Primary students' group metacognitive processes in a computer supported collaborative learning environment

The current understanding of students’ group metacognition is limited. The research on metacognition has focused mainly on the individual student. The aim of this study was to address the void by developing a conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments. An initial conceptual framework based on the literature from metacognition, cooperative learning, cooperative group metacognition, and computer supported collaborative learning was used to inform the study. In order to achieve the study aim, a design research methodology incorporating two cycles was used. The first cycle focused on the within-group metacognition for sixteen groups of primary school students working together around the computer; the second cycle included between-group metacognition for six groups of primary school students working together on the Knowledge Forum® CSCL environment. The study found that providing groups with group metacognitive scaffolds resulted in groups planning, monitoring, and evaluating the task and team aspects of their group work. The metacognitive scaffolds allowed students to focus on how their group was completing the problem-solving task and working together as a team. From these findings, a revised conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments was generated.

Learning in the third space : a sociocultural perspective on learning with analogies

Research on analogies in science education has focussed on student interpretation of teacher and textbook analogies, psychological aspects of learning with analogies and structured approaches for teaching with analogies. Few studies have investigated how analogies might be pivotal in students’ growing participation in chemical discourse. To study analogies in this way requires a sociocultural perspective on learning that focuses on ways in which language, signs, symbols and practices mediate participation in chemical discourse. This study reports research findings from a teacher-research study of two analogy-writing activities in a chemistry class. The study began with a theoretical model, Third Space, which informed analyses and interpretation of data. Third Space was operationalized into two sub-constructs called Dialogical Interactions and Hybrid Discourses. The aims of this study were to investigate sociocultural aspects of learning chemistry with analogies in order to identify classroom activities where students generate Dialogical Interactions and Hybrid Discourses, and to refine the operationalization of Third Space. These aims were addressed through three research questions. The research questions were studied through an instrumental case study design. The study was conducted in my Year 11 chemistry class at City State High School for the duration of one Semester. Data were generated through a range of data collection methods and analysed through discourse analysis using the Dialogical Interactions and Hybrid Discourse sub-constructs as coding categories. Results indicated that student interactions differed between analogical activities and mathematical problem-solving activities. Specifically, students drew on discourses other than school chemical discourse to construct analogies and their growing participation in chemical discourse was tracked using the Third Space model as an interpretive lens. Results of this study led to modification of the theoretical model adopted at the beginning of the study to a new model called Merged Discourse. Merged Discourse represents the mutual relationship that formed during analogical activities between the Analog Discourse and the Target Discourse. This model can be used for interpreting and analysing classroom discourse centred on analogical activities from sociocultural perspectives. That is, it can be used to code classroom discourse to reveal students’ growing participation with chemical (or scientific) discourse consistent with sociocultural perspectives on learning.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Leadership in problem-oriented policing

Purpose – The purpose of this paper is to explore the role of leadership in problem-oriented policing (POP). Design/methodology/approach – This paper uses interrupted time series models to isolate the impact on crime trends of a transformational leader's efforts to spearhead the implementation of a program of POP, called the problem solving model (PSM), in a southern state in Australia. Findings – This paper finds that the PSM led directly to an impact on overall crime, with a significant reduction in crimes per 100,000 persons per year after the introduction of the PSM. The majority of the overall crime drop attributable to implementation of POP was driven by reductions in property crime. It was noted that the leadership influence of the PSM was not effective in reducing all types of crime. Crimes against the person where not affected by the introduction of the PSM and public nuisance crimes largely followed the forecasted, upward trajectory. Practical implications – The driver behind the PSM was Commissioner Hyde and the success of the PSM is largely attributable to his strong commitment to transformational leadership and a top-down approach to implementation. These qualities encapsulate the original ideas behind POP that Goldstein (1979, 2003), back in 1979, highlighted as critical for the success of future POP programs. Social implications – Reducing crime is an important part of creating safe communities and improving quality of life for all citizens. This research shows that successful implementation of the PSM within South Australia under the strong leadership of Commissioner Hyde was a major factor in reducing property crime and overall crime rates. Originality/value – This paper is valuable because it demonstrates the link between strong leadership in policing, the commissioner's vision for POP and how his vision then translated into widespread adoption of POP. The study empirically shows that the statewide adoption of POP led to significant reductions in crime, particularly property crime.

Consumer’s persistence in solving their own problem with self‐service technology

An increasing range of technology services are now offered on a self-service basis. However, problems with self-service technologies (SSTs) occur at times due to the technical error, staff error, or consumers’ own mistakes. Considering the role of consumers as co-producers in the SST context, we aim to study consumer’s behaviours, strategies, and decision making in solving their problem with SST and identify the factors contributing to their persistence in solving the problem. This study contributes to the information systems research, as it is the first study that aims to identify such a process and the factors affecting consumers’ persistence in solving their problem with SST. A focus group with user support staff has been conducted, yielding some initial results that helped to conduct the next phases of the study. Next, using Critical Incident Technique, data will be gathered through focus groups with users, diary method, and think-aloud method.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Bridging STEM in a real-world problem

Engineering-based modeling activities provide a rich source of meaningful situations that capitalize on and extend students’ routine learning. By integrating such activities within existing curricula, students better appreciate how their school learning in mathematics and science applies to problems in the outside world...

Experience of problem-based learning (PBL) in virtual space : a phenomenographical study

This thesis reports the outcomes of an investigation into students’ experience of 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. Research was therefore focussed on discovering the qualitatively different ways that students experience PBL in virtual space. Data was collected in an electronic environment from a course, which adopted the PBL strategy and was delivered entirely in virtual space. Students in this course were asked to respond to open-ended questions designed to elicit their learning experience in the course. Data was analysed using the phenomenographical approach. This interpretative research method concentrated on mapping the qualitative differences in students’ interpretations of their experience in the course. Five qualitatively different ways of experiencing were discovered: Conception 1: ‘A necessary evil for program progression’; Conception 2: ‘Developing skills to understand, evaluate, and solve technical Engineering and Surveying problems’; Conception 3: ‘Developing skills to work effectively in teams in virtual space’; Conception 4: ‘A unique approach to learning how to learn’; Conception 5: ‘Enhancing personal growth’. Each conception reveals variation in how students attend to learning by PBL in virtual space. Results indicate that the design of students’ online learning experience was responsible for making students aware of deeper ways of experiencing PBL in virtual space. Results also suggest that the quality and quantity of interaction with the team facilitator may have a significant impact on the student experience in virtual PBL courses. The outcomes imply pedagogical strategies can be devised for shifting students’ focus as they engage in the virtual PBL experience to effectively manage the student learning experience and thereby ensure that they gain maximum benefit. The results from this research hold important ramifications for graduates with respect to their ease of transition into professional work as well as their later professional competence in terms of problem solving, ability to transfer basic knowledge to real-life engineering scenarios, ability to adapt to changes and apply knowledge in unusual situations, ability to think critically and creatively, and a commitment to continuous life-long learning and self-improvement.

A soft approach to solving hard problems in construction project management

Construction projects are faced with a challenge that must not be underestimated. These projects are increasingly becoming highly competitive, more complex, and difficult to manage. They become ‘wicked problems’, which are difficult to solve using traditional approaches. Soft Systems Methodology (SSM) is a systems approach that is used for analysis and problem solving in such complex and messy situations. SSM uses “systems thinking” in a cycle of action research, learning and reflection to help understand the various perceptions that exist in the minds of the different people involved in the situation. This paper examines the benefits of applying SSM to wicked problems in construction project management, especially those situations that are challenging to understand and difficult to act upon. It includes relevant examples of its use in dealing with the confusing situations that incorporate human, organizational and technical aspects.

Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Working together for Toby : early childhood student teachers engaging in collaborative problem-based learning around child abuse and neglect

Early childhood teacher education programs have a responsibility, amongst many, to prepare teachers for decision-making on real world issues, such as child abuse and neglect. Their repertoire of skills can be enhanced by engaging with others, either face-to-face or online, in authentic problem-based learning. This paper draws on a study of early childhood student teachers who engaged in an authentic learning experience, which was to consider and to suggest how they would act upon a real-life case of child abuse encountered in an early childhood classroom in Queensland. This was the case of Toby (a pseudonym), who was suspected of being physically abused at home. Students drew upon relevant legislation, policy and resource materials to tackle Toby’s case. The paper provides evidence of students grappling with the complexity of a child abuse case and establishing, through collaboration with others, a proactive course of action. The paper has a dual focus. First, it discusses the pedagogical context in which early childhood student teachers deal with issues of child abuse and neglect in the course of their teacher education program. Second, it examines evidence of students engaging in collaborative problem-solving around issues of child abuse and neglect and teachers’ responsibilities, both legal and professional, to the children and families they work with. Early childhood policy-makers, practitioners and teacher educators are challenged to consider how early childhood teachers are best equipped to deal with child protection and early intervention.

Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.