Learning through drama and other art forms enriches children's learning by expanding the possibilities for how children create and express meaning (Adomat, 2009; Berghoff, Egawa, & Harste, 2000). The arts are rarely suggested as a way of opening up broader understandings for young readers; yet drama has been shown to be beneficial in myriad ways…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

In this study, we seek to understand the beliefs that chemistry faculty hold when grading student solutions in problem solving situations. We are particularly interested in examining whether a conflict exists between the chemistry faculty beliefs and the score they assign to students' solutions. The three categorical values identified in a similar…

Sociodrama is an arts-based, action-oriented tool of individual and collective social exploration and creative problem solving that allows participants to explore and find potential resolutions to issues of concern and conflict in their lives. This article describes how Early Years educators can begin to implement basic sociodrama into their…

In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication in students' reasoning within a middle school algebra context. In this study, when…

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…

Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…

Building passion and potential for creative learning in higher education involves deliberately seeking to understand, appreciate, and teach for creativity. Recognizing the urgent need for creativity and problem solving skills, and understanding that instructors must embrace creative learning for themselves first, is central. Creativity cannot be…

New assessments that measure deeper learning--whether students understand challenging content and are able to apply that knowledge to think critically, solve problems, communicate their understanding, and work with their peers--are essential if students are to develop the competencies they need to succeed in an increasingly complex world. Such…

The purpose of this dissertation is twofold. First, the dissertation aims to critique "images of thought" in mathematics education which have ontological underpinnings that maintain oppressive practices and which prevent transformation. The second aim of the dissertation is to launch the transformation to a postcritical mathematics…

Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

The art gallery problem asks for the maximum number of stationary guards required to protect the interior of a polygonal art gallery with "n" walls. This article explores solutions to this problem and several of its variants. In addition, some unsolved problems involving the guarding of geometric objects are presented.