Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

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).

Neurocognitive profiles of people with comorbid depression and alcohol use : implications for psychological interventions

Depression and alcohol use disorders frequently co-occur and are highly prevalent. Both conditions are known to impair cognitive functioning, yet research into the role of these impairments in response to Cognitive Behaviour Therapy (CBT) is limited. The purpose of the present study was to examine the relationship between baseline neuropsychological performance, severity of depressive symptoms and alcohol use disorders. Participants with current depression and hazardous alcohol use were functioning in the average range on all neuropsychological measures prior to treatment entry. Baseline measures of drinking severity and a range of cognitive functions were inversely correlated. After controlling for other baseline variables, superior baseline cognitive functioning predicted greater reductions in depression severity after 17 weeks. These predictive effects occurred across both brief and extended interventions. Findings suggest that improvement in depression following psychological treatment is enhanced by greater fluid reasoning ability and is predicted by executive functioning, regardless of the treatment length or problem focus.

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.

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.

Imagery and strength of craving for eating, drinking and playing sport

The elaborated intrusion (EI) theory of desire (Kavanagh, Andrade, & May, 2005) attributes the motivational force of cravings to cognitive elaboration, including imagery, of apparently spontaneous thoughts that intrude into awareness. We report a questionnaire study in which respondents rated a craving for food or drink. Questionnaire items derived from EI theory formed a single factor alongside factors for anticipated reward/relief, resistance, and opportunity. In a multiple regression predicting strength of craving, the first three factors accounted for 36% of the variance. Opportunity did not enter the model. In a second study, the difference between individuals' strong and weak cravings to take part in a sporting activity was shown to be related to visual, auditory, and general imagery, and to anticipated reward or relief from engaging in the activity. Implications for treatment of craving-related disorders are discussed in the light of these results and of other research indicating that interference with imagery can reduce the strength of craving.

Comparison of methods for processing drinking water samples for the isolation of Myocbacterium avium and intracellulare

Several protocols for isolation of mycobacteria from water exist, but there is no established standard method. This study compared methods of processing potable water samples for the isolation of Mycobacterium avium and Mycobacterium intracellulare using spiked sterilized water and tap water decontaminated using 0.005% cetylpyridinium chloride (CPC). Samples were concentrated by centrifugation or filtration and inoculated onto Middlebrook 7H10 and 7H11 plates and Lowenstein-Jensen slants and into mycobacterial growth indicator tubes with or without polymyxin, azlocillin, nalidixic acid, trimethoprim, and amphotericin B. The solid media were incubated at 32°C, at 35°C, and at 35°C with CO2 and read weekly. The results suggest that filtration of water for the isolation of mycobacteria is a more sensitive method for concentration than centrifugation. The addition of sodium thiosulfate may not be necessary and may reduce the yield. Middlebrook M7H10 and 7H11 were equally sensitive culture media. CPC decontamination, while effective for reducing growth of contaminants, also significantly reduces mycobacterial numbers. There was no difference at 3 weeks between the different incubation temperatures.

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.

The innovation deficit in public services : the curious problem of too much efficiency and not enough waste and failure

It has long been recognised that government and public sector services suffer an innovation deficit compared to private or market-based services. This paper argues that this can be explained as an unintended consequence of the concerted public sector drive toward the elimination of waste through efficiency, accountability and transparency. Yet in an evolving economy this can be a false efficiency, as it also eliminates the 'good waste' that is a necessary cost of experimentation. This results in a systematic trade0off in the public sector between the static efficiency of minimizing the misuse of public resources and the dynamic efficiency of experimentation. this is inherently biased against risk and uncertainty and therein, explains why governments find service innovation so difficult. In the drive to eliminate static inefficiencies, many political systems have susequently overshot and stifled policy innovation. I propose the 'Red Queen' solution of adaptive economic policy.