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…

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)

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)

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…

This study examined the problem-solving strategies and systematic errors of (n=82) preservice elementary school teachers related to place value concepts and decimal representations of rational numbers. Problems were posed in the unfamiliar domain of numeration systems with bases other than base ten. (Contains 13 references.) (MKR)

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)

Interpersonal Process Recall (IPR) is a technique in which audiotapes are used to evoke students' memories concerning their own thinking. Reports a study using IPR to probe elementary students' (n=17) thinking during a problem-solving situation. Concluded that IPR has potential in classroom research. (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…

Reports on research designed to systematically examine how the use of personalized word problems as practice examples would affect learning and attitudes. A computer program was used to generate the problems. It was concluded that presenting problems in familiar contexts made materials more interesting and understandable for students. (PK)

Reports a study to examine careless errors fifth-grade students (n=58) make while solving mathematical word problems and explores the type of student who frequently makes such errors. Results indicated that frequency of these errors was significantly related to the noncognitive variables of the study. Discusses implications for remediation. (20…