987 resultados para Mathematical thinking


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Recent accounts by cognitive scientists of factors affecting cognition imply the need to reconsider current dominant conceptual theories about science learning. These new accounts emphasize the role of context, embodied practices and narrative-based representation rather than learners’ cognitive constructs. In this paper we analyze data from a longitudinal study of primary school children’s learning to outline a framework based on these contemporary accounts, and to delineate key points of difference from conceptual change perspectives. The findings suggest this framework provides strong theoretical and practical insights into how children learn and the key role of representational negotiation in this learning. We argue that the nature and process of conceptual change can be re-interpreted in terms of the development of students’ representational resources.

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In this study we explored the attitudes and beliefs of nine heterosexual adults towards gay male and female couples parenting children. We conceptualised participants' perceptions as one primary lens through which gay parenting is viewed. Based on the narratives provided, this lens comprised hetero-normative, homophobic or heterosexist assumptions and coloured the way in which participants perceived aspects of the concept of gay couples parenting children. At times, participants attempted to adjust their primary lens and adopt different views that initially suggested ambivalence and sometimes contradictory positions. Despite the range of attitudes and assumptions about same-sex parenting, consensus over the potential negative developmental impact on children raised by same-sex parents remained evident. Evidence suggests that same-sex parenting is already a reality in Westernised nations and has little or no bearing on the sexual orientation of children. However, concern that children be brought up with every opportunity to 'become' heterosexual, whether they are the product of same-sex or opposite-sex parents, remains evident.

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Creative problem solving is essential to technology education. In our research project we explored the suggestion that creativity may need to include a time of ‘non-thinking’ during which innovative responses to problem tasks are generated. The period of non-conscious cognitive process (NCCP) time is considered to be when the brain makes connections between independent ideas and when inappropriate responses can be forgotten, allowing more relevant responses to be made available for problem solving. Our research provided an opportunity for several primary school teachers to focus on enhancing creativity in technology education and to explore the notion of the NCCP time for creative problem solving. In this chapter we review the current literature on enhancing creativity and comment on how the teachers fostered creativity as they implemented a design, make and appraise technological task to produce recycling devices in their classrooms. Classes and children were observed and teachers interviewed about their perception of children’s creativity and the NCCP time. In this study, a time frame of only several days appears to be ideal for non-conscious cognitive processing to occur and more time may hinder creativity. These findings have implications for teachers of technology who assign the same day and time each week for technology learning.
During the non-task time, which included the NCCP time, children were able to discuss their ideas with family members. As children learn in social and cultural contexts, these discussions can be fruitful. The teachers indicated that peer discussions also played an important role after the generation of designs.

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When children are involved in design and technology activities, they are able to create solutions to problems, often in new and innovative ways. There have been few studies which have investigated how children work when undertaking technological activities and even fewer which have focused on children's thinking or knowledge while they have been involved in the production of a technological artifact. This paper reports on a research project involving 3 school, 4 classes and 80 children. The project focused on children's language, thinking and creativity while they designed and constructed a recycling device using recycled materials. Using children's written responses to key questions, we can highlight some of their thinking, knowledge and problem-solving strategies. It was clear from the children's responses that aspects of investigation, design, producation and evaluation were evident across all three sites. Findings on children's creativity and language were presented at previous Technology Education Research Conferences (TERC). 

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This case study looks at how a teacher used interactive exercises and exploratory investigations to reinforce concepts that have been learnt in a Year 8 Mathematics class. It highlights the practical problems faced by the teacher in terms of technical issues such as slow download times and logging on problems as well as class management issues. The findings are discussed in the light of the teacher’s mediation with the affordances of the Internet.

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The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 2005). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics.

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The issue of Middle Eastern democracy has long inspired lively academic debate and research from across the ideological and political spectrum. Despite their differences, much of this work measures the successes and failures of Middle Eastern democracy against the Western model, with its antecedents in the political machinations found in Athens during the 5th century B.C. However, there is growing evidence to suggest that the history of democracy began on the other side of the Occidental/Oriental line and can be traced as far back as the early Mesopotamian myths of Enuma Elish, through to the grand empires of the Babylonians, Assyrians, Egyptians and Phoenicians. In the interest of fostering a liberal, democratic and egalitarian Middle East, this paper concludes by suggesting that one strategy for re-thinking the Middle East’s democratisation is to engage the powerful discourses of the Middle East’s ancient, and democratic, past.

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Cognitive distortions have been afforded a key role in the offending behaviour of child sexual offenders. While the mechanisms underlying cognitive distortions are not fully understood, they are generally thought to reflect entrenched beliefs that distinguish child sexual offenders from other individuals. We investigated this hypothesis using a robust experimental technique called the lexical decision task. Child sexual offenders, offender controls, and non-offender controls completed a lexical decision task in which they responded to words that completed sentences in either an offence-supportive or nonoffence-supportive manner. Contrary to predictions, child sexual offenders did not respond faster to words that were consistent with offence-supportive beliefs, relative to controls. However, they did show accelerated recognition for word stems supporting external locus of control beliefs. These results highlight the need to use cognitive experimental methods to study child sexual offenders' beliefs, and the importance of investigating potential alternative drivers of cognitive distortions.

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Games are enjoyable, and research shows that learning to play games can boost learning. Many games use mathematical processes and strategies; this book outlines the context for using mathematics games in classrooms to promote active mathematics learning, curiosity and engaged thinking. There are suggestions for suitable commercially available games and explanations of the rules for card games, dominoes, alphabet games, dice games, drawing games and others. Ways of making a new game, or modifying an existing game are explored, and there are scores of ideas for using games to support mathematical concepts while having fun.