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 0904, April 2009: Presidents Message

President’s Report Hello fellow AITPM members, A few weeks ago we saw another example of all levels of Government pulling together in real time to try to deal with a major transport incident, this time it was container loads of ammonium nitrate falling off the Pacific Adventurer during Cyclone Hamish and the associated major oil spill due to piercing of its hull off Moreton Bay in southern Queensland. The oil spill was extensive, affecting beaches and estuaries from Moreton Island north to the Sunshine Coast; a coastal stretch of at least 60km. We saw the Queensland Government, Brisbane, Moreton Bay and Sunshine Coast Regional Council crews deployed quickly once the gravity of the situation was realised to clean up toxic oil on beaches and prevent extensive upstream contamination. Environmental agencies public and private were quick to respond to help affected wildlife. The Navy’s HMAS Yarra and another minesweeper were deployed to search for the containers in the coastal area in an effort to have them salvaged before all ammonium nitrate could leach into and harm marine habitat, which would have a substantial impact not only on that environment but also the fishing industry. all of this during the final fortnight before a State election.) While this could be branded as a maritime problem, the road transport and logistics system was crucial to the cleanup. The private vehicular ferries were enlisted to transport plant and equipment from Brisbane to Moreton Island. The plant themselves, such as graders, were drawn from road building and maintenance inventory. Hundreds of Councils’ staff were released from other activities to undertake the cleanup. While it will take some time for us to know the long term impacts of this incident, it seems difficult to fault “grassroots” government crews and their private counterparts, such as Island tourism staff, in the initial cleanup effort. From a traffic planning and management perspective, we should also remember that this sort of incident has happened on road and rail corridors in the past, albeit on lesser scales. It underlines that we do need to continue to protect communities, commercial interests, and the environment through rigorous heavy vehicle management, planning and management of dangerous goods routesincluding rail corridors through urban areas), and carefully considered incident and disaster recovery plans and protocols. I’d like to 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. SA Branch President Paul Morris informs me that we have had over 50 paper submissions to date, from which a very balanced and informative programme of sessions has been prepared. www.aitpm.com has all of the details about how to register, sponsor a booth, session, etc. Best regards all, Jon Bunker

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.

Early detection : a strategy to reduce risk and severity?

Despite changes in surgical techniques, radiotherapy targeting and the apparent earlier detection of cancers, secondary lymphoedema is still a significant problem for about 20–30% of those who receive treatment for cancer, although the incidence and prevalence does seem to be falling. The figures above generally relate to detection of an enlarged limb or other area, but it seems that about 60% of all patients also suffer other problems with how the limb feels, what can or cannot be done with it and a range of social or psychological issues. Often these ‘subjective’ changes occur before the objective ones, such as a change in arm volume or circumference. For most of those treated for cancer lymphoedema does not develop immediately, and, while about 60–70% develop it in the first few years, some do not develop lymphoedema for up to 15 or 20 years. Those who will develop clinically manifest lymphoedema in the future are, for some time, in a latent or hidden phase of lymphoedema. There also seems to be some risk factors which are indicators for a higher likelihood of lymphoedema post treatment, including oedema at the surgical site, arm dominance, age, skin conditions, and body mass index (BMI).

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.

Eco-retrofitting - from managerialism to design

As all environmental problems are caused by human systems of design, sustainability can be seen as a design problem. Given the massive energy and material flows through the built environment, sustainability simply cannot be achieved without the re-design of our urban areas. ‘Eco-retrofitting’, as used here, means modifying buildings and/or urban areas to create net positive social and environmental impacts – both on site and off site. While this has probably not been achieved anywhere as yet, myriad but untapped eco-solutions are already available which could be up-scaled to the urban level. It is now well established that eco-retrofitting buildings and cities with appropriate design technology can pay for itself through lower health costs, productivity increases and resource savings. Good design would also mean happier human and ecological communities at a much lower cost over time. In fact, good design could increase life quality and the life support services of nature while creating sustainable‘economic’growth. The impediments are largely institutional and intellectual, which can be encapsulated in the term ‘managerial’. There are, however, also systems design solutions to the managerial obstacles that seem to be stalling the transition to sustainable systems designs. Given the sustainability imperative, then, why is the adoption of better management systems so slow? The oral presentation will show examples of ways in which built environment design can create environments that not only reduce the ongoing damage of past design, but could theoretically generate net positive social and ecological outcomes over their life cycle. These illustrations show that eco-retrofitting could cost society less than doing nothing - especially given the ongoing renovations of buildings - but for managerial hurdles. The paper outlines on how traditional managerial approaches stand in the way of ‘design for ecosystem services’, and list some management solutions that have long been identified, but are not yet widely adopted. Given the pervasive nature of these impediments and their alternatives, they are presented by way of examples. A sampling of eco-retrofitting solutions are also listed to show that ecoretrofitting is a win-win-win solution that stands ready to be implemented by people having management skills and/or positions of influence.

When 'listeners can't talk' : comparing active listening in opening sequences of telephone and online counselling

While there is growing use of online counselling, little is known about its interactional organisation and how it compares to telephone counselling. This is despite past research suggesting that both counsellors and clients report the impact of the different modalities on the presentation and management of the counselling interaction. This paper compares the interactional affordances of telephone and online web counselling in opening sequences on Kids Help Line, a 24-hour Australian counselling service for children and young people up to the age of 25. We examine two ways that counsellors show active listening through response tokens and formulations. The analysis describes how counsellors’ use of minimal response tokens facilitate the clients’ problem presentation and are used in the management of turn taking and sequence organisation. For example, counsellors use the response token Mm hm to show that they understand that the client’s unit of talk to is not yet complete, and to affirm or invite the client to continue speaking. Formulations in phone and web counselling are another way that counsellors display active listening to re-present stretches of the clients’ preceding talk. In phone and web counselling, however, the respective modalities can complicate matters of turn transition and sequence organisation. By examining actual phone and online counselling sessions, this paper offers empirical demonstrations of the interactional affordances of phone and online counselling, and shows how the institutional practice of active listening is accomplished across different counselling modalities

Business Creation Processes in Australia : What Start-Up Attempts Get Up and Running, and Why? - A Preliminary Assessment

The Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE) is the largest study of new firm formation that has ever been undertaken in Australia. CAUSEE follows the development of several samples of new and emerging firms over time. In this report we focus on the drivers of outcomes – in terms of reaching an operational stage vs. terminating the effort – of 493 randomly selected nascent firms whose founders have been comprehensively interviewed on two occasions, 12 months apart. We investigate the outcome effects of three groups of variables: Characteristics of the Venture; Resources Used in the Start-Up Process and Characteristics of the Start-Up Process Itself.