Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

This article describes current goals for K-8 school mathematics and outlines 7 critical areas in which students frequently experience difficulty. Effective mathematics teaching is related to teaching that takes into account the 3 learning principles articulated in the National Research Council (2006) publication, "How Students Learn". Research…