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On structures in hypergraphs of models of a theory
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
Mathematics
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
Signalizers in groups of Lie type
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])
Categories without structures
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
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,
teacherâs initiation, teacherâs direction and strongly teacherâs 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, teacherâs preparation, studentâs motivation and apperception, various
interactions, small-group discussions, studentâs works sheet development, studentsâ presentations, teacherâs
facilitations, studentsâ 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 Studentsâ Character Building
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.ăTherefore, in addition to being a medium to enhance studentsâ understanding of mathematical concepts, mathematics education should also apply the principles of social activity while linking mathematical concepts to social issues.ăThis research is intended to reform mathematics learning so that it does not merely focus on studentsâ understanding of mathematical concepts, but also improve their quality through the application of âsocial justice in mathematics educationâ, while at the same time internalising issues related to social justice through the application of âsocial justice through mathematics educationâ concepts.ăThis study used action research as the research methodology considering its actionbased themes and characteristics, where the teacher performed and simultaneously reflected learning activities.ăThe findings obtained from this study are: (i) several challenges related to the application of âsocial justice in and through mathematics educationâ in mathematics learning area, among others, include the difficulty of changing the teacherâs 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 âsocial justice in and through mathematics educationâ in order to improve the quality of mathematics learning is felt to be ineffective because of the teacherâs ability to design and implement mathematics learning involving âsocial justice in mathematics learningâ and âsocial justice through mathematics learningâ remains adequate; and (iii) the application of âsocial justice in and through mathematics educationâ has a significant effect on student involvement in mathematics learning.ăIt is characterized by more active students in learning and more enthusiastic students in learning activities, because the material that is discussed very closely with studentsâ daily experiences.ă 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 studentsâ character.ăBy 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 studentsâ character building by using social justice issues
âNot Like a Big Gap, Something We Could Handleâ: Facilitating Shifts in Paradigm in the Supervision of Mathematics Graduates upon Entry into Mathematics Education
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 newcomersâoften students on a postgraduate programme in mathematics educationâneed 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 newcomersâ 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 studentsâ 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 activitiesâ 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
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Schoolsâ Strategies for Promoting Girlsâ Participation in Mathematics
Fewer girls than boys in England participate in post-compulsory mathematics. Previous studies have shown the significance to girls of their mathematics lessons and teachers, of cultural constructions of gender and mathematics, of career perceptions A multiple case-study project investigated institutions with unusually high participation by girls in mathematics. Focus groups and lesson observations were used to explore school pedagogy and culture. Common factors were: early preparation for demanding mathematics, a departmental ethos which encouraged student-teacher interactions in and out of lessons, teachers who explicitly and repeatedly confirmed that girls would succeed at mathematics A-level, appreciation of mathematics as opening doors to many careers
A Mathematician\u27s Overview of the Virginia Elementary Mathematics Specialist Program
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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