A case study of a beginning teacher's acculturation into the school mathematics tradition shows that the explanations and strategies that a teacher employs to cope with the tensions and contradictions that underlie the beliefs and practices of the school tradition can actually help sustain the tradition. (MKR)

Third- and fourth-grade students (n=401) were taught problem solving through structure-plus-writing, heuristics, or no explicit instruction. The structure-plus-writing group outperformed the heuristics group, and the gap widened 10 weeks after the treatment. Includes sample student-authored problems. (MKR)

Only 25% of fifth- and sixth-grade Chinese students (n=186) correctly solved a division-with-remainder computation task, about the same success rate as with American students, and only one-sixth of the students could interpret the result. (MKR)

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…

Investigates gender differences and the role of spatial visualization in problem solving in high school geometry. Reports that, whereas males and females differed in spatial visualization and in their performance, they did not differ in logical reasoning ability or in their use of geometric problem-solving strategies. (Author)

Investigated whether second grade children were aware that dealing without counting was sufficient to ensure equality of shares in a discrete sharing situation. Seventeen children were interviewed after watching a videotape of preschooler's actions on sharing activities. (YP)

This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. Significant effects in favor of the experimental group were found on an intermediate test and a posttest. (Author/CW)

Described are the strategies of 44 academic mathematicians on a set of computational estimation problems involving elementary multiplication and division. Discussion centers on the theoretical implications evident from pretest/posttest results in terms of the variety of strategies used and how the choice of strategy changed across the two tests.…

Results in 487 reports were integrated by meta-analysis to study characteristics of problem solvers, conditions for harder and easier problems, effects of different instructional methods on problem-solving performance, and effects of classroom-related conditions on problem-solving performance. Problem solving related positively to measures of…

Compared students who had four years of the University of Chicago School Mathematics Project (UCSMP) secondary curriculum to two distinct groups of comparable students at three different sites (one urban and two suburban). UCSMP students at all three sites achieved higher but registered little difference in attitude. (Contains 48 references.) (MDH)

Four third-grade and three fourth-grade students received individualized instruction on addition and subtraction of fractions for three weeks. Students overgeneralized the meanings of symbolic representations for whole numbers to fractions and vice versa. (MKR)