Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

This article extends a framework for the study of culture-cognition relations to problems of historical research and diachronic analysis. As an illustrative case, we focus on mathematics in Oksapmin communities located in a remote highland area in central New Guinea. The Oksapmin, like their neighboring Mountain-Ok groups to the West,…

Reviews the radical constructivism movement in mathematics education. Benefits identified include learner ownership of mathematical learning; importance of social interaction; and identification of principles for improving mathematics teaching and learning. Weaknesses identified include overzealousness of some radical constructivists; downplaying…