solution to an embedded challenge, through design of a primary healthcare model, was established and how the strategies described could be transferred and scaled to other rural and remote communities. Conclusion: Contextual differences make each rural and remote area unique. In this study, strategies that are described in the managing change literature were evident. The authors conclude that drawing on strong management of change principles could mean that a service model designed for one remote community might be transferrable to other communities. There is a strong relationship between children's health and their educational attainment. Poorer health, educational and social attainment are experienced by children and young people residing within the study area. Despite unique geographical contexts and demography, strategies that align strong leadership and effective management of change across three organisations were key and may make it possible to transfer a primary health care model designed to improve health and education outcomes for children and young people to other rural and remote communities. [ABSTRACT FROM AUTHOR]

Background: Speech and language therapists (SLTs) use videofluoroscopic swallow study (VFSS) results to manage dysphagia. Yet, in some services only doctors can directly request a VFSS, potentially creating workflow inefficiencies and delaying patient access to VFSS. An alternative model, where SLTs directly refer patients for VFSS, is used in many services in the UK and Australia. However, processes for implementing and sustaining this model have not been reported. Aims: To evaluate the implementation of an SLT‐led inpatient VFSS referring model using the Consolidated Framework for Implementation Research (CFIR) to ascertain implementation barriers, facilitators and critical sustainability factors. Methods & Procedures: This implementation evaluation examined stakeholder perceptions of implementing the SLT‐led VFSS referring model via interviews of (1) SLTs who treat and refer inpatients for VFSS; (2) doctors who manage and refer inpatients for VFSS; (3) radiologists; and (4) trained VFSS referring SLTs. The CFIR was used to prospectively guide implementation planning, evaluation and outcome reporting, regarding barriers, facilitators and sustainability factors. Outcomes & Results: Implementation facilitators were (1) the advantage of SLT‐led VFSS referring over the standard model (doctors referring), in promoting high‐quality VFSS referrals; (2) compatibility of the model with the SLT skill set; (3) supportive communication networks between staff groups; and (4) engaging stakeholders throughout implementation. Adequate availability of trained VFSS referring SLTs was both a barrier and a facilitator of implementation. It was also a critical sustainability factor, along with ongoing staff education and outcome monitoring. Conclusions & Implications: The CFIR supported systematic evaluation of implementation facilitators and barriers, and adjustment of factors critical for implementing and sustaining the new model. Findings may assist other organizations to establish the SLT‐led VFSS referring model. What this paper adds: What is already known on the subject: Models where SLTs directly refer patients for VFSS have been described in the literature, with evidence of appropriate referrals and adherence to radiation safety standards. However, the process for establishing and sustaining this referring model has not been published. What this paper adds to existing knowledge: This study describes the process and outcomes of implementing an SLT‐led VFSS referring model, using the CFIR. A key advantage of the new model that facilitated implementation was the improved quality of VFSS referrals compared with the standard referring model. Important facilitating factors in the environment were the compatibility of the model with SLTs' skillset and supportive communication network between doctors and SLTs. Initially, an implementation barrier was the inadequate availability of trained SLT referrers. Using proactive implementation strategies, more referrers were trained (which was a facilitating factor for implementing and sustaining the model). What are the potential or actual clinical implications of this work?: This study highlights that successful implementation requires more than just an effective model. Features of the environment require consideration to minimize barriers and optimize facilitating factors, supported by proactive implementation strategies. Planning and evaluating implementation processes and outcomes using a standardized implementation framework such as CFIR aided understanding of barriers and facilitators for introducing the SLT‐led VFSS referring model. This process may assist other services to implement the model. [ABSTRACT FROM AUTHOR]