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)

Discusses Vygotsky's theories about concept formation, his distinctions between everyday and theoretical concepts, and how empirical generalizations can lead to misconceptions. Examines the implications of these theories for mathematics instruction and its relationship to the current mathematics reform. (34 references) (MDH)

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

Argues that intuitive and computational knowledge can be combined by focusing more explicitly on referential and quantitative meanings in division of fractions problems. Recommends teaching mathematics as problem solving, communication, reasoning, and connections to help students overcome misunderstandings and connect their intuitive knowledge…

Focuses on the language used by elementary mathematics teachers and its relationship to students' understanding of mathematical concepts, as well as their misconceptions. Describes eight situations in which the use of precise, formal mathematical terms could be replaced by informal language, particularly when introducing new concepts. (TW)

Discusses diagnostic information which can be gained from students' writing and presents examples of each, including error patterns, insights into where instruction should begin, failure of students to make connections, difficulties with independent work, clarifying student understanding, and student beliefs and attitudes. (42 references) (MKR)

Presents a case study of a special education teacher candidate with a learning disability in mathematics. Issues discussed include the nature of learning disabilities in adults; possibility of workable interventions at the adult level; implications of these problems in teacher candidates; and implications for teacher education programs. (27…

Reports a study to examine careless errors fifth-grade students (n=58) make while solving mathematical word problems and explores the type of student who frequently makes such errors. Results indicated that frequency of these errors was significantly related to the noncognitive variables of the study. Discusses implications for remediation. (20…