Analyzes the problem-solving process and presents the dominance of the conjecture or theoretical aspect as a subtle relation between the data and the conjecture. Argues that conjectures are not necessarily subordinate to the data but play active roles in mathematical problem solving. Discusses the meaning of this dominance in the context of…

Investigates students' use of imagery in their mathematical activities. Findings indicate that image forming is crucial in doing mathematics. A student who fails to construct an image in a problem-solving situation is severely limited in giving meaning to the situation. Contains 21 references. (JRH)

Previous studies indicate that many early elementary school children have the misconception that whole number subtraction is a commutative operation. The degree and character of this subtraction error was investigated in this longitudinal study. Results obtained from three groups of students with different number abilities provided further…

Discusses an exploratory study that examines student interpretation of remainders in division as applied to word problems in a restrictive school setting and in a real-world, out-of-school setting. Concludes that students lack the ability to map computational results to the real-world context. Contains 16 references. (DDR)

Assesses children's structural understanding of combinatorial problems when presented in a variety of task situations. Provides an explanatory model of students' combinatorial understandings that informs teaching and assessment. Addresses several components of children's structural understanding of elementary combinatorial problems. (Contains 50…

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Informal Assessment sometimes interprets enthusiasm and confidence in mathematics for cognitive competence. Presented are two case studies of interviews conducted to study the affective and reflective capacities underlying children's mathematical thinking during a nonroutine problem-solving task. (MDH)

Describes a study which concluded that, to restructure the mathematics curriculum, modification of existing teaching practices is required. Recommends that practices be modified to enable students to construct effective knowledge bases and become active learners. Contains 38 references. (DDR)

In this study, third- and fourth-grade pupils were tested to see if they could consistently distinguish between measurement and partition division word problems and to observe their patterns of preference. Both before and after instruction, significant proportions of the students could distinguish the two division situations. (MNS)

Content analysis of 7 mathematics textbook series, grades 1-8, found that textbooks published after 1989 (when NCTM Standards were published) showed shifts of emphasis among content areas; changes in amount of content development, drill, word problems, and problem solving; and increased use of estimation and calculators. (13 references) (MKR)

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)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (YP)

Presented are examples of how the terminology used in typical rate questions is misunderstood by a large proportion of students. Explanations based on both interviews and paper-and-pencil tests are given as to why this phenomenon exists. (MNS)

This review of the research on mathematical problem solving is focused on learning disabled students. Categories discussed include characteristics of learning disabled problem solvers, strategies they use, instruction facilitating strategy learning, cognitive strategies, and problem solving strategies. Implications for instruction and research are…

Suggests that involving Russian experts in solving concrete educational problems and providing curriculum development in the United States could be very useful. A primary goal would be to change the attitudes and beliefs of teachers and to extend teachers' views on teaching mathematics. (AIM)