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.

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.

Can Risk Management boost the supply of Affordable Housing Development and Management?

A shortage of affordable housing is a major problem in Australia today. This is mainly due to the limited supply of affordable housing that is provided by the non-government housing sector. Some private housing developers see the provision of affordable housing for lower income people as a high risk investment which offers a lower return than broader market-based housing. The scarcity of suitable land, a limited government ‘subsidy’, and increasing housing costs have not provided sufficient development incentives to encourage their investment despite the existing high demand for affordable housing. This study analyses the risk management process conducted by some private and not-for-profit housing providers in South East Queensland, and draws conclusions about the relationship between risk assessments/responses and past experiences. In-depth interviews of selected non-government housing providers have been conducted to facilitate an understanding of their approach to risk assessment/response in developing and in managing affordable housing projects. These developers use an informal risk management process as part of their normal business process in accordance with industry standards. A simple qualitative matrix has been used to analyse probability and impacts using a qualitative scale - low, medium and high. For housing providers who have considered investing in affordable housing but have not yet implemented any such projects, affordable housing development is seen as an opportunity that needs to be approached with caution. The risks associated with such projects and the levels of acceptance of these are not consistently identified by current housing providers. Many interviewees agree that the recognition of financial risk and the fear of community rejection of such housing projects have restrained them from committing to such investment projects. This study suggests that implementing improvements to the risk mitigation and management framework may assist in promoting the supply of affordable housing by non-government providers.

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.

Determining the psychosocial predictors of living, living-related, and posthumous organ donation

The worldwide organ shortage occurs despite people’s positive organ donation attitudes. The discrepancy between attitudes and behaviour is evident in Australia particularly, with widespread public support for organ donation but low donation and communication rates. This problem is compounded further by the paucity of theoretically based research to improve our understanding of people’s organ donation decisions. This program of research contributes to our knowledge of individual decision making processes for three aspects of organ donation: (1) posthumous (upon death) donation, (2) living donation (to a known and unknown recipient), and (3) providing consent for donation by communicating donation wishes on an organ donor consent register (registering) and discussing the donation decision with significant others (discussing). The research program used extended versions of the Theory of Planned Behaviour (TPB) and the Prototype/Willingness Model (PWM), incorporating additional influences (moral norm, self-identity, organ recipient prototypes), to explicate the relationship between people’s positive attitudes and low rates of organ donation behaviours. Adopting the TPB and PWM (and their extensions) as a theoretical basis overcomes several key limitations of the extant organ donation literature including the often atheoretical nature of organ donation research, thefocus on individual difference factors to construct organ donor profiles and the omission of important psychosocial influences (e.g., control perceptions, moral values) that may impact on people’s decision-making in this context. In addition, the use of the TPB and PWM adds further to our understanding of the decision making process for communicating organ donation wishes. Specifically, the extent to which people’s registering and discussing decisions may be explained by a reasoned and/or a reactive decision making pathway is examined (Stage 3) with the novel application of the TPB augmented with the social reaction pathway in the PWM. This program of research was conducted in three discrete stages: a qualitative stage (Stage 1), a quantitative stage with extended models (Stage 2), and a quantitative stage with augmented models (Stage 3). The findings of the research program are reported in nine papers which are presented according to the three aspects of organ donation examined (posthumous donation, living donation, and providing consent for donation by registering or discussing the donation preference). Stage One of the research program comprised qualitative focus groups/interviews with university students and community members (N = 54) (Papers 1 and 2). Drawing broadly on the TPB framework (Paper 1), content analysed responses revealed people’s commonly held beliefs about the advantages and disadvantages (e.g., prolonging/saving life), important people or groups (e.g., family), and barriers and motivators (e.g., a family’s objection to donation), related to living and posthumous organ donation. Guided by a PWM perspective, Paper Two identified people’s commonly held perceptions of organ donors (e.g., altruistic and giving), non-donors (e.g., self-absorbed and unaware), and transplant recipients (e.g., unfortunate, and in some cases responsible/blameworthy for their predicament). Stage Two encompassed quantitative examinations of people’s decision makingfor living (Papers 3 and 4) and posthumous (Paper 5) organ donation, and for registering and discussing donation wishes (Papers 6 to 8) to test extensions to both the TPB and PWM. Comparisons of health students’ (N = 487) motivations and willingness for living related and anonymous donation (Paper 3) revealed that a person’s donor identity, attitude, past blood donation, and knowing a posthumous donor were four common determinants of willingness, with the results highlighting students’ identification as a living donor as an important motive. An extended PWM is presented in Papers Four and Five. University students’ (N = 284) willingness for living related and anonymous donation was tested in Paper Four with attitude, subjective norm, donor prototype similarity, and moral norm (but not donor prototype favourability) predicting students’ willingness to donate organs in both living situations. Students’ and community members’ (N = 471) posthumous organ donation willingness was assessed in Paper Five with attitude, subjective norm, past behaviour, moral norm, self-identity, and prior blood donation all significantly directly predicting posthumous donation willingness, with only an indirect role for organ donor prototype evaluations. The results of two studies examining people’s decisions to register and/or discuss their organ donation wishes are reported in Paper Six. People’s (N = 24) commonly held beliefs about communicating their organ donation wishes were explored initially in a TPB based qualitative elicitation study. The TPB belief determinants of intentions to register and discuss the donation preference were then assessed for people who had not previously communicated their donation wishes (N = 123). Behavioural and normative beliefs were important determinants of registering and discussing intentions; however, control beliefs influenced people’s registering intentions only. Paper Seven represented the first empirical test of the role of organ transplant recipient prototypes (i.e., perceptions of organ transplant recipients) in people’s (N = 465) decisions to register consent for organ donation. Two factors, Substance Use and Responsibility, were identified and Responsibility predicted people’s organ donor registration status. Results demonstrated that unregistered respondents were the most likely to evaluate transplant recipients negatively. Paper Eight established the role of organ donor prototype evaluations, within an extended TPB model, in predicting students’ and community members’ registering (n = 359) and discussing (n = 282) decisions. Results supported the utility of an extended TPB and suggested a role for donor prototype evaluations in predicting people’s discussing intentions only. Strong intentions to discuss donation wishes increased the likelihood that respondents reported discussing their decision 1-month later. Stage Three of the research program comprised an examination of augmented models (Paper 9). A test of the TPB augmented with elements from the social reaction pathway in the PWM, and extensions to these models was conducted to explore whether people’s registering (N = 339) and discussing (N = 315) decisions are explained via a reasoned (intention) and/or social reaction (willingness) pathway. Results suggested that people’s decisions to communicate their organ donation wishes may be better explained via the reasoned pathway, particularly for registering consent; however, discussing also involves reactive elements. Overall, the current research program represents an important step toward clarifying the relationship between people’s positive organ donation attitudes but low rates of organ donation and communication behaviours. Support has been demonstrated for the use of extensions to two complementary theories, the TPB and PWM, which can inform future research aiming to explicate further the organ donation attitude-behaviour relationship. The focus on a range of organ donation behaviours enables the identification of key targets for future interventions encouraging people’s posthumous and living donation decisions, and communication of their organ donation preference.