Browsing by Subject "mathematics"

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    Mathematics for Economists
    (2014-08-21) Eyal, Katherine
    This resources consists of comprehensive notes, tutorials and solutions for Honours level economics. Material covered includes linear algebra, comparative statics, optimisation, integration and differential equations and systems of difference and differential equations, eigenvalues, complex numbers. These notes, tutorials and solutions cover the basic tools and applications in order to prepare the student for the study of Macroeconomics, Microeconomics and Econometrics at an intermediate and advanced level.
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    Quantitative methods for economics
    (2011) Eyal, Katherine
    Mathematical economics involves the application of mathematics to the theoretical aspects of economic analysis, while econometrics deals with the study of empirical observations using statistical methods of estimation and hypothesis testing. These two are complementary - theories must be tested against empirical data for validity and statistical work needs economic theory as a guide in order to determine the appropriate direction of research. This resource contains tutorials and solutions for mathematics and econometrics and can be used by educators or students in introductory economics courses.
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    Teachers' beliefs: understanding the thinking of secondary mathematics teachers as a starting point for improved professional development
    (2015) Muller, Sara Louise; Paxton, Moragh
    This thesis explores the beliefs of mathematics teachers working in a rural school in South Africa. This is premised on the argument that understanding the beliefs of teachers is a necessary, even if insufficient, prerequisite to designing effective teacher development programmes. I postulate that take-up rates of new content and teaching methods are low due to unmanaged cognitive conflict with pre-existing beliefs about the nature of teaching. A broad review of the literature on beliefs as a concept is conducted to establish theoretical grounding for the study of beliefs as an abstract object of analysis (Green, 1971; Nespor, 1987; Pajares, 1992). I particularly refer to Ernest's (1989) models of mathematics epistemology, and Adler's (2001) dilemmas of teaching mathematics in multilingual classrooms. Multiple studies of mathematics teachers' beliefs are drawn upon to relate beliefs to classroom practice. Qualitative data on two mathematics teachers working in a rural school in the Eastern Cape was gathered over the period of a month, using ethnographic methods as outlined by Thompson (1992) for gathering evidence of beliefs. Primary data, which consisted of pre-interviews, multiple lesson observations and stimulated-recall post-interviews, was analysed for evidence of teacher beliefs. Secondary data, in the form of a researcher journal and socio-economic information about the school, was also gathered to provide rich context data in which to situate the teachers' work. Particular attention was paid to teacher beliefs about teaching and learning, mathematics and language. Further evidence for beliefs was then obtained through close examination of an observation extract using classroom discourse analysis. The main finding of this thesis was that not only does a school's context provide logistical constraints to curriculum implementation and pedagogical change, but that the worldviews of teachers affect their interpretation of the curriculum (Chapman, 2002). Significantly, a relationship between the mathematics epistemology a teacher holds and their ability to admit language as a critical pedagogical factor is suggested. I conclude that detailed understanding of what teachers believe may provide a productive approach for teacher development programmes that aim to effect change.
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    Open Access
    Tensors and Relativity Course
    (2014-08-22) Dunsby, Peter K S
    This website contains lecture notes on Special and General Relativity, with a mathematical approach. The first part is exclusively dedicated to Special Relativity and its mathematical treatment using Tensors. The last four subjects go through General Relativity, explaining its principles, the effects of gravity and how to apply Tensors to the study of curvature of space. The topics in this resource include: Mathematical Tools and Linear Algebra and Tensors in General physics; General Relativity; Mathematics in relativity; Tensors in relativity; and Special relativity. The image used is Special Relativity by Wonderlane and is licensed under a Creative Commons Attribution license.
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    Why OER ?
    (2013) Mitchell, Veronica; Klopper, Juan
    This video resource is a valuable contribution to promoting Open Educational Resources (OER) for educators to understand how teaching material can be produced and shared. Dr Juan Klopper's willingness to share his expertise and passion with the wider world is an example of good practice where knowledge is for the public good. This video can be an inspiration to other educators to open up their classrooms and to be a producer of OER. In addition it encourages students to realize the flexibility gained from a flipped classroom approach to learning. Dr Klopper's popular website with YouTube teaching tutorials in Surgery, Mathematics and Physics and video edits has been viewed by over 160,000 people worldwide (August 2013).