Analogies are known to foster concept learning, whereas discovery learning is effective for transfer. By combining discovery learning and analogies or similarities of concepts, attractive new arrangements emerge, but do they maintain both concept and transfer effects? Unfortunately, there is a lack of data confirming such combined effectiveness.…

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

Presents the template method developed by Galileo for calculating areas of geometric shapes constructed of uniform density and thickness. The method compares the weight of a shape of known area to the weight of a shape of unknown area. Applies this hands-on method to problems involving calculus, Pythagorean's theorem, and cycloids. (MDH)

Presents activities to create designs with different arrangements of square tiles, which gives students an opportunity to make conjectures about perimeter and to make convincing arguments to justify those conjectures. Includes worksheets. (MKR)

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…