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).

AITPM Email Newsletter Volume 0905, May 2009: Presidents Message

President’s Message Hello fellow AITPM members, We’ve been offered a lot of press lately about the Federal Government’s plan for the multibillion dollar rollout of its high speed broadband network, which at the moment is being rated to a speed of 100Mb/s. This seems fantastic in comparison to the not atypical 250 to 500kb/s that I receive on my metropolitan cable broadband, which incidentally my service provider rates at theoretical speeds of up to 8 Mb/s. I have no doubt that such a scheme will generate significant advantages to business and consumers. However, I also have some reservations. Only a few of years ago I marvelled at my first 256Mb USB stick, which cost my employer about $90. Last month I purchased a 16Gb stick with a free computer carry bag for $80, which on the back of my envelope has given me about 72 times the value of my first USB stick not including the carry bag! I am pretty sure the technology industry will find a way to eventually push a lot more than 100Mb/s down the optic fibre network just as they have done with pushing several Mb/s ADSL2 down antique copper wire. This makes me wonder about the general problem of inbuilt obsolescence of all things high-tech due to rapid advances in the tech industry. As a transport professional I then think to myself that our industry has been moving forward at somewhat of a slower pace. We certainly have had major milestones having significant impacts, such as the move from horse and cart to the self propelled motor vehicle, sealing and formal geometric design of roads, development of motorways, signalisation of intersections, coordination of networks, to simulation modelling for real time adaptive control (perhaps major change has been at a frequency of 30 years or so?). But now with ITS truly penetrating the transport market, largely thanks to the in-car GPS navigator, smart phone, e-toll and e-ticket, I believe that to avoid our own obsolescence we’re going to need to “plan for ITS” rather than just what we seem to have been doing up until now, that is, to get it out there. And we’ll likely need to do it at a faster pace. It will involve understanding how to data mine enormous data sets, better understanding the human/machine interface, keeping pace with automotive technology more closely, resolving the ethical and privacy chestnuts, and in the main actually planning for ITS to make peoples’ lives easier rather than harder. And in amongst this we’ll need to keep pace with the types of technology advances similar to my USB stick example above. All the while we’ll be making a brand new set of friends in the disciplines that will morph into ITS along with us. Hopefully these will all be “good” problems for our profession to have. I should close in reminding everyone again that AITPM’s flagship event, the 2009 AITPM National Conference, Traffic Beyond Tomorrow, is being held in Adelaide from 5 to 7 August. www.aitpm.com has all of the details about how to register, sponsor a booth, session, etc. Best regards all, Jon Bunker

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.

Risk-assessment practices in the private rental sector : implications for low-income renters (Final Report)

This report focuses on risk-assessment practices in the private rental market, with particular consideration of their impact on low-income renters. It is based on the fieldwork undertaken in the second stage of the research process that followed completion of the Positioning Paper. The key research question this study addressed was: What are the various factors included in ‘risk-assessments’ by real estate agents in allocating ‘affordable’ tenancies? How are these risks quantified and managed? What are the key outcomes of their decision-making? The study builds on previous research demonstrating that a relatively large proportion of low-cost private rental accommodation is occupied by moderate- to high-income households (Wulff and Yates 2001; Seelig 2001; Yates et al. 2004). This is occurring in an environment where the private rental sector is now the de facto main provider of rental housing for lower-income households across Australia (Seelig et al. 2005) and where a number of factors are implicated in patterns of ‘income–rent mismatching’. These include ongoing shifts in public housing assistance; issues concerning eligibility for rent assistance; ‘supply’ factors, such as loss of low-cost rental stock through upgrading and/or transfer to owner-occupied housing; patterns of supply and demand driven largely by middle- to high-income owner-investors and renters; and patterns of housing need among low-income households for whom affordable housing is not appropriate. In formulating a way of approaching the analysis of ‘risk-assessment’ in rental housing management, this study has applied three sociological perspectives on risk: Beck’s (1992) formulation of risk society as entailing processes of ‘individualisation’; a socio-cultural perspective which emphasises the situated nature of perceptions of risk; and a perspective which has drawn attention to different modes of institutional governance of subjects, as ‘carriers of specific indicators of risk’. The private rental market was viewed as a social institution, and the research strategy was informed by ‘institutional ethnography’ as a method of enquiry. The study was based on interviews with property managers, real estate industry representatives, tenant advocates and community housing providers. The primary focus of inquiry was on ‘the moment of allocation’. Six local areas across metropolitan and regional Queensland, New South Wales, and South Australia were selected as case study localities. In terms of the main findings, it is evident that access to private rental housing is not just a matter of ‘supply and demand’. It is also about assessment of risk among applicants. Risk – perceived or actual – is thus a critical factor in deciding who gets housed, and how. Risk and its assessment matter in the context of housing provision and in the development of policy responses. The outcomes from this study also highlight a number of salient points: 1.There are two principal forms of risk associated with property management: financial risk and risk of litigation. 2. Certain tenant characteristics and/or circumstances – ability to pay and ability to care for the rented property – are the main factors focused on in assessing risk among applicants for rental housing. Signals of either ‘(in)ability to pay’ and/or ‘(in)ability to care for the property’ are almost always interpreted as markers of high levels of risk. 3. The processing of tenancy applications entails a complex and variable mix of formal and informal strategies of risk-assessment and allocation where sorting (out), ranking, discriminating and handing over characterise the process. 4. In the eyes of property managers, ‘suitable’ tenants can be conceptualised as those who are resourceful, reputable, competent, strategic and presentable. 5. Property managers clearly articulated concern about risks entailed in a number of characteristics or situations. Being on a low income was the principal and overarching factor which agents considered. Others included: - unemployment - ‘big’ families; sole parent families - domestic violence - marital breakdown - shift from home ownership to private rental - Aboriginality and specific ethnicities - physical incapacity - aspects of ‘presentation’. The financial vulnerability of applicants in these groups can be invoked, alongside expressed concerns about compromised capacities to manage income and/or ‘care for’ the property, as legitimate grounds for rejection or a lower ranking. 6. At the level of face-to-face interaction between the property manager and applicants, more intuitive assessments of risk based upon past experience or ‘gut feelings’ come into play. These judgements are interwoven with more systematic procedures of tenant selection. The findings suggest that considerable ‘risk’ is associated with low-income status, either directly or insofar as it is associated with other forms of perceived risk, and that such risks are likely to impede access to the professionally managed private rental market. Detailed analysis suggests that opportunities for access to housing by low-income householders also arise where, for example: - the ‘local experience’ of an agency and/or property manager works in favour of particular applicants - applicants can demonstrate available social support and financial guarantors - an applicant’s preference or need for longer-term rental is seen to provide a level of financial security for the landlord - applicants are prepared to agree to specific, more stringent conditions for inspection of properties and review of contracts - the particular circumstances and motivations of landlords lead them to consider a wider range of applicants - In particular circumstances, property managers are prepared to give special consideration to applicants who appear worthy, albeit ‘risky’. The strategic actions of demonstrating and documenting on the part of vulnerable (low-income) tenant applicants can improve their chances of being perceived as resourceful, capable and ‘savvy’. Such actions are significant because they help to persuade property managers not only that the applicant may have sufficient resources (personal and material) but that they accept that the onus is on themselves to show they are reputable, and that they have valued ‘competencies’ and understand ‘how the system works’. The parameters of the market do shape the processes of risk-assessment and, ultimately, the strategic relation of power between property manager and the tenant applicant. Low vacancy rates and limited supply of lower-cost rental stock, in all areas, mean that there are many more tenant applicants than available properties, creating a highly competitive environment for applicants. The fundamental problem of supply is an aspect of the market that severely limits the chances of access to appropriate and affordable housing for low-income rental housing applicants. There is recognition of the impact of this problem of supply. The study indicates three main directions for future focus in policy and program development: providing appropriate supports to tenants to access and sustain private rental housing, addressing issues of discrimination and privacy arising in the processes of selecting suitable tenants, and addressing problems of supply.

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.

The moment of exchange : risk, vulnerability, responsibility

Any cycle of production and exchange – be it economic, cultural or aesthetic – involves an element of risk. It involves uncertainty, unpredictability, and a potential for new insight and innovation (the boom) as well as blockages, crises and breakdown (the bust). In performance, the risks are plentiful – economic, political, social, physical and psychological. The risks people are willing to take depend on their position in the exchange (performer, producer, venue manager or spectator), and their aesthetic preferences. This paper considers the often uncertain, confronting or ‘risky’ moment of exchange between performer, spectator and culture in Live Art practices. Encompassing body art, autobiographical art, site-specific art and other sorts of performative intervention in the public sphere, Live Art eschews the artifice of theatre, breaking down barriers between art and life, artist and spectator, to speak back to the public sphere, and challenge assumptions about bodies, identities, memories, relationships and histories. In the process, Live Art frequently privileges an uncertain, confrontational or ‘risky’ mode of exchange between performer, spectator and culture, as a way of challenging power structures. This paper examines the moment of exchange in terms of risk, vulnerability, responsibility and ethics. Why the romance with ‘risky’ behaviours and exchanges? Who is really taking a risk? What risk? With whose permission (or lack thereof)? What potential does a ‘risky’ exchange hold to destabilise aesthetic, social or political norms? Where lies the fine line between subversive intervention in the public sphere and sheer self-indulgence? What are the social and ethical implications of a moment of exchange that puts bodies, beliefs or social boundaries at ‘risk’? In this paper, these questions are addressed with reference to historical and contemporary practices under the broadly defined banner of Live Art, from the early work of Abrovamic and Burden, through to contemporary Australian practitioners like Fiona McGregor.

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.