Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Successful outcomes in vocational education and training courses : how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate vocational education, training (VET) and teaching, Indigenous learners’ needs, employer cultural and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty-nine teachers/trainers/teacher aides and two hundred and thirty-one students consented to participate in the project. Nine VET courses were nominated to be the focus on the study. This paper focuses on questionnaire and interview responses from four trainers, two teacher aides and six students. In recent years a considerable amount of funding has been allocated to increasing Indigenous Peoples’ participation in education and employment. This increased funding is predicated on the assumption that it will make a difference and contribute to closing the education gap between Indigenous and non-Indigenous Australians (Council of Australia Governments, 2009). The central tenet is that access to education for Indigenous People will create substantial social and economic benefits for regional and remote Indigenous People. The project’s aim is to address some of the issues associated with the gap. To achieve the aims, the project adopted a mixed methods design aimed at benefitting research participants and included: participatory collaborative action research (Kemmis & McTaggart, 1988) and, community research (Smith, 1999). Participatory collaborative action research refers to a is a “collective, self-reflective enquiry undertaken by participants in social situations in order to improve the rationality and justice of their own social and educational practices” (Kemmis et al., 1988, p. 5). Community research is described as an approach that “conveys a much more intimate, human and self-defined space” (p. 127). Community research relies on and validates the community’s own definitions. As the project is informed by the social at a community level, it is described as “community action research or emancipatory research” (Smith, 1999, p. 127). It seeks to demonstrate benefit to the community, making positive differences in the lives of Indigenous People and communities. The data collection techniques included survey questionnaires, video recording of teaching and learning processes, teacher reflective video analysis of teaching, observations, semi-structured interviews and student numeracy testing. As a result of these processes, the findings indicate that VET course teachers work hard to adopt contextualising strategies to their teaching, however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned historically. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.

Towards brain-based sensor fusion for navigating robots

Current state of the art robot mapping and navigation systems produce impressive performance under a narrow range of robot platform, sensor and environmental conditions, in contrast to animals such as rats that produce “good enough” maps that enable them to function under an incredible range of situations. In this paper we present a rat-inspired featureless sensor-fusion system that assesses the usefulness of multiple sensor modalities based on their utility and coherence for place recognition during a navigation task, without knowledge as to the type of sensor. We demonstrate the system on a Pioneer robot in indoor and outdoor environments with abrupt lighting changes. Through dynamic weighting of the sensors, the system is able to perform correct place recognition and mapping where the static sensor weighting approach fails.

A comparison of perceived crash risk among cyclists and drivers in Brisbane

The Queensland Government has implemented strategies promoting a shift from individual car use to active transport, a transition which requires drivers to adapt to sharing the road with increased numbers of people cycling through transport network. For this to occur safely, changes in both road infrastructure and road user expectations and behaviors will be needed. Creating separate cycle infrastructure does not remove the need for cyclists to commence, cross or finish travel on shared roads. Currently intersections are one of the predominant shared road spaces where crashes result in cyclists being injured or killed. This research investigates how Brisbane cyclists and drivers perceive risk when interacting with other road users at intersections. The current study replicates a French study conducted by co-authors Chaurand and Delhomme in 2011 and extends it to assess gender effects which have been reported in other Australian cycling research. An online survey was administered to experienced cyclists and drivers. Participants rated the level of risk they felt when imagining a number of different road situations. Based on the earlier French study it is expected that perceived crash risk will be influenced both by the participant’s mode of travel and the type of interacting vehicle and perceived risk will be greater when the interaction is with a car than a bicycle. It is predicted that risk perception will decrease as the level of experience increases and that male participants will have a higher perception of skill and lower perception of risk than females. The findings of this Queensland study will provide a valuable insight into perceived risk and the traffic behaviours of drivers and cyclists when interacting with other road users and results will be available for presentation at the Congress.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Analysis of environmental efficiency variation : a materials balance approach

Recent literature has argued that environmental efficiency (EE), which is built on the materials balance (MB) principle, is more suitable than other EE measures in situations where the law of mass conversation regulates production processes. In addition, the MB-based EE method is particularly useful in analysing possible trade-offs between cost and environmental performance. Identifying determinants of MB-based EE can provide useful information to decision makers but there are very few empirical investigations into this issue. This article proposes the use of data envelopment analysis and stochastic frontier analysis techniques to analyse variation in MB-based EE. Specifically, the article develops a stochastic nutrient frontier and nutrient inefficiency model to analyse determinants of MB-based EE. The empirical study applies both techniques to investigate MB-based EE of 96 rice farms in South Korea. The size of land, fertiliser consumption intensity, cost allocative efficiency, and the share of owned land out of total land are found to be correlated with MB-based EE. The results confirm the presence of a trade-off between MB-based EE and cost allocative efficiency and this finding, favouring policy interventions to help farms simultaneously achieve cost efficiency and MP-based EE.

Analysis of productive performance of crop production systems: an integrated analytical framework

Recent literature has argued that environmental efficiency (EE), which is built on the materials balance (MB) principle, is more suitable than other EE measures in situations where the law of mass conversation regulates production processes. In addition, the MB-based EE method is particularly useful in analysing possible trade-offs between cost and environmental performance. Identifying determinants of MB-based EE can provide useful information to decision makers but there are very few empirical investigations into this issue. This article proposes the use of data envelopment analysis and stochastic frontier analysis techniques to analyse variation in MB-based EE. Specifically, the article develops a stochastic nutrient frontier and nutrient inefficiency model to analyse determinants of MB-based EE. The empirical study applies both techniques to investigate MB-based EE of 96 rice farms in South Korea. The size of land, fertiliser consumption intensity, cost allocative efficiency, and the share of owned land out of total land are found to be correlated with MB-based EE. The results confirm the presence of a trade-off between MB-based EE and cost allocative efficiency and this finding, favouring policy interventions to help farms simultaneously achieve cost efficiency and MP-based EE.

The effect of overnight sleep deprivation after competitive rugby league matches on postmatch physiological and perceptual recovery

PURPOSE: This study examined the effects of overnight sleep deprivation on recovery following competitive rugby league matches. METHODS: Eleven male, amateur rugby league players performed two competitive matches, followed by either a normal night's sleep (~8h; CONT) or a sleep deprived night (~0h; SDEP) in a randomised fashion. Testing was conducted the morning of the match, and immediately post-match, 2h post and the next morning (16h post-match). Measures included counter-movement jump (CMJ) distance, knee extensor maximal voluntary contraction (MVC), voluntary activation (VA), venous blood creatine kinase (CK) and C-reactive protein (CRP), perceived muscle soreness and a word-colour recognition cognitive function test. Percent change between post- and 16h post-match was reported to determine the effect of the intervention the next morning. RESULTS: Large effects indicated a greater post- to 16h post-match percentage decline in CMJ distance following SDEP compared to CONT (P=0.10-0.16; d=0.95-1.05). Similarly, the percentage decline in incongruent word-colour reaction times were increased in SDEP trials (P=0.007; d=1.75). Measures of MVC did not differ between conditions (P=0.40-0.75; d=0.13-0.33), though trends for larger percentage decline in VA were detected in SDEP (P=0.19; d=0.84). Further, large effects indicated higher CK and CRP responses 16h post-match during SDEP compared to CONT (P=0.11-0.87; d=0.80-0.88). CONCLUSIONS: Sleep deprivation negatively affected recovery following a rugby league match, specifically impairing CMJ distance and cognitive function. Practitioners should promote adequate post-match sleep patterns or adjust training demands the next day to accommodate the altered physical and cognitive state following sleep deprivation.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Evaluation of Attacks and Countermeasures in Large Scale Networks

Computer worms represent a serious threat for modern communication infrastructures. These epidemics can cause great damage such as financial losses or interruption of critical services which support lives of citizens. These worms can spread with a speed which prevents instant human intervention. Therefore automatic detection and mitigation techniques need to be developed. However, if these techniques are not designed and intensively tested in realistic environments, they may cause even more harm as they heavily interfere with high volume communication flows. We present a simulation model which allows studies of worm spread and counter measures in large scale multi-AS topologies with millions of IP addresses.

ECMO : the clinician’s view

Background: Extra corporeal membrane oxygenation (ECMO) is a complex rescue therapy used to provide cardiac and/or respiratory support for critically ill patients who have failed maximal conventional medical management. ECMO is based on a modified cardiopulmonary bypass (CPB) circuit, and can provide cardiopulmonary support for up-to several months. It can be used in a veno venous configuration for isolated respiratory failure, (VV-ECMO), or in a veno arterial configuration (VA-ECMO) where support is necessary for cardiac +/- respiratory failure. The ECMO circuit consists of five main components: large bore cannulae (access cannulae) for drainage of the venous system, and return cannulae to either the venous (in VV-ECMO) or arterial (in VA ECMO) system. An oxygenator, with a vast surface area of hollow filaments, allows addition of oxygen and removal of carbon dioxide; a centrifugal blood pump allows propulsion of blood through the circuit at upto 10 L/minute; a control module and a thermoregulatory unit, which allows for exact temperature control of the extra corporeal blood. Methods: The first successful use of ECMO for ARDS in adults occurred in 1972, and its use has become more commonplace over the last 30 years, supported by the improvement in design and biocompatibility of the equipment, which has reduced the morbidity associated with this modality. Whilst the use of ECMO in neonatal population has been supported by numerous studies, the evidence upon which ECMO was integrated into adult practice was substantially less robust. Results: Recent data, including the CESAR study (Conventional Ventilatory Support versus Extra corporeal membrane oxygenation for Severe Respiratory failure) has added a degree of evidence to the role of ECMO in such a patient population. The CESAR study analysed 180 patients, and confirmed that ECMO was associated with an improved rate of survival. More recently, ECMO has been utilized in numerous situations within the critical care area, including support in high-risk percutaneous interventions in cardiac catheter lab; the operating room, emergency department, as well in specialized inter-hospital retrieval services. The increased understanding of the risk:benefit profile of ECMO, along with a reduction in morbidity associated with its use will doubtless lead to a substantial rise in the utilisation of this modality. As with all extra-corporeal circuits, ECMO opposes the basic premises of the mammalian inflammation and coagulation cascade where blood comes into foreign circulation, both these cascades are activated. Anti-coagulation is readily dealt with through use of agents such as heparin, but the inflammatory excess, whilst less macroscopically obvious, continues un-abated. Platelet consumption and neutrophil activation occur rapidly, and the clinician is faced with balancing the need of anticoagulation for the circuit, against haemostasis in an acutely bleeding patient. Alterations in pharmacokinetics may result in inadequate levels of disease modifying therapeutics, such as antibiotics, hence paradoxically delaying recovery from conditions such as pneumonia. Key elements of nutrition and the innate immune system maysimilarly be affected. Summary: This presentation will discuss the basic features of ECMO to the nonspecialist, and review the clinical conundrum faced by the team treating these most complex cases.

Bike share : a synthesis of the literature

This paper begins by providing an overview of bike share programs, followed by a critical examination of the growing body of literature on these programs. This synthesis of previous works, both peer-reviewed and grey, includes an identification of the current gaps in knowledge related to the impacts of bike sharing programs. This synthesis represents a critically needed evaluation of the current state of global bike share research, in order to better understand, and maximize the effectiveness of current and future programs. Several consistent themes have emerged within the growing body of research on bike share programs. Firstly, the importance bike share members place on convenience and value for money appears paramount in their motivation to sign up and use these programs. Secondly, and somewhat counter intuitively, scheme members are more likely to own and use private bicycles than non-members. Thirdly, users demonstrate a greater reluctance to wear helmets than private bicycle riders and helmets have acted as a deterrent in jurisdictions in which helmets are mandatory. Finally, and perhaps most importantly from a sustainable transport perspective, the majority of scheme users are substituting from sustainable modes of transport rather than the car.