82 resultados para 280402 Mathematical Logic and Formal Languages


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The progress of a nationally representative sample of 3632 children was followed from early childhood through to primary school, using data from the Longitudinal Study of Australian Children (LSAC). The aim was to examine the predictive effects of different aspects of communicative ability, and of early vs. sustained identification of speech and language impairment, on children's achievement and adjustment at school. Four indicators identified speech and language impairment: parent-rated expressive language concern; parent-rated receptive language concern; use of speech-language pathology services; below average scores on the adapted Peabody Picture Vocabulary Test-III. School outcomes were assessed by teachers' ratings of language/literacy ability, numeracy/mathematical thinking and approaches to learning. Comparison of group differences, using ANOVA, provided clear evidence that children who were identified as having speech and language impairment in their early childhood years did not perform as well at school, two years later, as their non-impaired peers on all three outcomes: Language and Literacy, Mathematical Thinking, and Approaches to Learning. The effects of early speech and language status on literacy, numeracy, and approaches to learning outcomes were similar in magnitude to the effect of family socio-economic factors, after controlling for child characteristics. Additionally, early identification of speech and language impairment (at age 4-5) was found to be a better predictor of school outcomes than sustained identification (at aged 4-5 and 6-7 years). Parent-reports of speech and language impairment in early childhood are useful in foreshadowing later difficulties with school and providing early intervention and targeted support from speech-language pathologists and specialist teachers.

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Background: The transition to school is a sensitive period for children in relation to school success. In the early school years, children need to develop positive attitudes to school and have experiences that promote academic, behavioural and social competence. When children begin school there are higher expectations of responsibility and independence and in the year one class, there are more explicit academic goals for literacy and numeracy and more formal instruction. Most importantly, children’s early attitudes to learning and learning styles have an impact on later educational outcomes. Method: Data were drawn from The Longitudinal Study of Australian Children (LSAC). LSAC is a cross-sequential cohort study funded by the Australian Government. In these analyses, Wave 2 (2006) data for 2499 children in the Kindergarten Cohort were used. Children, at Wave 2, were in the first year of formal school. They had a mean age of 6.9 years (SD= 0.26). Measures included a 6-item measure of Approaches to Learning (task persistence, independence) and the Academic Rating Scales for language and literacy and mathematical thinking. Teachers rated their relationships with children on the short form of the STRS. Results: Girls were rated by their teachers as doing better than boys on Language and literacy, Approaches to learning; and they had a better relationship with their teacher. Children from an Aboriginal or Torres Strait Island (ATSI) background were rated as doing less well on Language and Literacy and Mathematical thinking and on their Approaches to learning. Children from high Socio Economic Position families are doing better on teacher rated Language and Literacy, Mathematical thinking, Approaches to learning and they had a better relationship with their teacher. Conclusions: Findings highlight the importance of key demographic variables in understanding children’s early school success.

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This paper reports on a replication of earlier studies into a possible hierarchy of programming skills. In this study, the students from whom data was collected were at a university that had not provided data for earlier studies. Also, the students were taught the programming language Python, which had not been used in earlier studies. Thus this study serves as a test of whether the findings in the earlier studies were specific to certain institutions, student cohorts, and programming languages. Also, we used a non–parametric approach to the analysis, rather than the linear approach of earlier studies. Our results are consistent with the earlier studies. We found that students who cannot trace code usually cannot explain code, and also that students who tend to perform reasonably well at code writing tasks have also usually acquired the ability to both trace code and explain code.

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In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

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Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

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This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.

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Background: The transition to school is a sensitive period for children in relation to school success. In the early school years, children need to develop positive attitudes to school and have experiences that promote academic, behavioural and social competence. When children begin school there are higher expectations of responsibility and independence and in the year one class, there are more explicit academic goals for literacy and numeracy and more formal instruction. Most importantly, children’s early attitudes to learning and learning styles have an impact on later educational outcomes. Method: Data were drawn from The Longitudinal Study of Australian Children (LSAC). LSAC is a cross-sequential cohort study funded by the Australian Government. In these analyses, Wave 2 (2006) data for 2499 children in the Kindergarten Cohort were used. Children, at Wave 2, were in the first year of formal school. They had a mean age of 6.9 years (SD= 0.26). Measures included a 6-item measure of Approaches to Learning (task persistence, independence) and the Academic Rating Scales for language and literacy and mathematical thinking. Teachers rated their relationships with children on the short form of the STRS. Results: Girls were rated by their teachers as doing better than boys on Language and literacy, Approaches to learning; and they had a better relationship with their teacher. Children from an Aboriginal or Torres Strait Island (ATSI) background were rated as doing less well on Language and Literacy and Mathematical thinking and on their Approaches to learning. Children from high Socio Economic Position families are doing better on teacher rated Language and Literacy, Mathematical thinking, Approaches to learning and they had a better relationship with their teacher. Conclusions: Findings highlight the importance of key demographic variables in understanding children’s early school success.

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This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

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In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

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This paper presents evidence of an apparent connection between ball lightning and a green fireball. On the evening of the 16th May 2006 at least three fireballs were seen by many people in the skies of Queensland, Australia. One of the fireballs was seen passing over the Great Divide about 120 km west of Brisbane, and soon after, a luminous green ball about 30 cm in diameter was seen rolling down the slope of the Great Divide. A detailed description given by a witness indicates that the phenomenon was probably a highly luminous form of ball lightning. An hypothesis presented in this paper is that the passage of the Queensland fireball meteor created an electrically conductive path between the ionosphere and ground, providing energy for the ball lightning phenomenon. A strong similarity is noted between the Queensland fireball and the Pasamonte fireball seen in New Mexico in 1933. Both meteors exhibit a twist in the tail that could be explained by hydrodynamic forces. The possibility that multiple sightings of fireballs across South East Queensland were produced owing to fragments from comet 73P Schwassmann-Wachmann 3 is discussed.

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In computational linguistics, information retrieval and applied cognition, words and concepts are often represented as vectors in high dimensional spaces computed from a corpus of text. These high dimensional spaces are often referred to as Semantic Spaces. We describe a novel and efficient approach to computing these semantic spaces via the use of complex valued vector representations. We report on the practical implementation of the proposed method and some associated experiments. We also briefly discuss how the proposed system relates to previous theoretical work in Information Retrieval and Quantum Mechanics and how the notions of probability, logic and geometry are integrated within a single Hilbert space representation. In this sense the proposed system has more general application and gives rise to a variety of opportunities for future research.

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While hybrid governance arrangements have been a major element of organisational architecture for some time, the contemporary operating environment has brought to the fore new conditions and expectations for the governance of entities that span conventional public sector departments, private firms and community organisations or groups. These conditions have resulted in a broader array of mixed governance configurations including Public Private Partnerships, alliances, and formal and informal collaborations. In some such arrangements, market based or ‘complete’ contractual relationships have been introduced to replace or supplement existing traditional ‘hierarchical’ and/or newer relational ‘network-oriented’ institutional associations. While there has been a greater reliance on collaborative or relational contracts as an underpinning institutional model, other modes of hierarchy and market may remain in operation. The success of these emergent hybrid forms has been mixed. There are examples of hybrids that have been well adopted, achieving the desired goals of efficiency, effectiveness and financial accountability; while others have experienced implementation problems which have undermined their results. This paper postulates that the cultural and institutional context within which hybrids operate may contribute to the implementation processes employed and the level of success attained. The paper explores hybrid arrangements through three cases of the use of inter-organisational arrangements in three different national contexts. Distilling the various elements of hybrids and the impact of institutional context will provide important insights for those charged with the responsibility for the formation and key infrastructure and public value development.

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The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

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Technology-mediated collaboration process has been extensively studied for over a decade. Most applications with collaboration concepts reported in the literature focus on enhancing efficiency and effectiveness of the decision-making processes in objective and well-structured workflows. However, relatively few previous studies have investigated the applications of collaboration schemes to problems with subjective and unstructured nature. In this paper, we explore a new intelligent collaboration scheme for fashion design which, by nature, relies heavily on human judgment and creativity. Techniques such as multicriteria decision making, fuzzy logic, and artificial neural network (ANN) models are employed. Industrial data sets are used for the analysis. Our experimental results suggest that the proposed scheme exhibits significant improvement over the traditional method in terms of the time–cost effectiveness, and a company interview with design professionals has confirmed its effectiveness and significance.

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With the advent of live cell imaging microscopy, new types of mathematical analyses and measurements are possible. Many of the real-time movies of cellular processes are visually very compelling, but elementary analysis of changes over time of quantities such as surface area and volume often show that there is more to the data than meets the eye. This unit outlines a geometric modeling methodology and applies it to tubulation of vesicles during endocytosis. Using these principles, it has been possible to build better qualitative and quantitative understandings of the systems observed, as well as to make predictions about quantities such as ligand or solute concentration, vesicle pH, and membrane trafficked. The purpose is to outline a methodology for analyzing real-time movies that has led to a greater appreciation of the changes that are occurring during the time frame of the real-time video microscopy and how additional quantitative measurements allow for further hypotheses to be generated and tested.