Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Challenged is the traditional model for the transmission of mathematics in the elementary school classroom. An inquiry approach to learning mathematics is proposed and supported with results of a year long research project that exposed second graders to mathematical learning experiences using this approach. (MDH)

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…

Discusses an introductory mathematics course for six year olds which incorporates visual reflection of essential links and relationships, broad and flexible approaches, student actions, and meaningful cooperation of students. The four topics covered are determination of attributes, symbolic representation of relations and transformations, the…

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)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)