125 resultados para foundations of mathematics


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Explaining the survival and failure of firms is an important issue for researchers and managers of firms in society. Ecological approaches to the study of firms have existed for over 100 years, and have been increasingly popular during the past 40 years, especially since the pioneering works of Hannan and Freeman on one hand, and Aldrich on the other. This paper, in keeping with recent developments elsewhere in mainstream ecology outlines and positions the theoretical and philosophical foundations of an alternative ecological approach, autecology, that has not yet been formulated for the study of firms. The autecological approach affords the individual firm more autonomy in creating its own future evolutionary trajectory. The idea of an ecological complex is developed to provide clear focus on what is central to the application of autecology to the study of firms. The paper also considers several emergent research opportunities that highlight the potential value of employing an autecological approach to the study of firms.

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This thesis investigated how a year-4 teacher used a pedagogical approach referred to as the Gradual Release of Responsibility (GRR) model of instruction for teaching Science Inquiry Skills in a primary classroom. Through scaffolding her students' learning using the GRR, the teacher guided her students towards developing an understanding about Scientific Inquiry leading to the foundations of scientific literacy. A learning environment was established in which students engaged in rich conversations, designed and conducted experiments using fair testing procedures, analysed and offered justifications for results, and negotiated knowledge claims in ways similar to some of those in the scientific community.

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This thesis evaluates the security of Supervisory Control and Data Acquisition (SCADA) systems, which are one of the key foundations of many critical infrastructures. Specifically, it examines one of the standardised SCADA protocols called the Distributed Network Protocol Version 3, which attempts to provide a security mechanism to ensure that messages transmitted between devices, are adequately secured from rogue applications. To achieve this, the thesis applies formal methods from theoretical computer science to formally analyse the correctness of the protocol.

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Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

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We analyzed the development of 4th-grade students’ understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students’ initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computersimulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students’ progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students’ final models indicated increasing levels of probabilistic understanding.