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Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Shannon O.S. Driskell
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Shannon O.S. Driskell
This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.
Multilevel And Multidimensional Hadamard Matrices, Sarah Adams, Matthew Crawford, Caitlin Greeley, Bryce Lee, Mathav Murugan
Multilevel And Multidimensional Hadamard Matrices, Sarah Adams, Matthew Crawford, Caitlin Greeley, Bryce Lee, Mathav Murugan
Sarah Spence Adams
Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n. We also define multidimensional MHMs and prove an analogous existence result.
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G so that adjacent vertices get labels at least distance two apart and vertices at distance two get distinct labels. A hole is an unused integer within the range of integers used by the labeling. The lambda number of a graphG, denoted λ(G), is the minimum span taken over all L(2,1)-labelings of G. The hole index of a graph G, denoted ρ(G), is the minimum number of holes taken over all L(2,1)-labelings with span exactly λ(G). Georges and Mauro [On the structure of graphs …
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Sarah Spence Adams
An L(2,1)-labeling of a graph G is a function f:V(G)→{0,1,…,k} such that |f(x)−f(y)|≥2 if x and y are adjacent vertices, and |f(x)−f(y)|≥1 if x and y are at distance 2. Such labelings were introduced as a way of modeling the assignment of frequencies to transmitters operating in close proximity within a communications network. The lambda number of G is the minimum k over all L(2,1)-labelings of G. This paper considers the lambda number of the matched sum of two same-order disjoint graphs, wherein the graphs have been connected by a perfect matching between the two vertex sets. Matched sums have …
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
Sarah Spence Adams
We introduce a construction technique for generalized complex linear processing orthogonal designs, which are p × n matrices X satisfying XHX = fI, where f is a complex quadratic form, I is the identity matrix, and Xhas complex entries. These matrices generalize the familiar notions of orthogonal designs and generalized complex orthogonal designs. We explain the application of these matrices to space–time block coding for multiple-antenna wireless communications. In particular, we discuss the practical strengths of the space–time block codes constructed via our proposed technique.
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Aaron Hoffman
We study the interaction of small amplitude, long-wavelength solitary wavesin the Fermi–Pasta–Ulam model with general nearest-neighbour interactionpotential. We establish global-in-time existence and stability of counterpropagatingsolitary wave solutions. These solutions are close to the linearsuperposition of two solitary waves for large positive and negative values oftime; for intermediate values of time these solutions describe the interactionof two counter-propagating pulses. These solutions are stable with respectto perturbations in L2 and asymptotically stable with respect to perturbationswhich decay exponentially at spatial ±∞.
Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth
Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth
John B. Geddes
Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.