Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a…

Results of two studies using the Esper paradigm to determine development of rule application and discovery are reported. Subjects learned and generalized when rule and structure were provided, but there was little evidence of rule discovery. Manipulations of memory and attention facilitated learning, but only attention facilitated rule discovery.…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

Used 2 12-year-old children to investigate deductive and inductive reasoning in plane geometry. A LOGO microworld was programmed to measure distances and turns relative to points on the plane. Learning environments like this may enhance formation of inductive geometrical understandings. (Contains 44 references.) (LDR)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)