This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

The statistical concept of sampling is often given little direct attention, typically reduced to the mantra "take a random sample". This low resource and adaptable activity demonstrates sampling and explores issues that arise due to biased sampling.

Most teachers try to avoid having students experience uncertainty in their schoolwork. But if we want to prepare students to tackle complex problems (and the uncertainty that accompanies such problems), we must give them learning experiences that involve feeling unsure and sometimes even confused. Beghetto presents five strategies that help…

Preservice teachers are typically educated in university settings and learn teaching methodology through coursework. Many preservice teachers find themselves underprepared for handling challenging situations in art classrooms. Teaching is very often influenced by contextual factors such as the space and design of the classroom, demographics and…

The aim of this article is twofold: first, to identify and address three central divisions in the field of authentic education that introduce ambiguity and at times inconsistencies within the field of authentic education. These divisions concern a) the relationship between autonomy and authenticity; b) the division between the two basic attitudes…

Although the human mind resists confusion, this feeling of disequilibrium nurtures learning. Newkirk, the author quotes, says intelligence is not a matter of being smart--it is the capacity to view difficulty as an opportunity to stop, reassess, and employ strategies for making sense of problems. These same habits of mind define reflection, a…

In teaching leadership development we have developed and revised a model of teamwork and collaboration, which has yielded innovative and positive results. Our study draws on insights from more than 90 project teams, gathered over twelve years of a mid-career executive education program designed specifically to teach collaborative leadership. The…