This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. Ways of reasoning deductively are highlighted, using examples drawn from observations of young students. One-step deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple…

This research evaluates the effectiveness of computer-mediated support for students' individual and collaborative argumentation. "Convince Me" is a "reasoner's workbench" program that aids students in generating and analyzing arguments, providing feedback on argument coherence from a general computational model. Laboratory studies indicate that…

A cross-sectional study examined age differences in children's conceptions of early U.S. history. Students in grades 2, 3, 6, and 8 (n=281) were asked to respond to a question about how the United States became a country. Their essays show significant changes with age. Older students were more likely to include errors of historical fact in their…

Multilevel visual models can make teaching and learning theories more easily understood. The idea of graphic visualizationas developed in this model utilizes three stages of abstract concept formation dealing with concrete visualization, abstract visualization, and abstract generalization, which would provide the learner with an intuitive grasp of…

The natural environment rings with mathematical sounds, as can be seen in the logarithmic spirals of elephant tusks, the hexagonal shapes of snowflakes and honeycomb cells, the rhythmic spouting of gysers, and in the circular growth of microscopic sea plants. Photographs reveal the mathematical relationships of familiar objects. (Author)

Translated from the English; research supported by the Delegation generale a la Recherche scientifique et technique, CNRS, Paris, France; special issue on "Changing Linguistics." (DD)

Suggests intelligence tests are culture bound and as such miss many abilities particularly those of minority groups. (ST)

Argues that the classroom situation may be a detriment to learning. (DD)

School achievement was positively related to performance on the abstract task and was generally unrelated to performance on the concrete task. (Authors)

A classroom activity is described which encourages students to determine the use of an artifact from the pre-Columbian Iraquois. Primary emphasis is on creative and productive thinking. (JB)

Affirms that the inquiry procedure, most suitable when investigative skills are needed, requires adequate curriculum design and materials, research resources, and teacher preparation. (DS)