Losing their marbles : syntax-free programming for assessing problem-solving skills

Novice programmers have difficulty developing an algorithmic solution while simultaneously obeying the syntactic constraints of the target programming language. To see how students fare in algorithmic problem solving when not burdened by syntax, we conducted an experiment in which a large class of beginning programmers were required to write a solution to a computational problem in structured English, as if instructing a child, without reference to program code at all. The students produced an unexpectedly wide range of correct, and attempted, solutions, some of which had not occurred to their teachers. We also found that many common programming errors were evident in the natural language algorithms, including failure to ensure loop termination, hardwiring of solutions, failure to properly initialise the computation, and use of unnecessary temporary variables, suggesting that these mistakes are caused by inexperience at thinking algorithmically, rather than difficulties in expressing solutions as program code.

A genetic algorithm for the multi-source and multi-sink minimum vertex cut problem and its applications

We present a new penalty-based genetic algorithm for the multi-source and multi-sink minimum vertex cut problem, and illustrate the algorithm’s usefulness with two real-world applications. It is proved in this paper that the genetic algorithm always produces a feasible solution by exploiting some domain-specific knowledge. The genetic algorithm has been implemented on the example applications and evaluated to show how well it scales as the problem size increases.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Modelling urban public transit users' route choice behaviour: review and outlook

This paper reviews the main development of approaches to modelling urban public transit users’ route choice behaviour from 1960s to the present. The approaches reviewed include the early heuristic studies on finding the least cost transit route and all-or-nothing transit assignment, the bus common line problem and corresponding network representation methods, the disaggregate discrete choice models which are based on random utility maximization assumptions, the deterministic use equilibrium and stochastic user equilibrium transit assignment models, and the recent dynamic transit assignment models using either frequency or schedule based network formulation. In addition to reviewing past outcomes, this paper also gives an outlook into the possible future directions of modelling transit users’ route choice behaviour. Based on the comparison with the development of models for motorists’ route choice and traffic assignment problems in an urban road area, this paper points out that it is rewarding for transit route choice research to draw inspiration from the intellectual outcomes out of the road area. Particularly, in light of the recent advancement of modelling motorists’ complex road route choice behaviour, this paper advocates that the modelling practice of transit users’ route choice should further explore the complexities of the problem.

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).

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.