One of the most common misconceptions about probability is the belief that successive outcomes of a random process are not independent. This belief has been dubbed the "gambler's fallacy". The belief that non-normative expectations such as the gambler's fallacy are widely held has inspired probability and statistics instruction that attempts to…

This paper evaluates the strengths and limitations of a computer tutor designed to help students understand physics concepts. The tutor uses a teaching strategy called "bridging analogies" that previous research has demonstrated to be successful in one-to-one tutoring. The strategy is designed to remedy misconceptions by appealing to existing…

Students of reasoning have long tried to understand how people revise systems of beliefs. This paper maintains that people often change their beliefs in ways driven by considerations of explanatory coherence. In this report, a computational model is described of how experimental subjects revise their naive beliefs about physical motion. First,…

Discussed are possible reasons behind the inconsistencies in the learning of calculus. Implicated are students' beliefs, mathematical paradigms including concept image and concept definition, language use, and curriculum sequencing. (KR)