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Steffe, Leslie P.; Cobb, Paul – Focus on Learning Problems in Mathematics, 1998
Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…
Descriptors: Arithmetic, Concept Formation, Constructivism (Learning), Division
Graeber, Anna O.; Baker, Kay M. – Focus on Learning Problems in Mathematics, 1991
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…
Descriptors: Concept Formation, Division, Elementary Education, Elementary School Mathematics
Kaput, James J. – Focus on Learning Problems in Mathematics, 1989
Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)
Descriptors: Cognitive Structures, Computer Assisted Instruction, Division, Elementary School Mathematics
Miller, Susan Peterson; Harris, Carolyn A.; Strawser, Sherri; Jones, W. Paul; Mercer, Cecil D. – Focus on Learning Problems in Mathematics, 1998
Reports on the findings obtained from teaching initial multiplication concepts, skills, and principles to students with disabilities, low-achieving students, and students who were achieving normally in inclusive, general-education settings. Contains 52 references. (ASK)
Descriptors: Arithmetic, Elementary School Mathematics, Grade 2, Inclusive Schools
Schmittau, Jean – Focus on Learning Problems in Mathematics, 1991
Structure of mathematical concept of multiplication and its integration into conceptual system, with respect to formal and informal aspects of understanding for 10 university students, are investigated through linear scale assessment of examples for prototypical effects and through follow-up interview which included direct explanations of…
Descriptors: Classification, Cognitive Mapping, Cognitive Structures, Comprehension
Davydov, V. V. – Focus on Learning Problems in Mathematics, 1992
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)
Descriptors: Cognitive Development, Cognitive Processes, Concept Formation, Elementary Education
Anderson, Ann – Focus on Learning Problems in Mathematics, 1995
Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)
Descriptors: Addition, Algebra, Exponents (Mathematics), Grade 9
Tirosh, Dina; Graeber, Anna O. – Focus on Learning Problems in Mathematics, 1990
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)
Descriptors: Abstract Reasoning, Arithmetic, Cognitive Development, Cognitive Structures
