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In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of progressions—mathematical concepts, instructional activities, number choices, and student solutions—and that the progressions were embedded within each other. This study contributes to the field’s understanding of the ways in which expert teachers make use of curriculum- and research-based progressions in their teaching practices. 相似文献
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Martin Land 《Foundations of Physics》2003,33(8):1157-1175
In relativistic classical and quantum mechanics with Poincaré-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. The formulation of a covariant canonical framework for the evolving events leads to a dynamical theory in which mass conservation is demoted from a priori constraint to the status of conserved Noether current for a certain class of interactions. In pre-Maxwell electrodynamics—the local gauge theory associated with this framework —events induce five local off-shell fields, which mediate interactions between instantaneous events, not between the worldlines which represent entire particle histories. The fifth field, required to compensate for dependence of gauge transformations on the evolution parameter, enables the exchange of mass between particles and fields. In the equilibrium limit, these pre-Maxwell fields are pushed onto the zero-mass shell, but during interactions there is no mechanism regulating the mass that photons may acquire, even when event trajectories evolve far into the spacelike region. This feature of the off-shell formalism requires the application of some ad hoc mechanism for controlling the photon mass in two opposite physical domains: the low energy motion of a charged event in classical Coulomb scattering, and the renormalization of off-shell quantum electrodynamics. In this paper, we discuss a nonlocal, higher derivative correction to the photon kinetic term, which provides regulation of the photon mass in a manner which preserves the gauge invariance and Poincaré covariance of the original theory. We demonstrate that the inclusion of this term is equivalent to an earlier solution to the classical Coulomb problem, and that the resulting quantum field theory is renormalized. 相似文献
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Alfred Landé 《International Journal of Theoretical Physics》1968,1(1):51-60
The doctrine of wave-particle duality and complementarity has been regarded since the late 1920's as the only possible interpretation of observations such as electron diffraction through crystals and screens with two slits as well as other coherence phenomena. Physicists have been unaware that those apparent wave features can be accounted for, without supernatural dual manifestations made palatable by semi-philosophical renunciation, by the unitary quantum mechanics of matter particles alone if one only is consistent enough to admit that there are three (rather than only two) conservation laws of mechanics, hence there are three (rather than two) corresponding selection rules, forE, P and also for the linear momentump, restricting the mechanical activity of time-, angular-periodic, and also of space-periodic systems. This clears up the mystery of dualism in a physical manner without philosophical subtleties and leads to a great simplification of the quantum ideology. 相似文献
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P.L. Land 《Journal of Physics and Chemistry of Solids》1973,34(11):1839-1845
The dependence of electronic conductivity and composition of ceria on oxygen pressure is described by equilibrium equations for a material containing oxygen vacancies, divacancies, cerium interstitials and polarons, where these defects are considered to include distorted zones of material. The analyses takes the extension of simple “point defects” into proper account, whereas earlier analyses have not. It is concluded that available data can be explained by polarons in equilibrium with isolated oxygen vacancies, but not with divacancies or interstitial cerium ions. 相似文献