This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

Learning to question is essential for determining pathways of conservation and development in southwestern Amazonia during a time of rapid global environmental change. Teaching such an approach in graduate science programs in regional universities can be done using play-acting and simulation exercises. Multiple working hypotheses help students…

Nuclear magnetic resonance (NMR) spectroscopy is widely used by chemists. Furthermore, the use of NMR spectroscopy to solve structures of macromolecules or to examine protein-ligand interactions is popular. Yet, few students entering graduate education in biological sciences have been introduced to this method or its utility. Over the last six…

Every day physicians make judgments about patient management and diagnosis based on less than perfect information from many different sources. Judgment and decision-making research has taught us a great deal about such decisions, but these insights rarely find their way into the medical curriculum. One productive line of investigation in the study…

This article describes the journey that one elementary school took in examining the roles and responsibilities of the principal, teachers, students, and school environment in supporting mathematical understanding as described by the NCTM Standards. (Contains 2 tables and a bibliography.)

Students have used Cogito.org to pose and/or solve math problems and brain teasers, share their experiences in academic competitions, debate the pros and cons of using biofuels for energy, design an alien world based on sound scientific principles, and expand their cultural understanding by connecting with students from around the world.…

Teachers know their students must struggle and grapple with authentic tasks in order to grow stronger. Classroom teachers of the gifted know that their students cannot advance cognitively without facing relevant and challenging material that demands higher level thinking and reasoning. Therefore, the teacher of gifted mathematics students must…

Photonovels look like comic books but contain photographs instead of drawings. Because photonovels combine pictures and everyday language, adult ESL learners can use them to communicate their thoughts and ideas. Photonovels can also be an aid in learning spoken and written English. This article describes a photonovel project that one of the…

Research shows that mathematically gifted students learn differently from their same age group peers. They require curriculum to be differentiated to meet their specific learning styles (Johnson, 2000). Studies have shown that formal instruction in elementary school classrooms often lacks challenge for the gifted learner since courses in regular…

This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…

This article looks at students doing mathematics through the lens of (artistic) performance. (Contains 10 figures.)

Response-to-Intervention is a new method of service delivery being implemented in schools. However, the lack of emphasis on the flexible nature of Response-to-Intervention and the varying descriptions of its features within the literature may lead to confusion among school professionals. In order to provide more uniformity among the literature, 5…

This article presents major results of TIMSS, along with practical suggestions and questions that mathematics teachers can ask themselves in terms of how to apply the results to the improvement of their practice.

Recently, attention has been paid to computer and video games as a medium for learning. This article provides a way of conceptualizing them as possibility spaces for learning. It provides an overview of two research programs: (1) an after-school program using commercial games to develop deep expertise in game play and game creation, and (2) an…

On the first day of Principles of Accounting classes, students learn the fundamental accounting equation from which all financial accounting practice emerge. The accounting equation is the criterion by which companies are valued and by which company performance is measured. This activity simplifies assets, liabilities, and owners' equity to the…