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)

Many worthwhile mathematical activities can be generated by an overgeneralization. Some conjectures and their verification are described, with some exploration of historical procedures. (MNS)

Describes a study that explores secondary school students' conceptions of division by zero. Examines whether students identify expressions involving division by zero as undefined or tend to assign them numerical values. Studies students' justifications and analyzes the effects of age and level of achievement in mathematics on students' responses…

Investigates secondary mathematics teachers' (N=4) memories of learning mathematics, their beliefs about their mathematics instructional practice, and their definitions of mathematics in order to locate possible connections between teachers' mathematical experiences and their beliefs about mathematics and mathematics teaching. (Contains 15…

Examines a model for mathematics teacher education that provides beginning teachers an opportunity to grapple with the relationship between their own mathematical knowledge and conceptually-based teaching. (Contains 21 references.) (ASK)

A new potential for using microcomputers to help secondary school students learn mathematics through self-diagnosis and self-remediation is contrasted with current uses of computers for diagnosis and remediation. Research findings and software are cited in the discussion. (MNS)

Using computers to provide diagnosis and remediation in mathematics is emphasized. Some essential features of technology-supported learning environments are discussed, as well as features that facilitate their use. Illustrated is a computer environment for learning algebra. (MNS)

This is a report of an application of the interpretation of errors and springboards in a real-life situation. If and why we need to reduce fractions is considered. (MNS)

A common mistake in adding fractions involves the confusion betwen the concepts of fraction and ratio. A coherent system to operate with ratios is developed. (MNS)

Several intuitive proofs for evaluating specific infinite expressions are given. Observations on intuition and errors in mathematics are included. (MNS)

Presents a study designed to explore whether a student's use of the graphing calculator during instruction will affect their concept of function, how students' participation in a conceptual change assignment affects their concept of function, and how the graphing calculator and the conceptual change assignment interact with one another to…

Presented are examples of how the terminology used in typical rate questions is misunderstood by a large proportion of students. Explanations based on both interviews and paper-and-pencil tests are given as to why this phenomenon exists. (MNS)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)