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Exemplifying definitions: a case of a square 总被引：1，自引：1，他引：0
In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their
understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective
secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility
and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition
should entail and, moreover, contrast their pedagogical preferences with mathematical considerations. 相似文献
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Roza Leikin 《Journal of Mathematics Teacher Education》2003,6(4):297-329
The aim of the study presented in this paper was to explore factors that influence teachers' problem-solving preferences in the process of (a) solving a problem, (b) explaining it to a peer, (c) liking it, and (d) teaching it. About 170 mathematics teachers took part in the different stages of the study. A special mathematical activity was designed to examine factors that influence teachers' problem-solving preferences and to develop teachers' preferences concerning whether to use symmetry when solving the problems. It was implemented and explored in an in-service program for professional development of high-school mathematics teachers. As a result, three interrelated factors that influence teachers' problem-solving preferences were identified: (i) Two patterns in teachers' problem-solving behavior, i.e., teachers' tendency to apply a stereotypical solution to a problem and teachers' tendency to act according to problem-solving beliefs, (ii) the way in which teachers characterize a problem-solving strategy, (iii) teachers' familiarity with a particular problem-solving strategy and a mathematical topic to which the problem belongs. Findings were related to teachers' developing thinking in solving problems and using them with their students. The activity examined in this paper may serve as a model for professional development of mathematic teachers and be useful for different professional development programs. 相似文献
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Orit Zaslavsky Olive Chapman Roza Leikin 《Journal of Mathematics Teacher Education》2000,3(3):201-203
Editorial Board
Guest Editorial 相似文献4.
This article describes the views of the Tatar educators Rizaetdin Fakhretdin and Gabdulla Bubi on the fundamental problems of family education. Until recently, the works of these educators were not widely known in the pedagogical community, but it is now becoming more popular. These writings have great potential to shape modern people, socialization, and family values. 相似文献
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AbstractThe relationships between politics and teacher education have become increasingly close over recent decades in many contexts around the world, often causing significant challenges as well as some opportunities. In this article, we draw on a project on the reform of teacher education in Russia and through a comparison with the development of teacher education policy in England – especially over the last forty years – we explore how the evolution of a new politics in both contexts has affected policy on teaching and teacher education. Looking, for example, at ‘post-communism’ and ‘neoliberalism’ and their respective impacts on political systems, a number of contradictions and paradoxes are identified, when comparisons are drawn between the two systems. 相似文献
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Ilana Waisman Mark Leikin Shelley Shaul Roza Leikin 《International Journal of Science and Mathematics Education》2014,12(3):669-696
In this study, we examine the impact and the interplay of general giftedness (G) and excellence in mathematics (EM) on high school students’ mathematical performance associated with translations from graphical to symbolic representations of functions, as reflected in cortical electrical activity (by means of ERP—event-related potentials—methodology). We report on findings of comparative data analysis based on 75 right-handed male high school students (16?–?18 years old) divided into four research groups designed by a combination of EM and G factors. Effects of EM factor appeared at the behavioral and electrophysiological levels. The fifth group of participants included 9 students with extraordinary mathematical abilities (S-MG: super mathematically gifted). We found that in EM participants, the G factor has no impact on the performance associated with translation between representations of the functions. The highest overall electrical activity is found in excelling in mathematics students who are not identified as generally gifted (NG-EM students). This increased electrical activity can be an indicator of increased cognitive load in this group of students. We identified accumulative and unique characteristics of S-MG at the behavioral and electrophysiological levels. We explain the findings by the nature of the tasks used in the study. We argue that a combination of the ERP techniques along with more traditional educational research methods enables obtaining reliable measures on the mental processing involved in learning mathematics and mathematical problem solving. 相似文献
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The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers’ knowledge. It is aimed at exploring the development of teachers’ mathematical and pedagogical conceptions associated with systematic employment of multiple-solution tasks (MSTs) in a “problem-solving” course for prospective mathematics teachers (PMTs). Our attention to teachers’ mathematical conceptions focused on the development of PMTs’ problem-solving competences. Our attention to teachers’ meta-mathematical and pedagogical conceptions focused on changes in teachers’ views concerning the level of interest and level of difficulty of the mathematical tasks. We differentiated between the systematic and craft modes of professional development integrated in the course. Systematic mode involved problem-solving sessions and reflective discussions on collective solution spaces. Craft mode involved interviewing school students. The study demonstrates the effectiveness of MSTs for PMTs’ professional development. 相似文献
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We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses they teach can serve teachers in their work with school students, and on the changes they would implement if their courses were designed specifically for prospective teachers. We constructed profiles of the four mathematicians based on their responses to a clinical interview. We employed the construct of mathematics teacher-educators’ triad in the reflective analysis of our findings and extended the construct based on the results of this study. In conclusion, we commented on potential ways to draw stronger connections between university mathematics and the mathematics taught in schools. 相似文献