Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Problem solving in a middle school robotics design classroom

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, Labview programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social construction of meaning. There was a focus on the effect of teachers’ goals and the rules they enacted upon student use of the flow chart planning tool, and the tools of the programming language Labview and Lego construction. It was found that the articulation of a teacher’s goals via rules and divisions of labour helped to form distinct communities of learning and influenced the development of different problem solving strategies. The use of the planning tool flow charting was associated with continuity of approach, integration of problem solutions including appreciation of the nexus between construction and programming, and greater educational transformation. Students who flow charted defined problems in a more holistic way and demonstrated more methodical, insightful and integrated approaches to their use of tools. The findings have implications for teaching in design dominated learning environments.

The problem of measurement indeterminacy in complex neurobiological movement systems

In the study of complex neurobiological movement systems, measurement indeterminacy has typically been overcome by imposing artificial modelling constraints to reduce the number of unknowns (e.g., reducing all muscle, bone and ligament forces crossing a joint to a single vector). However, this approach prevents human movement scientists from investigating more fully the role, functionality and ubiquity of coordinative structures or functional motor synergies. Advancements in measurement methods and analysis techniques are required if the contribution of individual component parts or degrees of freedom of these task-specific structural units is to be established, thereby effectively solving the indeterminacy problem by reducing the number of unknowns. A further benefit of establishing more of the unknowns is that human movement scientists will be able to gain greater insight into ubiquitous processes of physical self-organising that underpin the formation of coordinative structures and the confluence of organismic, environmental and task constraints that determine the exact morphology of these special-purpose devices.

Innovative approaches to intervention for problem drinking

Purpose of review: To critique the recent literature on telephone, correspondence-based, and computerized interventions for alcohol problems, which enhance or substitute for practitioner-delivered treatments. Recent findings: There is an unmet need for screening, assessment and intervention for alcohol problems, in part because of the difficulty in accessing such treatment within the current health care system. Research on the efficacy of correspondence or electronic (for example Internet-based) interventions is beginning to emerge. In the period 2003–2004 we identified nine acceptability or feasibility studies of these approaches and seven efficacy trials covering a wide range of settings. These modes of intervention are acceptable to patients and the public, and with careful planning, can be implemented in a variety of settings. Treatment trials demonstrate the efficacy of these interventions in reducing hazardous drinking by university students, in delaying initiation of heavy drinking in children and adolescents, and, intriguingly, in addressing insomnia among recovering alcoholics. Summary: There is strong support among potential users for alcohol interventions that employ telephone assistance, written correspondence, and the Internet. These new technologies offer the prospect of increasing the reach of interventions for problem drinking and being cost- effective alternatives or supplements to face-to-face health service delivery.

An evaluation of brief correspondence programs for problem drinkers

The provision of accessible and cost-effective treatment to a large number of problem drinkers is a significant challenge to health services. Previous data suggest that a correspondence intervention may assist in these efforts. We recruited 277 people with alcohol abuse problems and randomly allocated them to immediate cognitive behavioral treatment by correspondence (ICBT), 2 months in a waiting list (WL2-CBT), self-monitoring (SM2-CBT), or extended self-monitoring (SM6-CBT). Everyone received correspondence CBT after the control period. Over 2 months later, no drop in alcohol intake occurred in the waiting list, and CBT had a greater impact than SM. No further gains from SM were seen after 2 months. Effects of CBT were well maintained and were equivalent, whether it was received immediately or after 2 to 6 months of self-monitoring. Weekly alcohol intake fell 48% from pretreatment to 18.6 alcohol units at 12 months. Our results confirmed that correspondence CBT for alcohol abuse was accessible and effective for people with low physical dependence.

Problem-based learning (PBL) in Virtual Space : Developing experiences for professional development

This book reports the outcomes of an investigation into discovering the qualitatively different ways that students experience Problem-based learning (PBL)in virtual space. PBL is increasingly being used in many fields including engineering education. At the same time, many engineering education providers are turning to online distance education. Unfortunately there is a dearth of research into what constitutes an effective learning experience for adult learners who undertake PBL instruction through online distance education. Data were collected from a course which adopted the PBL strategy and was delivered entirely in virtual space. Students were asked to respond to open-ended questions designed to elicit their learning experiences. Data were analysed using the phenomenographic approach. Five qualitatively different ways of experiencing PBL in virtual space were discovered. Results indicate that the design of students' online learning experience was responsible for making students aware of deeper ways of experienceing PBL in virtual space. The outcomes imply that pedagogical strategies can be devised for shifting students' focus as they engage in virtual PBL.

The Alcohol Helplessness Scale and its prediction of depression among problem drinkers

Event-specific scales commonly have greater power than generalized scales in prediction of specific disorders and in testing mediator models for predicting such disorders. Therefore, in a preliminary study, a 6-item Alcohol Helplessness Scale was constructed and found to be reliable for a sample of 98 problem drinkers. Hierarchical multiple regression and its derivative path analysis were used to test whether helplessness and self-efficacy moderate or mediate the link between alcohol dependence and depression, A test of a moderation model was not supported, whereas a test of a mediation model was supported. Helplessness and self-efficacy both significantly and independently mediated between alcohol dependence and depression. Nevertheless, a significant direct effect of alcohol dependence on depression also remained.

Brief opportunistic intervention : the role of psychologists in initiating self-change amongst problem drinkers

Excessive consumption of alcohol is a serious public health problem. While intensive treatments are suitable for those who are physically dependent on alcohol, they are not cost-effective options for the vast majority of problem drinkers who are not dependent. There is good evidence that brief interventions are effective in reducing overall alcohol consumption, alcohol-related problems, and health-care utilisation among nondependent problem drinkers. Psychologists are in an ideal position to opportunistically detect people who drink excessively and to offer them brief advice to reduce their drinking. In this paper we outline the process involved in providing brief opportunistic screening and intervention for problem drinkers. We also discuss methods that psychologists can employ if a client is not ready to reduce drinking, or is ambivalent about change. Depending on the client's level of motivation to change, psychologists can engage in either an education-clarification approach, a commitment-enhancement approach, or a skills-training approach. Routine engagement in opportunistic intervention is an important public-health approach to reducing alcohol-related harm in the community.

Robot navigation in sensor space

This thesis investigates the problem of robot navigation using only landmark bearings. The proposed system allows a robot to move to a ground target location specified by the sensor values observed at this ground target posi- tion. The control actions are computed based on the difference between the current landmark bearings and the target landmark bearings. No Cartesian coordinates with respect to the ground are computed by the control system. The robot navigates using solely information from the bearing sensor space. Most existing robot navigation systems require a ground frame (2D Cartesian coordinate system) in order to navigate from a ground point A to a ground point B. The commonly used sensors such as laser range scanner, sonar, infrared, and vision do not directly provide the 2D ground coordi- nates of the robot. The existing systems use the sensor measurements to localise the robot with respect to a map, a set of 2D coordinates of the objects of interest. It is more natural to navigate between the points in the sensor space corresponding to A and B without requiring the Cartesian map and the localisation process. Research on animals has revealed how insects are able to exploit very limited computational and memory resources to successfully navigate to a desired destination without computing Cartesian positions. For example, a honeybee balances the left and right optical flows to navigate in a nar- row corridor. Unlike many other ants, Cataglyphis bicolor does not secrete pheromone trails in order to find its way home but instead uses the sun as a compass to keep track of its home direction vector. The home vector can be inaccurate, so the ant also uses landmark recognition. More precisely, it takes snapshots and compass headings of some landmarks. To return home, the ant tries to line up the landmarks exactly as they were before it started wandering. This thesis introduces a navigation method based on reflex actions in sensor space. The sensor vector is made of the bearings of some landmarks, and the reflex action is a gradient descent with respect to the distance in sensor space between the current sensor vector and the target sensor vec- tor. Our theoretical analysis shows that except for some fully characterized pathological cases, any point is reachable from any other point by reflex action in the bearing sensor space provided the environment contains three landmarks and is free of obstacles. The trajectories of a robot using reflex navigation, like other image- based visual control strategies, do not correspond necessarily to the shortest paths on the ground, because the sensor error is minimized, not the moving distance on the ground. However, we show that the use of a sequence of waypoints in sensor space can address this problem. In order to identify relevant waypoints, we train a Self Organising Map (SOM) from a set of observations uniformly distributed with respect to the ground. This SOM provides a sense of location to the robot, and allows a form of path planning in sensor space. The navigation proposed system is analysed theoretically, and evaluated both in simulation and with experiments on a real robot.

Aberrations and pupil location under corneal topography and Hartmann-Shack illumination conditions

PURPOSE. This study was conducted to determine the magnitude of pupil center shift between the illumination conditions provided by corneal topography measurement (photopic illuminance) and by Hartmann-Shack aberrometry (mesopic illuminance) and to investigate the importance of this shift when calculating corneal aberrations and for the success of wavefront-guided surgical procedures. METHODS. Sixty-two subjects with emmetropia underwent corneal topography and Hartmann-Shack aberrometry. Corneal limbus and pupil edges were detected, and the differences between their respective centers were determined for both procedures. Corneal aberrations were calculated using the pupil centers for corneal topography and for Hartmann-Shack aberrometry. Bland-Altmann plots and paired t-tests were used to analyze the differences between corneal aberrations referenced to the two pupil centers. RESULTS. The mean magnitude (modulus) of the displacement of the pupil with the change of the illumination conditions was 0.21 ± 0.11 mm. The effect of this pupillary shift was manifest for coma corneal aberrations for 5-mm pupils, but the two sets of aberrations calculated with the two pupil positions were not significantly different. Sixty-eight percent of the population had differences in coma smaller than 0.05 µm, and only 4% had differences larger than 0.1 µm. Pupil displacement was not large enough to significantly affect other higher-order Zernike modes. CONCLUSIONS. Estimated corneal aberrations changed slightly between photopic and mesopic illumination conditions given by corneal topography and Hartmann-Shack aberrometry. However, this systematic pupil shift, according to the published tolerances ranges, is enough to deteriorate the optical quality below the theoretically predicted diffraction limit of wavefront-guided corneal surgery.

Transportation disadvantage determination framework : space-time organisation measure in determining transportation disadvantage

Transportation disadvantage has been recognised to be the key source of social exclusion. Therefore an appropriate process is required to investigate and seek to resolve this problem. Currently, determination of Transportation Disadvantage is postulate based on income, poverty and mobility level. Transportation disadvantage may best regard be based on accessibility perspectives as they represent inability of the individual to access desired activities. This paper attempts to justify a process in determining transportation disadvantage by incorporating accessibility and social transporation conflict as the essence of a framework. The framework embeds space time organisation within the dimension of accessibility to identify a rigorous definition of transportation disadvantage. In developing the framework, the definition, dimension, component and measure of accessibility were scrutinised. The findings suggest the definition and dimension are the significant approach of research to evaluate travel experience of the disadvantaged. Concurrently, location accessibility measures will be incorprated to strenghten the determination of accessibility level. Literature review in social exclusion and mobility-related exclusion identified the dimension and source of transportation disadvantage. It was revealed that the appropriate approach to justify trasnportation disadvantaged is to incorporate space-time organisation within the studied components. The suggested framework is an inter-related process consisting of component of accessibility; individual, networking (transport system) and activities (destination). The integration and correlation among the components shall determine the level of transportation disadvantage. Prior findings are used to retrieve the spatial distribution of transportation disadvantaged and appropriate policies are developed to resolve the problems.

Scheduling trains as a blocking parallel-machine job shop scheduling problem

In this paper, the train scheduling problem is modelled as a blocking parallel-machine job shop scheduling (BPMJSS) problem. In the model, trains, single-track sections and multiple-track sections, respectively, are synonymous with jobs, single machines and parallel machines, and an operation is regarded as the movement/traversal of a train across a section. Due to the lack of buffer space, the real-life case should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold the train until next section on the routing becomes available. Based on literature review and our analysis, it is very hard to find a feasible complete schedule directly for BPMJSS problems. Firstly, a parallel-machine job-shop-scheduling (PMJSS) problem is solved by an improved shifting bottleneck procedure (SBP) algorithm without considering blocking conditions. Inspired by the proposed SBP algorithm, feasibility satisfaction procedure (FSP) algorithm is developed to solve and analyse the BPMJSS problem, by an alternative graph model that is an extension of the classical disjunctive graph models. The proposed algorithms have been implemented and validated using real-world data from Queensland Rail. Sensitivity analysis has been applied by considering train length, upgrading track sections, increasing train speed and changing bottleneck sections. The outcomes show that the proposed methodology would be a very useful tool for the real-life train scheduling problems

Sustaining the sustainable? Developing a practice and problem-led new media praxis

In this chapter I introduce an ecological-philosophical approach to artmaking that has guided my work over the past 16 years. I call this ‘Ecosophical praxis’. To illustrate how this infuses and directs my research methodologies, I draw upon a case study called Knowmore (House of Commons), an emerging interactive installation due for first showings in late 2008. This allows me to tease out the complex interrelationships between research and practice within my work, and describe how they comment upon and model these eco-cultural theories. I conclude with my intentions and hopes for the continued emergence of a contemporary eco-political modality of new media praxis that self-reflexively questions how we might re-focus future practices upon ‘sustaining the sustainable’.

Nanoparticle melting as a Stefan moving boundary problem

The melting of spherical nanoparticles is considered from the perspective of heat flow in a pure material and as a moving boundary (Stefan) problem. The dependence of the melting temperature on both the size of the particle and the interfacial tension is described by the Gibbs-Thomson effect, and the resulting two-phase model is solved numerically using a front-fixing method. Results show that interfacial tension increases the speed of the melting process, and furthermore, the temperature distribution within the solid core of the particle exhibits behaviour that is qualitatively different to that predicted by the classical models without interfacial tension.