The theory of Teaching for Abstraction was used to construct a unit for teaching percentages in Grade 6. The unit focused on percentage as a multiplicative relationship and put more emphasis on why percentages are used than on how they are calculated. Analysis of the data collected showed that many students did learn to apply percentages meaningfully, although the level of achievement was not a...

Artificial neural networks (ANNs) are typically highly nonlinear systems which finely tuned via the optimization of their associated, nonconvex loss functions. In many cases, gradient any such function has superlinear growth, making use widely accepted (stochastic) descent methods, based on Euler numerical schemes, problematic. We offer a new learning algorithm an appropriately constructed vari...