We have proved this theorem, it is true, only when k > 0. If h = 0 it is, however, merely an obvious consequence of Theorem I. We come now at last to our most important result, though one which is, at bottom, less far reaching than Theorem II, namely THEOREM III. If e is an arbitrarily given positive constant, a continuous, real function g(x) exists such that 0 < g(x) < e and such that the syst...

Science standards across 44 states in the United States are often assumed to be equivalent because they all based on National Research Council’s (NRC) Framework for K-12 Education. Twenty of those adopted Next Generation Standards (NGSS), which is NRC Framework, and 24 other developed their own Framework-based science standards. In this article, two related studies described that focused assess...

How do we learn non-physical properties of physical objects? We explored how the statistical structure of events can be a source of object property learning. Twenty-five participants saw sequences of visual events surrounding two distinct objects. Object identity determined 1) the direction of a high transition probability between two events, and 2) the frequency of two other events. Learning w...

Abstract Although the effects of professional development programs on teachers’ noticing skills have attracted considerable interest among mathematics education researchers, little is known about developmental process prospective within initial teacher education. This paper examines extent to which are developed through courses taken program using exemplarily topic division fractions. The study...