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Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.
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Donna KotsopoulosEmail: |
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彭大成 《衡阳师范学院学报》2009,30(1)
经过近一百多年来前人对船山思想的发掘与宣传,特别是新中国建立前后几代马克思主义学者对船山思想的发掘与研究,船山哲学思想的宏富内容已越来越为学术界所了解:船山哲学无论在唯物论、认识论、辩证法、历史观方面,都达到了当时中国甚至世界的最高水平.以船山思想为主要标志的湖湘文化,代表了中国传统文化中最先进的文化,为培育湖南几代风云人物、推动中国社会进步发挥了极其重要的作用. 相似文献
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Stefan Krumm Matthias Ziegler Markus Buehner 《Learning and individual differences》2008,18(2):248-257
The present paper contributes to individual difference research in the field of working memory (WM) and reasoning and their contribution to the prediction of real-life criteria. Therefore, a broad WM test battery, a well-established measure of reasoning, and school grades were applied. It is argued that abilities as assessed with the WM component coordination are relevant for good performances at school, especially for science courses. The verbal task of the WM component storage in the context of processing was assumed to be relevant for the prediction of performance in language courses. As expected, reasoning turned out to be the best predictor of school grades. However, it was also confirmed that variance shared by coordination and reasoning can explain school performance, especially as concerns science courses. The verbal storage in the context of processing task significantly accounted for variance in language courses above and beyond reasoning. Thus, the present study provided further insights into the differential validity of different WM components. 相似文献
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周毅 《阜阳师范学院学报(社会科学版)》2010,(6):94-97
逻辑推理和法律推理的关系十分密切,法律推理是逻辑推理的一般方法在法律领域中广泛、综合的运用,逻辑推理是法律推理重要的理性工具之一。法律推理中的逻辑推理形式必须是有效的,有效的逻辑推理可以消解裁判中的任意性,避免谬误,帮助获得正当的裁判结论。 相似文献
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朱鹏飞 《江西教育学院学报》2000,21(2):7-10
文章对审美判断过程中的心理机制作了详尽论述,进而认为审美判断过程虽然以直感的方式表现出来,但其本质上是一种求真、向善、审形式美的逻辑推理。另外,文章还对审美判断和审美判断过程两个概念进行了区分。 相似文献
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数学推理有两种截然不同的推理方式:原创性推理和模仿性推理.数学推理的认知成分和结构包括:阅读、分析、探索、计划、实施、验证等6个环节.原创性推理和模仿性推理的差异主要体现在阅读、分析、探索、计划这4个认知成分上,前者更注重深层理解、内在比较、再结构化、适时调整目标,后者更多采用记忆、类比、联结方式作推理动力.换句话说,原创性推理更强调思维的自主性、发散性.教师在教学中应注重学生的原创性自主思维. 相似文献
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The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on
the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by
one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing
displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and
draws relationships with the perspectives of embodied cognition and intersubjectivity. 相似文献
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Elif Ekin Akşit 《Gender and education》2011,23(3):299-311
Education can cease to be a showcase for political projects and start serving women’s lives only when the agency of women in their own education is acknowledged. In this paper I have addressed issues concerning harem education to emphasise that possible solutions to issues of girls’ education require an awareness concerning the history of girls’ education in different geographies. In this article, this agency is pursued in the homosocial production of knowledge in the harem, which is an exoticised space. Questioning the limitations and benefits of the concept of the harem is especially important in understanding processes such as the accommodation of public practices of education in women’s homes. Using Foucault’s concept of heterotopia, the harem is contextualised to shed light upon its liberating and dominating aspects, as a sphere where public and private practices of education converge. 相似文献
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David E. Engen 《Communication quarterly》2013,61(1):41-57
The present essay argues that the cultivation of a communicative imagination should be a primary objective in the undergraduate communication curriculum. The essay begins by exploring and defining what is meant by the term communicative imagination. It then examines the role complex and challenging narratives can play in helping our students cultivate their communicative imaginations and, in so doing, prepare themselves for effective and humane participation in their increasingly complex social worlds. 相似文献
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Patricia A. Alexander Emily M. Grossnickle Alexandra List Carla M. Firetto 《Journal of Experimental Education》2016,84(1):119-151
Relational reasoning is the foundational cognitive ability to discern meaningful patterns within an informational stream, but its reliable and valid measurement remains problematic. In this investigation, the measurement of relational reasoning unfolded in three stages. Stage 1 entailed the establishment of a research-based conceptualization of the construct and the development of a corresponding Test of Relational Reasoning (TORR). Stage 2 focused on the reliability and validity of data from the TORR. Analyses showed the data from the TORR to be reliable indicators of students' ability to reason relationally, and TORR performance predicted students' performance on SAT verbal and math problems. Stage 3 examined the underlying structure of the construct through Confirmatory Factor Analysis (CFA). Of the three CFA models tested, models with dedicated factors for analogical, anomalous, antinomous, and antithetical reasoning were deemed the best fit for the data. 相似文献
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陈基秀 《广西教育学院学报》2002,(6):143-144
本从三个方面阐析了中学语教学中如何对学生进行想象力训练。首先,让学生从感性到理性对想象力有比较科学的认识,其次,在阅读教学,作教学课外游戏中进行想象力训练。最后,在教师指导下让学生独立地进行想象力训练。 相似文献
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Victoria Chan 《Teaching in Higher Education》2013,18(4):505-518
In higher education teaching, enhancing learner autonomy has become a key concern for curriculum planners and classroom teachers. The significant body of research about learner autonomy in language learning over the last 20 years (e.g. Holec 1981, 1988; Riley 1985; Dickinson 1987, 1992; Wenden & Rubin 1987; Little, 1991; Dam, 1995; Benson & Voller, 1997) has indicated an on-going search for more understanding of how learner autonomy can be implemented in different contexts. This paper is based on a research study which was conducted in the Hong Kong Polytechnic University in Hong Kong. The study explores learners' attitudes and expectations of language learning, teacher and learner roles, their learning preferences and perceptions of learner autonomy. The paper reports the results and discusses their implication on the development of a learner-centred approach in higher education. 相似文献