2,357,138 research outputs found

    On structures in hypergraphs of models of a theory

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    We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types of models of a theory, are given

    Signalizers in groups of Lie type

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    We classify all CG(t)-signalizers, where G is a finite group of Lie type and t is an automorphism of G of prime order s > 3. Our results extend existing work by Korchagina ([Ko], [Ko2])

    Mathematics

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    This chapter discusses mathematics. It is part of a collection which examines educational practice and professional thinking from pre-school and primary, through secondary, further and higher education; and locates Scottish education within its social, cultural and political context

    Mathematics Specialists Task Force Report

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    Categories without structures

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    The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.Comment: 28 page

    Developing The Attitude And Creativity In Mathematics Education

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    The structures in a traditionally-organized classroom of mathematics teaching can usually be linked readily with the routine classroom activities of teacher-exposition and teacher-supervised desk work, teacher’s initiation, teacher’s direction and strongly teacher’s expectations of the outcome of student learning. If the teacher wants to develop appropriate attitude and creativities in mathematics teaching learning it needs for him to develop innovation in mathematics teaching. The teacher may face challenge to develop various style of teaching i.e. various and flexible method of teaching, discussion method, problem-based method, various style of classroom interaction, contextual and or realistic mathematics approach. To develop mathematical attitude and creativity in mathematics teaching learning processes, the teacher may understand the nature and have the highly skill of implementing the aspects of the following: mathematics teaching materials, teacher’s preparation, student’s motivation and apperception, various interactions, small-group discussions, student’s works sheet development, students’ presentations, teacher’s facilitations, students’ conclusions, and the scheme of cognitive development.In the broader sense of developing attitude and creativity of mathematics learning, the teacher may needs to in-depth understanding of the nature of school mathematics, the nature of students learn mathematics and the nature of constructivism in learning mathematics. Key Word: mathematical attitude, creativity in mathematics, innovation of mathematics teaching,school mathematics

    Social Justice in and through Mathematics Education: For Improving the Quality of Mathematics Teaching and Internalising Students’ Character Building

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    Aside from being one of the systematically arranged disciplines, mathematics is also a social construction that views humans as active subjects in building knowledge through interaction with the surrounding environment. Therefore, in addition to being a medium to enhance students’ understanding of mathematical concepts, mathematics education should also apply the principles of social activity while linking mathematical concepts to social issues. This research is intended to reform mathematics learning so that it does not merely focus on students’ understanding of mathematical concepts, but also improve their quality through the application of ‘social justice in mathematics education’, while at the same time internalising issues related to social justice through the application of ‘social justice through mathematics education’ concepts. This study used action research as the research methodology considering its actionbased themes and characteristics, where the teacher performed and simultaneously reflected learning activities. The findings obtained from this study are: (i) several challenges related to the application of ‘social justice in and through mathematics education’ in mathematics learning area, among others, include the difficulty of changing the teacher’s mindset on how to teach mathematics to students equitably (socially) and how to foster teacher sensitivity in designing mathematics learning that integrated justice issues into mathematics learning; (ii) the implementation of the principle of ‘social justice in and through mathematics education’ in order to improve the quality of mathematics learning is felt to be ineffective because of the teacher’s ability to design and implement mathematics learning involving ‘social justice in mathematics learning’ and ‘social justice through mathematics learning’ remains adequate; and (iii) the application of ‘social justice in and through mathematics education’ has a significant effect on student involvement in mathematics learning. It is characterized by more active students in learning and more enthusiastic students in learning activities, because the material that is discussed very closely with students’ daily experiences.  Furthermore, the findings of this study are expected to contribute to the reform of mathematics education, especially those related to productive mathematics learning, the planting of effective mathematical concepts in students, equitable mathematics learning, and simultaneously internalizing social justice issues through the application of concepts, such as building students’ character. By using the elements in the planning and reflection of lessons, teachers are able to develop a comprehensive guide for improving the quality of their lessons and at the same time internalize students’ character building by using social justice issues

    “Not Like a Big Gap, Something We Could Handle”: Facilitating Shifts in Paradigm in the Supervision of Mathematics Graduates upon Entry into Mathematics Education

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    Mathematics is the discipline that a significant majority of most incoming researchers in mathematics education have prior qualifications and experience in. Upon entry into the field of mathematics education research, these newcomers–often students on a postgraduate programme in mathematics education–need a broadened understanding on how to read, converse, write and conduct research in the largely unfamiliar territory of mathematics education. The intervention into the practices of post-graduate teaching and supervision in the field of mathematics education that I describe here aims at fostering this broadened understanding and thus facilitating newcomers’ participation in the practices of the mathematics education research community. Here I outline the theoretical underpinnings of the intervention and exemplify one of its parts (an Activity Set designed to facilitate incoming students’ engagement with the mathematics education research literature). I supplement the discussion of the intervention with comments sampled from student interview and student written evaluation data as well as observations of the activities’ implementation. The main themes touched upon include: learning how to identify appropriate mathematics education literature; reading increasingly more complex writings in mathematics education; coping with the complexity of literate mathematics education discourse; working towards a contextualised understanding of literate mathematics education discourse. I conclude with indicating the directions that the intervention, and its evaluation, is currently taking and a brief discussion of broader implications, theoretical as well as concerning the supervision and teaching of post-graduate students in mathematics education

    A Mathematician\u27s Overview of the Virginia Elementary Mathematics Specialist Program

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    This article discusses the mathematics component of the Mathematics Specialist master\u27s degree program in the Virginia Mathematics Specialist Project (VMSP). It includes my personal views on the significant mathematical knowledge and skills that Mathematics Specialists need, the mathematics that is taught in the Mathematics Specialist courses, and my thoughts on what appear to be the substantial mathematical abilities and aptitudes that are required by successful Mathematics Specialists in their work. The interpretations I present are highly personal and are undoubtedly dependent on my personal history, a short description of which is given (see Appendix A)
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