Our research aims to identify domain-specific similarities and differences of externalized cognitive structures. Cognitive structure, also known as knowledge structure or structural knowledge, is conceived as the manner in which an individual organizes the relationships of concepts in memory. By diagnosing these structures precisely, even…

Explores what kinds of calculus-related insights seem to typify calculus-related reasoning. Introduces "qualitative calculus" in which learning is focused on synthesis. Discusses the resemblance and difference between traditional calculus and qualitative calculus, advantages of learning qualitative calculus, and how understanding qualitative…

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…

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…

Describes the "SemNet" software and some of its uses as an educational and research tool, with emphasis on the similarities and differences between concept mapping and semantic networking. (PR)

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)

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…