Attempts to reveal students' (N=800) misconceptions regarding quadratic functions, and identifies conceptual obstacles that may impede students' understanding. Findings indicate that the conceptual obstacles identified were fairly pervasive. Discusses the educational implications of the findings. Contains 34 references. (JRH)

Discusses students' preconceptions of randomness and offers an alternative way to think about the concept using the idea of complexity. That is, the randomness of a sequence can be measured by the difficulty of encoding it. Methods of judging complexity and implications for teaching are discussed. (Contains 30 references.) (MKR)

Summarizes the history of the mathematical idea of function and presents questionnaire data from (n=117) mathematics teachers. Results showed that teachers had a tendency to think only in terms of continuous functions, yet had little skill in constructing continuous functions. They scarcely considered discontinuous functions. (14 references) (MKR)

Discussed are some situations students face that result in cognitive conflict, possible sources of these conflicts, and strategies which students use to resolve, remove, or circumvent them. A global account for observed systematic errors is offered based on a general problem-solving rule called the "Matching Rule." (KR)