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)

Proposes elements of a model of knowledge structures used in comprehending and generating graphs. Uses the competence model to attempt to organize and interpret findings on misconceptions in graphing. Discusses two types of common misconceptions; treating the graph as a picture and slope-height confusions. (YP)

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)

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)

Explores the extent to which presentations about multiplication and division involving decimals within three series of mathematics textbooks for grades three through eight help students to counter common learner misconceptions about multiplication and division. Results indicate that theory on conceptual change with its concomitant research have…

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)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

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…

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)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…