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Relationships Between Prior Experiences, Current Teaching Contexts, And Novice Teachers' Use Of Concrete Representation For Mathematics Instruction, Elizabeth Lee Johnson
Relationships Between Prior Experiences, Current Teaching Contexts, And Novice Teachers' Use Of Concrete Representation For Mathematics Instruction, Elizabeth Lee Johnson
Theses and Dissertations
This case study documents the perceived influences on three novice elementary teachers’ use of concrete representations for teaching mathematics. In order to develop mathematical proficiency, students need access to a variety of representations (i.e. pictures, words, symbols, concrete materials, and real world contexts) to make sense of mathematical ideas. Three sources of data were collected: video-recorded lessons, interviews, and a focus group. Analyses indicated that although concrete representations were accessible to all three teachers, they were least used among the available representations. Verbal expression was most prominent, followed closely by abstract written symbols. Technology, which was not one of the …
On The Group Of Transvections Of Ade-Diagrams, Marvin Jones
On The Group Of Transvections Of Ade-Diagrams, Marvin Jones
Theses and Dissertations
In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kn (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : Gf,S ! SL(Z)n where g(X) = P−1XP where P is the change of basis matrix for S to H.