Learning through modelling in the primary years

Many nations are highlighting the need for a renaissance in the mathematical sciences as essential to the well-being of all citizens (e.g., Australian Academy of Science, 2006; 2010; The National Academies, 2009). Indeed, the first recommendation of The National Academies’ Rising Above the Storm (2007) was to vastly improve K–12 science and mathematics education. The subsequent report, Rising Above the Gathering Storm Two Years Later (2009), highlighted again the need to target mathematics and science from the earliest years of schooling: “It takes years or decades to build the capability to have a society that depends on science and technology . . . You need to generate the scientists and engineers, starting in elementary and middle school” (p. 9). Such pleas reflect the rapidly changing nature of problem solving and reasoning needed in today’s world, beyond the classroom. As The National Academies (2009) reported, “Today the problems are more complex than they were in the 1950s, and more global. They’ll require a new educated workforce, one that is more open, collaborative, and cross-disciplinary” (p. 19). The implications for the problem solving experiences we implement in schools are far-reaching. In this chapter, I consider problem solving and modelling in the primary school, beginning with the need to rethink the experiences we provide in the early years. I argue for a greater awareness of the learning potential of young children and the need to provide stimulating learning environments. I then focus on data modelling as a powerful means of advancing children’s statistical reasoning abilities, which they increasingly need as they navigate their data-drenched world.

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...

Handbook of International Research in Mathematics Education [3rd Ed.]

"This third edition ofthe Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field."--Publisher website

Creative design and the generative evolutionary paradigm

Design as seen from the designer's perspective is a series of amazing imaginative jumps or creative leaps. But design as seen by the design historian is a smooth progression or evolution of ideas that they seem self-evident and inevitable after the event. But the next step is anything but obvious for the artist/creator/inventor/designer stuck at that point just before the creative leap. They know where they have come from and have a general sense of where they are going, but often do not have a precise target or goal. This is why it is misleading to talk of design as a problem-solving activity - it is better defined as a problem-finding activity. This has been very frustrating for those trying to assist the design process with computer-based, problem-solving techniques. By the time the problem has been defined, it has been solved. Indeed the solution is often the very definition of the problem. Design must be creative-or it is mere imitation. But since this crucial creative leap seem inevitable after the event, the question must arise, can we find some way of searching the space ahead? Of course there are serious problems of knowing what we are looking for and the vastness of the search space. It may be better to discard altogether the term "searching" in the context of the design process: Conceptual analogies such as search, search spaces and fitness landscapes aim to elucidate the design process. However, the vastness of the multidimensional spaces involved make these analogies misguided and they thereby actually result in further confounding the issue. The term search becomes a misnomer since it has connotations that imply that it is possible to find what you are looking for. In such vast spaces the term search must be discarded. Thus, any attempt at searching for the highest peak in the fitness landscape as an optimal solution is also meaningless. Futhermore, even the very existence of a fitness landscape is fallacious. Although alternatives in the same region of the vast space can be compared to one another, distant alternatives will stem from radically different roots and will therefore not be comparable in any straightforward manner (Janssen 2000). Nevertheless we still have this tantalizing possibility that if a creative idea seems inevitable after the event, then somehow might the process be rserved? This may be as improbable as attempting to reverse time. A more helpful analogy is from nature, where it is generally assumed that the process of evolution is not long-term goal directed or teleological. Dennett points out a common minsunderstanding of Darwinism: the idea that evolution by natural selection is a procedure for producing human beings. Evolution can have produced humankind by an algorithmic process, without its being true that evolution is an algorithm for producing us. If we were to wind the tape of life back and run this algorithm again, the likelihood of "us" being created again is infinitesimally small (Gould 1989; Dennett 1995). But nevertheless Mother Nature has proved a remarkably successful, resourceful, and imaginative inventor generating a constant flow of incredible new design ideas to fire our imagination. Hence the current interest in the potential of the evolutionary paradigm in design. These evolutionary methods are frequently based on techniques such as the application of evolutionary algorithms that are usually thought of as search algorithms. It is necessary to abandon such connections with searching and see the evolutionary algorithm as a direct analogy with the evolutionary processes of nature. The process of natural selection can generate a wealth of alternative experiements, and the better ones survive. There is no one solution, there is no optimal solution, but there is continuous experiment. Nature is profligate with her prototyping and ruthless in her elimination of less successful experiments. Most importantly, nature has all the time in the world. As designers we cannot afford prototyping and ruthless experiment, nor can we operate on the time scale of the natural design process. Instead we can use the computer to compress space and time and to perform virtual prototyping and evaluation before committing ourselves to actual prototypes. This is the hypothesis underlying the evolutionary paradigm in design (1992, 1995).

User-designer collaboration during the early stage of the product development process

As an understanding of users' tacit knowledge and latent needs embedded in user experience has played a critical role in product development, users’ direct involvement in design has become a necessary part of the design process. Various ways of accessing users' tacit knowledge and latent needs have been explored in the field of user-centred design, participatory design, and design for experiencing. User-designer collaboration has been used unconsciously by traditional designers to facilitate the transfer of users' tacit knowledge and to elicit new knowledge. However, what makes user-designer collaboration an effective strategy has rarely been reported on or explored. Therefore, interaction patterns between the users and the designers in three industry-supported user involvement cases were studied. In order to develop a coding system, collaboration was defined as a set of coordinated and joint problem solving activities, measured by the elicitation of new knowledge from collaboration. The analysis of interaction patterns in the user involvement cases revealed that allowing users to challenge or modify their contextual experiences facilitates the transfer of knowledge and new knowledge generation. It was concluded that users can be more effectively integrated into the product development process by employing collaboration strategies to intensify the depth of user involvement.

An investigation into the use of a blended model of learning in a first year accounting subject

The weaknesses of ‗traditional‘ modes of instruction in accounting education have been widely discussed. Many contend that the traditional approach limits the ability to provide opportunities for students to raise their competency level and allow them to apply knowledge and skills in professional problem solving situations. However, the recent body of literature suggests that accounting educators are indeed actively experimenting with ‗non-traditional‘ and ‗innovative‘ instructional approaches, where some authors clearly favour one approach over another. But can one instructional approach alone meet the necessary conditions for different learning objectives? Taking into account the ever changing landscape of not only business environments, but also the higher education sector, the premise guiding the collaborators in this research is that it is perhaps counter productive to promote competing dichotomous views of ‗traditional‘ and ‗non-traditional‘ instructional approaches to accounting education, and that the notion of ‗blended learning‘ might provide a useful framework to enhance the learning and teaching of accounting. This paper reports on the first cycle of a longitudinal study, which explores the possibility of using blended learning in first year accounting at one campus of a large regional university. The critical elements of blended learning which emerged in the study are discussed and, consistent with the design-based research framework, the paper also identifies key design modifications for successive cycles of the research.

Report : enabling team collaboration with pervasive and mobile computing : cost benefit analysis methodology

Construction is an information intensive industry in which the accuracy and timeliness of information is paramount. It observed that the main communication issue in construction is to provide a method to exchange data between the site operation, the site office and the head office. The information needs under consideration are time critical to assist in maintaining or improving the efficiency at the jobsite. Without appropriate computing support this may increase the difficulty of problem solving. Many researchers focus their research on the usage of mobile computing devices in the construction industry and they believe that mobile computers have the potential to solve some construction problems that leads to reduce overall productivity. However, to date very limited observation has been conducted in terms of the deployment of mobile computers for construction workers on-site. By providing field workers with accurate, reliable and timely information at the location where it is needed, it will support the effectiveness and efficiency at the job site. Bringing a new technology into construction industry is not only need a better understanding of the application, but also need a proper preparation of the allocation of the resources such as people, and investment. With this in mind, an accurate analysis is needed to provide clearly idea of the overall costs and benefits of the new technology. A cost benefit analysis is a method of evaluating the relative merits of a proposed investment project in order to achieve efficient allocation of resources. It is a way of identifying, portraying and assessing the factors which need to be considered in making rational economic choices. In principle, a cost benefit analysis is a rigorous, quantitative and data-intensive procedure, which requires identification all potential effects, categorisation of these effects as costs and benefits, quantitative estimation of the extent of each cost and benefit associated with an action, translation of these into a common metric such as dollars, discounting of future costs and benefits into the terms of a given year, and summary of all cost and benefit to see which is greater. Even though many cost benefit analysis methodologies are available for a general assessment, there is no specific methodology can be applied for analysing the cost and benefit of the application of mobile computing devices in the construction site. Hence, the proposed methodology in this document is predominantly adapted from Baker et al. (2000), Department of Finance (1995), and Office of Investment Management (2005). The methodology is divided into four main stages and then detailed into ten steps. The methodology is provided for the CRC CI 2002-057-C Project: Enabling Team Collaboration with Pervasive and Mobile Computing and can be seen in detail in Section 3.

Work engagement and its antecedents in high-risk occupations : a police service case study

Introduction: Work engagement is a recent application of positive psychology and refers to a positive, fulfilling, work-related state of mind characterized by vigor, dedication and absorption. Despite theoretical assumptions, there is little published research on work engagement, due primarily to its recent emergence as a psychological construct. Furthermore, examining work engagement among high-stress occupations, such as police, is useful because police officers are generally characterized as having a high level of work engagement. Previous research has identified job resources (e.g. social support) as antecedents of work engagement. However detailed evaluation of job demands as an antecedent of work engagement within high-stress occupations has been scarce. Thus our second aim was to test job demands (i.e. monitoring demands and problem-solving demands) and job resources (i.e. time control, method control, supervisory support, colleague support, and friend and family support) as antecedents of work engagement among police officers. Method: Data were collected via a self-report online survey from one Australian state police service (n = 1,419). Due to the high number of hypothesized antecedent variables, hierarchical multiple regression analysis was employed rather than structural equation modelling. Results: Work engagement reported by police officers was high. Female officers had significantly higher levels of work engagement than male officers, while officers at mid-level ranks (sergeant) reported the lowest levels of work engagement. Job resources (method control, supervisor support and colleague support) were significant antecedents of three dimensions of work engagement. Only monitoring demands were significant antecedent of the absorption. Conclusion: Having healthy and engaged police officers is important for community security and economic growth. This study identified some common factors which influence work engagement experienced by police officers. However, we also note that excessive work engagement can yield negative outcomes such as psychological distress.

Maternal support for autonomy : relationships with persistence for children with Down syndrome and typically developing children

Maternal behaviors and child mastery behaviors were examined in 25 children with Down syndrome and 43 typically developing children matched for mental age (24–36 months). During a shared problem-solving task, there were no group differences in maternal directiveness or support for autonomy, and mothers in the two groups used similar verbal strategies when helping their child. There were also no group differences in child mastery behaviors, measured as persistence with two optimally challenging tasks. However, the two groups differed in the relationships of maternal style with child persistence. Children with Down syndrome whose mothers were more supportive of their autonomy in the shared task displayed greater persistence when working independently on a challenging puzzle, while children of highly directive mothers displayed lower levels of persistence. For typically developing children, persistence was unrelated to maternal style, suggesting that mother behaviors may have different causes or consequences in the two groups.

Computer attitude and classroom computers

Computers not only increase the speed and efficiency of our mental efforts, but in the process they also alter the problem-solving tasks we are faced with and, in so doing, they alter the cognitive processes we use to solve problems. Computers are fundamentally changing our forms of thinking (Colc & Griffin, 1980). Therefore, the computer should be seen as not only having the potential to amplify human mental capabilities, but also of providing a catalyst for intellectual development.

Decision-making style and self-concept

The Flinders Decision-Making Questionnaire (FDMQ) (Mann, 1982), which measures three decision-making styles and decision-making self-esteem, and the Self-Description Questionnaire III (SDQ HI) (Marsh & O'Neill, 1984), which measures 13 facets of self-concept; were administered to 475 university students to investigate some of the tenets of Janis and Mann's (1976, 1977) conflict model of decision-making and to further investigate the influence of self-concept on decision-making behaviours. The findings empirically validated Janis and Mann's (1977) link between decision-making self-esteem and decision-making style. Modest relationships, in the predicted direction, were found between decision-making self-esteem and the three decision-making styles (Vigilance, Defensive Avoidance, and Hypervigilance). In addition, specific facets of self-concept (General, Verbal, Academic, Honesty/Reliability and Problem-Solving Self Concepts) were related to self-reported decision-making behaviours.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

Visuacy, imagination, and engagement

Australia’s National Review of Visual Education (DEEWR, 2009) asserts the primacy of visual language ability, or ‘visuacy” in problem-solving. This paper reports on a recent university/schools research project with ‘at risk’ middle school students in which visuacy was promoted as a primary medium for obtaining data relating to issues of immediate concern to the students. Using a students-as-researchers approach, the project investigated middle school students’ perspectives on school engagement and disengagement. In this project, novice researchers used a variety of data gathering methods including photography, video interviews and drawn images as well as more traditional verbal methods, such as interviews, and quantitative methods, such as questionnaires. Engaging student imagination was a key focus of the approach taken by the project, acknowledging that student participants may be reluctant to enter dialogue with teachers and researchers on matters to which they have previously had little input. Students who have previously been marginalized and prevented from contributing their voices to educational forums often have difficulty in adjusting to the novelty of collaborative research with adults (Rudduck, 2003) and may be uncertain of their own place in the relationship that defines teacher/student interactions. It is argued that the project’s promotion of visuacy, alongside more traditional literacies and numeracy in education research, helped to overcome these concerns, engaged the imaginations of the student researchers, and provided a medium for the expression of the voices of marginalised young people.

Engaging students in programming

Poor student engagement and high failure rates in first year units were addressed at the Queensland University of Technology (QUT) with a course restructure involving a fresh approach to introducing programming. Students’ first taste of programming in the new course focused less on the language and syntax, and more on problem solving and design, and the role of programming in relation to other technologies they are likely to encounter in their studies. In effect, several technologies that have historically been compartmentalised and taught in isolation have been brought together as a breadth-first introduction to IT. Incorporating databases and Web development technologies into what used to be a purely programming unit gave students a very short introduction to each technology, with programming acting as the glue between each of them. As a result, students not only had a clearer understanding of the application of programming in the real world, but were able to determine their preference or otherwise for each of the technologies introduced, which will help them when the time comes for choosing a course major. Students engaged well in an intensely collaborative learning environment for this unit which was designed to both support the needs of students and meet industry expectations. Attrition from the unit was low, with computer laboratory practical attendance rates for the first time remaining high throughout semester, and the failure rate falling to a single figure percentage.