Defines a generalization as "a descriptive statement of broad application indicating a relationship between two or more concepts." Argues that successful teaching about generalizations can only occur when students understand the relationship between concepts and facts. Discusses four issues and four approaches related to teaching…

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Maintains that a major theme in Lev Vygotsky's later research was concept formation or conceptual development in child development. States that Vygotsky argued that the acquisition of mature academic concepts forms the crowning achievement of adolescence. Argues that the view raises a number of criticisms. (CFR)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Reviews research of writing activities that help identify student misconceptions and serve as a vehicle for knowledge construction. (29 references) (MDH)

Discussed is how the concept of equivalence can relate various segments of a mathematics program and help students develop an appreciation of the unity of mathematics. Activities and examples of equivalence at all grade levels are included. (KR)

Reports results of procedures directed at isolating and identifying students' difficulties in comprehending the concepts involved in lessons about gas exchange and respiration. Indicates that pupils (n=137) had deficient understanding of prerequisite concepts and tended to operate at the concrete operational level, whereas the highly abstract…

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Describes and illustrates the Monomial Sums Approach, a graphical learning strategy, facilitated by microcomputer capabilities that allow easy manipulation and exploration of graphical representations of polynomial functions. Reduces emphasis on memorized rules in favor of qualitative understanding of functional behavior, visualization of…

Focuses on the language used in mathematics instruction and the ways in which teachers assist students in constructing the formal language of mathematics. Strategies to help students connect vocabulary with mathematical concepts include using teacher modeling, writing, cooperative learning, and having students define words in their own language.…

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…

Attempts to express a group of children's understanding of inversion, retrograde, and retrograde-inversion as it applies to musical composition and color schemes. The children, ages six to nine, displayed idiosyncratic approaches to the problems. Discusses the possible implications for symbolic language and cognitive development. (MJP)

Developmental changes in the understanding and use of the logic of experimental control were addressed with three tasks in a longitudinal study. In all three tasks, understanding of experimental control was assessed by production measures (children were asked to test potential causal relations in a multivariable situation) and by choice/evaluation…

Project META (Metacognitive Enhancing Teaching Activities) is a 3-year naturalistic case study designed to explicitly enhance the metacognitive capabilities of learners in order to illuminate the nature of metacognitive interactions among elementary students and to describe the impact this type of enhancement has on the formation of students'…

This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…