779 resultados para Discrete Mathematics Learning


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Speeding remains a significant contributing factor to road trauma internationally, despite increasingly sophisticated speed management strategies being adopted around the world. Increases in travel speed are associated with increases in crash risk and crash severity. As speed choice is a voluntary behaviour, driver perceptions are important to our understanding of speeding and, importantly, to designing effective behavioural countermeasures. The four studies conducted in this program of research represent a comprehensive approach to examining psychosocial influences on driving speeds in two countries that are at very different levels of road safety development: Australia and China. Akers’ social learning theory (SLT) was selected as the theoretical framework underpinning this research and guided the development of key research hypotheses. This theory was chosen because of its ability to encompass psychological, sociological, and criminological perspectives in understanding behaviour, each of which has relevance to speeding. A mixed-method design was used to explore the personal, social, and legal influences on speeding among car drivers in Queensland (Australia) and Beijing (China). Study 1 was a qualitative exploration, via focus group interviews, of speeding among 67 car drivers recruited from south east Queensland. Participants were assigned to groups based on their age and gender, and additionally, according to whether they self-identified as speeding excessively or rarely. This study aimed to elicit information about how drivers conceptualise speeding as well as the social and legal influences on driving speeds. The findings revealed a wide variety of reasons and circumstances that appear to be used as personal justifications for exceeding speed limits. Driver perceptions of speeding as personally and socially acceptable, as well as safe and necessary were common. Perceptions of an absence of danger associated with faster driving speeds were evident, particularly with respect to driving alone. An important distinction between the speed-based groups related to the attention given to the driving task. Rare speeders expressed strong beliefs about the need to be mindful of safety (self and others) while excessive speeders referred to the driving task as automatic, an absent-minded endeavour, and to speeding as a necessity in order to remain alert and reduce boredom. For many drivers in this study, compliance with speed limits was expressed as discretionary rather than mandatory. Social factors, such as peer and parental influence were widely discussed in Study 1 and perceptions of widespread community acceptance of speeding were noted. In some instances, the perception that ‘everybody speeds’ appeared to act as one rationale for the need to raise speed limits. Self-presentation, or wanting to project a positive image of self was noted, particularly with respect to concealing speeding infringements from others to protect one’s image as a trustworthy and safe driver. The influence of legal factors was also evident. Legal sanctions do not appear to influence all drivers to the same extent. For instance, fear of apprehension appeared to play a role in reducing speeding for many, although previous experiences of detection and legal sanctions seemed to have had limited influence on reducing speeding among some drivers. Disregard for sanctions (e.g., driving while suspended), fraudulent demerit point use, and other strategies to avoid detection and punishment were widely and openly discussed. In Study 2, 833 drivers were recruited from roadside service stations in metropolitan and regional locations in Queensland. A quantitative research strategy assessed the relative contribution of personal, social, and legal factors to recent and future self-reported speeding (i.e., frequency of speeding and intentions to speed in the future). Multivariate analyses examining a range of factors drawn from SLT revealed that factors including self-identity (i.e., identifying as someone who speeds), favourable definitions (attitudes) towards speeding, personal experiences of avoiding detection and punishment for speeding, and perceptions of family and friends as accepting of speeding were all significantly associated with greater self-reported speeding. Study 3 was an exploratory, qualitative investigation of psychosocial factors associated with speeding among 35 Chinese drivers who were recruited from the membership of a motoring organisation and a university in Beijing. Six focus groups were conducted to explore similar issues to those examined in Study 1. The findings of Study 3 revealed many similarities with respect to the themes that arose in Australia. For example, there were similarities regarding personal justifications for speeding, such as the perception that posted limits are unreasonably low, the belief that individual drivers are able to determine safe travel speeds according to personal comfort with driving fast, and the belief that drivers possess adequate skills to control a vehicle at high speed. Strategies to avoid detection and punishment were also noted, though they appeared more widespread in China and also appeared, in some cases, to involve the use of a third party, a topic that was not reported by Australian drivers. Additionally, higher perceived enforcement tolerance thresholds were discussed by Chinese participants. Overall, the findings indicated perceptions of a high degree of community acceptance of speeding and a perceived lack of risk associated with speeds that were well above posted speed limits. Study 4 extended the exploratory research phase in China with a quantitative investigation involving 299 car drivers recruited from car washes in Beijing. Results revealed a relatively inexperienced sample with less than 5 years driving experience, on average. One third of participants perceived that the certainty of penalties when apprehended was low and a similar proportion of Chinese participants reported having previously avoided legal penalties when apprehended for speeding. Approximately half of the sample reported that legal penalties for speeding were ‘minimally to not at all’ severe. Multivariate analyses revealed that past experiences of avoiding detection and punishment for speeding, as well as favourable attitudes towards speeding, and perceptions of strong community acceptance of speeding were most strongly associated with greater self-reported speeding in the Chinese sample. Overall, the results of this research make several important theoretical contributions to the road safety literature. Akers’ social learning theory was found to be robust across cultural contexts with respect to speeding; similar amounts of variance were explained in self-reported speeding in the quantitative studies conducted in Australia and China. Historically, SLT was devised as a theory of deviance and posits that deviance and conformity are learned in the same way, with the balance of influence stemming from the ways in which behaviour is rewarded and punished (Akers, 1998). This perspective suggests that those who speed and those who do not are influenced by the same mechanisms. The inclusion of drivers from both ends of the ‘speeding spectrum’ in Study 1 provided an opportunity to examine the wider utility of SLT across the full range of the behaviour. One may question the use of a theory of deviance to investigate speeding, a behaviour that could, arguably, be described as socially acceptable and prevalent. However, SLT seemed particularly relevant to investigating speeding because of its inclusion of association, imitation, and reinforcement variables which reflect the breadth of factors already found to be potentially influential on driving speeds. In addition, driving is a learned behaviour requiring observation, guidance, and practice. Thus, the reinforcement and imitation concepts are particularly relevant to this behaviour. Finally, current speed management practices are largely enforcement-based and rely on the principles of behavioural reinforcement captured within the reinforcement component of SLT. Thus, the application of SLT to a behaviour such as speeding offers promise in advancing our understanding of the factors that influence speeding, as well as extending our knowledge of the application of SLT. Moreover, SLT could act as a valuable theoretical framework with which to examine other illegal driving behaviours that may not necessarily be seen as deviant by the community (e.g., mobile phone use while driving). This research also made unique contributions to advancing our understanding of the key components and the overall structure of Akers’ social learning theory. The broader SLT literature is lacking in terms of a thorough structural understanding of the component parts of the theory. For instance, debate exists regarding the relevance of, and necessity for including broader social influences in the model as captured by differential association. In the current research, two alternative SLT models were specified and tested in order to better understand the nature and extent of the influence of differential association on behaviour. Importantly, the results indicated that differential association was able to make a unique contribution to explaining self-reported speeding, thereby negating the call to exclude it from the model. The results also demonstrated that imitation was a discrete theoretical concept that should also be retained in the model. The results suggest a need to further explore and specify mechanisms of social influence in the SLT model. In addition, a novel approach was used to operationalise SLT variables by including concepts drawn from contemporary social psychological and deterrence-based research to enhance and extend the way that SLT variables have traditionally been examined. Differential reinforcement was conceptualised according to behavioural reinforcement principles (i.e., positive and negative reinforcement and punishment) and incorporated concepts of affective beliefs, anticipated regret, and deterrence-related concepts. Although implicit in descriptions of SLT, little research has, to date, made use of the broad range of reinforcement principles to understand the factors that encourage or inhibit behaviour. This approach has particular significance to road user behaviours in general because of the deterrence-based nature of many road safety countermeasures. The concept of self-identity was also included in the model and was found to be consistent with the definitions component of SLT. A final theoretical contribution was the specification and testing of a full measurement model prior to model testing using structural equation modelling. This process is recommended in order to reduce measurement error by providing an examination of the psychometric properties of the data prior to full model testing. Despite calls for such work for a number of decades, the current work appears to be the only example of a full measurement model of SLT. There were also a number of important practical implications that emerged from this program of research. Firstly, perceptions regarding speed enforcement tolerance thresholds were highlighted as a salient influence on driving speeds in both countries. The issue of enforcement tolerance levels generated considerable discussion among drivers in both countries, with Australian drivers reporting lower perceived tolerance levels than Chinese drivers. It was clear that many drivers used the concept of an enforcement tolerance in determining their driving speed, primarily with the desire to drive faster than the posted speed limit, yet remaining within a speed range that would preclude apprehension by police. The quantitative results from Studies 2 and 4 added support to these qualitative findings. Together, the findings supported previous research and suggested that a travel speed may not be seen as illegal until that speed reaches a level over the prescribed enforcement tolerance threshold. In other words, the enforcement tolerance appears to act as a ‘de facto’ speed limit, replacing the posted limit in the minds of some drivers. The findings from the two studies conducted in China (Studies 2 and 4) further highlighted the link between perceived enforcement tolerances and a ‘de facto’ speed limit. Drivers openly discussed driving at speeds that were well above posted speed limits and some participants noted their preference for driving at speeds close to ‘50% above’ the posted limit. This preference appeared to be shaped by the perception that the same penalty would be imposed if apprehended, irrespective of what speed they travelling (at least up to 50% above the limit). Further research is required to determine whether the perceptions of Chinese drivers are mainly influenced by the Law of the People’s Republic of China or by operational practices. Together, the findings from both studies in China indicate that there may be scope to refine enforcement tolerance levels, as has happened in other jurisdictions internationally over time, in order to reduce speeding. Any attempts to do so would likely be assisted by the provision of information about the legitimacy and purpose of speed limits as well as risk factors associated with speeding because these issues were raised by Chinese participants in the qualitative research phase. Another important practical implication of this research for speed management in China is the way in which penalties are determined. Chinese drivers described perceptions of unfairness and a lack of transparency in the enforcement system because they were unsure of the penalty that they would receive if apprehended. Steps to enhance the perceived certainty and consistency of the system to promote a more equitable approach to detection and punishment would appear to be welcomed by the general driving public and would be more consistent with the intended theoretical (deterrence) basis that underpins the current speed enforcement approach. The use of mandatory, fixed penalties may assist in this regard. In many countries, speeding attracts penalties that are dependent on the severity of the offence. In China, there may be safety benefits gained from the introduction of a similar graduated scale of speeding penalties and fixed penalties might also help to address the issue of uncertainty about penalties and related perceptions of unfairness. Such advancements would be in keeping with the principles of best practice for speed management as identified by the World Health Organisation. Another practical implication relating to legal penalties, and applicable to both cultural contexts, relates to the issues of detection and punishment avoidance. These two concepts appeared to strongly influence speeding in the current samples. In Australia, detection avoidance strategies reported by participants generally involved activities that are not illegal (e.g., site learning and remaining watchful for police vehicles). The results from China were similar, although a greater range of strategies were reported. The most common strategy reported in both countries for avoiding detection when speeding was site learning, or familiarisation with speed camera locations. However, a range of illegal practices were also described by Chinese drivers (e.g., tampering with or removing vehicle registration plates so as to render the vehicle unidentifiable on camera and use of in-vehicle radar detectors). With regard to avoiding punishment when apprehended, a range of strategies were reported by drivers from both countries, although a greater range of strategies were reported by Chinese drivers. As the results of the current research indicated that detection avoidance was strongly associated with greater self-reported speeding in both samples, efforts to reduce avoidance opportunities are strongly recommended. The practice of randomly scheduling speed camera locations, as is current practice in Queensland, offers one way to minimise site learning. The findings of this research indicated that this practice should continue. However, they also indicated that additional strategies are needed to reduce opportunities to evade detection. The use of point-to-point speed detection (also known as sectio

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The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

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The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.

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This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov’s stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.

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Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

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This paper reports on three primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

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Direct instruction, an approach that is becoming familiar to Queensland schools that have high Aboriginal and Torres Strait Islander populations, has been gaining substantial political and popular support in the United States of America [USA], England and Australia. Recent examples include the No Child Left Behind policy in the USA, the British National Numeracy Strategy and in Australia, Effective Third Wave Intervention Strategies. Direct instruction, stems directly from the model created in the 1960s under a Project Follow Through grant. It has been defined as a comprehensive system of education involving all aspects of instruction. Now in its third decade of influencing curriculum, instruction and research, direct instruction is also into its third decade of controversy because of its focus on explicit and highly directed instruction for learning. Characteristics of direct instruction are critiqued and discussed to identify implications for teaching and learning for Indigenous students.

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In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

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This important work describes recent theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Chapters survey research on pattern classification with binary-output networks, including a discussion of the relevance of the Vapnik Chervonenkis dimension, and of estimates of the dimension for several neural network models. In addition, Anthony and Bartlett develop a model of classification by real-output networks, and demonstrate the usefulness of classification with a "large margin." The authors explain the role of scale-sensitive versions of the Vapnik Chervonenkis dimension in large margin classification, and in real prediction. Key chapters also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient, constructive learning algorithms. The book is self-contained and accessible to researchers and graduate students in computer science, engineering, and mathematics

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The problem of decision making in an uncertain environment arises in many diverse contexts: deciding whether to keep a hard drive spinning in a net-book; choosing which advertisement to post to a Web site visitor; choosing how many newspapers to order so as to maximize profits; or choosing a route to recommend to a driver given limited and possibly out-of-date information about traffic conditions. All are sequential decision problems, since earlier decisions affect subsequent performance; all require adaptive approaches, since they involve significant uncertainty. The key issue in effectively solving problems like these is known as the exploration/exploitation trade-off: If I am at a cross-roads, when should I go in the most advantageous direction among those that I have already explored, and when should I strike out in a new direction, in the hopes I will discover something better?

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This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.