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…

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…

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)

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…

Discusses a case study in which the cognitive monitoring moves of a pair of preservice elementary education teachers were examined during cooperative problem-solving tasks. Concludes that assuming different roles during the problem-solving experience can be an effective strategy and a potentially helpful learning experience. (31 references) (MDH)

Ties together the educational threads of teaching thinking skills and improving the intellectual performance in deaf learners. Identifies six criteria for curriculum or research decisions related to teaching for higher-level problem solving. Applications of these ideas to mathematics are left to the reader. (MDH)

This paper describes student performance and beliefs regarding fractions resulting from a five-phase approach toward developing mathematical intuition via physical materials. Interviews with students using this approach and with students using a conventional textbook approach indicated significant differences in problem-solving abilities and…

Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH)

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

Presents a study that indicates that second grade students (n=117) do select manipulatives that match the story context in measurement and partition division word problems, that they can solve division word problems, especially when matched manipulatives are used, and that division without remainders are more accessible to solution. (39…