Ideas for the development of creative exploration in mathematics are offered, including games to play in class (e.g., card games and tangrams), competitions (sample problems), clubs and math evenings (math relays and treasure hunts), projects (possible topics in patchwork quilting, art, and music), and math camps. (DB)

Discusses the mathematics education philosophy of J. W. A. Young and how it compares to the principles in the National Council of Teachers of Mathematic's "Curriculum and Evaluation Standards for School Mathematics." Elaborates on Young's views concerning rote learning, establishing connections between mathematics and other disciplines,…

Curriculum and teaching should be dialogic, multifaceted, critical experiences, not merely exchanges of information. Discusses the teacher's role in stimulating thinking processes and getting urban students to ask questions about class material and their own world. (CJS)

Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)

College-level student inquiry projects are not easy to evaluate within the parameters of the academic grading system. One form of rubric-guided assessment has specific advantages in addressing both performance and product by allowing weighting of criteria, flexibility of criteria and standards based on the project, defining the major aspects of…

Three companies (Voyager Expanded Learning, Mindsurf, and EXPLORE) have introduced after-school programs that emphasize stress-free academic enrichment activities. The companies differ, but share a fun-learning concept, maintain low staff-child ratios of about 1:8, and serve grades K-8. The operative words are flexibility and affordability. Some…

Defines the questions that are the basis of developmental-action inquiry. Outlines the type of theory and practice that supports and reflects such inquiry, and highlights how different such integrated research/practice is from empirical positivism. (Author/CCM)

Outlines the discovery of an advanced calculus class based on the generalization of the relationship between the volume of a right circular cone and the volume of a right cylinder with same height and base radius while studying solids of revolution. Relates the course of discovery and concludes with plans to use it to try to generate the same…

Explains four instructional approaches with varied learning processes and provides guidelines for the use of each. Describes receptive instruction, that is highly controlled; behavioral instruction that assumes learning occurs through a gradual building of skills; the situated guided discovery approach, including constructivism and social…

Discusses the incompatibility of fast-paced questioning techniques and inquiry-oriented science instruction. Encourages increasing the time allowed for students to construct responses to teacher questions, and utilizing a system of rewards and punishments that supports students working out their own ideas with experiments. (DDR)

Describes an approach that motivates preservice teachers to become involved in the scientific experience. The approach involves a science demonstration or activity that is done both in and out of class in which students report observations using a Vee diagram. Includes assessment procedures. (DDR)

This article discusses using questioning techniques for encouraging purposeful inquiry among gifted students in elementary grades through college levels. A variety of questioning strategies is recommended, focusing primarily on the higher end of Bloom's taxonomy to engage students in higher level thinking. A classroom example is provided.…

Today's best constructivist teaching reflects the legacies of educational visionaries such as John Dewey, Jean Piaget, Lev Vygotsky, Reuven Feuerstein, Howard Gardner, and Marian Diamond. Creative cognitive designs stem from three essential elements: creative teaching genius, excellent instructional methods, and expansive, interconnective…

Establishing schooling/larger world connections is critical for adolescents. The contextual learning approach views learning as most effective when information is presented within a familiar framework. Employing puzzles, hands-on learning activities, project-based learning, contextual connections, applied math, mentoring, and wider audiences…

This article describes a study into the role of heuristic support in facilitating discovery learning through simulation-based learning. The study compares the use of two such learning environments in the physics domain of collisions. In one learning environment (implicit heuristics) heuristics are only used to provide the learner with guidance…