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.

While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and…

The present study investigates the statistical consequences of attribute misspecification in the rule space method for cognitively diagnostic measurement. The two types of attribute misspecifications examined in the present study are exclusion of an essential attribute (which affects problem-solving performance) and inclusion of a superfluous…

Adolescent identity and parent-adolescent conflict have each attracted considerable research interest. However, few studies have examined the important link between the two constructs. The present study examined the associations between adolescent identity processing styles and adolescent conflict resolution styles in the mother-adolescent dyad.…

In this study we explored the relation between private speech and task mastery by using the microgenetic method to examine the language and performance of 13 children aged 4 and 5 as they gained expertise with a spatial, multi-step planning task across 6 sessions. Seven of the 13 children's performances across these sessions were characterized by…

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

During creative problem-solving, designers frequently come across a variety of rich visual displays. While browsing for different sources of information, pictorial representations of existing concepts take prominence. However, once designers start generating new solution ideas to design problems, they often become too attached to some of the…