Across all cases, however, incorporating dynamic manipulation into mathematical discourse moved implicitly beyond established norms when dragging was used to focus attention on continuous dynamic variation, rather than being treated as an efficient means of generating multiple static figures.
The analysis suggests that while elements of mathematical practices can be developed, moving towards mathematical modes of enquiry may require more explicit, consistent, and longitudinal attention to problem-solving approaches to support orientational change.
A mathematical model of moving bed coal gasification is used to determine the performance of two U.S. coals in a pressurized Lurgi gasifier.
The mathematical model involves moving boundaries governed by a fourth order nonlinear partial differential equation which contains a nonlocal term corresponding to the electrical field and a nonlinear term corresponding to the curvature.
In particular, although the HRC and motion energy models differ in terms of their intuition and neuronal bases, both models rely on the same mathematical fact about moving visual stimuli motion causes pairs of spatially separated points to become correlated when a stimulus moves from one location towards the other (Adelson and Bergen, 1985; van Santen and Sperling, 1985).
This technique greatly reduces the mathematical complexity of the moving boundary problem which is represented by a system of coupled partial differential governing equations, to a system of coupled ordinary differential equations.
Equations (16)–(19) demonstrate that the first function combination uses the simplest mathematical functions and by moving from the first function combination to the last, model complexity increases.
Now we're in a world where we have the ability to take data and try to understand the physical world again, moving from mathematical models to data models, to reveal new things about the world.
The analysis presented in this paper suggests that while elements of mathematical practices can be developed, moving towards an encompassing orientation to mathematical modes of enquiry may require more central focus on problem-solving approaches to achieve a change in orientation.
