Students often view their role as that of a replicator, rather than a creator, of mathematical arguments. We aimed to engage our students more fully in the creation process, helping them to see themselves as legitimate proof creators. In this paper, we describe an instructional activity (i.e., the "group proof activity") that is…

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

Continual assessment of student understanding is a crucial aspect of teaching. The adoption of the Common Core State Standards for Mathematics (CCSSM) represents raised expectations for the level and depth of mathematical understanding that is expected of our students. But new standards also mean new tests. What those tests will be like is of…

The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the…

The Magic Mathworks Travelling Circus is a touring maths lab--in and of itself, a good thing. When children enter it, they find particular pieces of apparatus captioned with particular challenges--which is perhaps not such a good thing. Students are faced with an apparatus that can do only one thing, and so are not encouraged to look again at…

Describes how a sixth grade teacher and her eleven students (with a typical range of math abilities) explored the mathematical concept of "infinity" through play. Discusses the pedagogy of critical/creative thinking. (SR)

Explores the following classical problem: given any 30 points on a circle, join them in pairs by segments in all possible ways. What is the greatest number of nonoverlapping regions into which the interior of the circle can be separated? Presents strategies for solving this problem. (PK)