The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)

Thirty-four third graders matched 14 foldout shapes (nets) with seven polyhedra. They had more success associating nets containing triangular regions than nets with only rectangular regions. It was easier to identify nets of pyramids and of a triangular prism when the lateral faces were distributed around the bases. (MNS)

A total of 169 third-grade pupils were used as the final sample in an examination of information matching ability involving haptic, auditory, and visual modalities in relation to mathematics achievement. Significant correlations were found between matching abilities involving the haptic modality and mathematics achievement, higher than found with…

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)

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)

The relative efficacy of two approaches to teaching basic multiplication facts to third graders is examined. Support was indicated for the thinking strategies approach. Results also indicated it was possible to train teachers in two days of inservice education. (MP)

Explores cognitive operations such as coordination, integration, and structuring as manifested in a spatial context. Relates spatial thinking to enumeration strategies. Interviews with 45 third graders and 78 fifth graders suggest that students initially see arrays of cubes as uncoordinated sets of faces, later as space-filling structures. (FDR)

Examined were the effects of student cognitive entry behavior, prescribed mastery level, and information about criterion on mathematics achievement. Studied were 36 third graders assigned to four levels of being informed. Findings differed for children at low and high entry levels. (MNS)

Fifth graders performed better than third graders on discovering the function rule relating two number pairs. Task difficulty and mode of presentation (graphic or symbolic) varied by function. The children seemed ready to relinquish a hypothesis in the face of disconfirming evidence. (MNS)

Third- through sixth-grade mathematically talented students (n=306) enrolled in a flexibly paced university mathematics course far exceeded the normative achievement gains expected over a one-year period. Restricting such students to a rigid instructional pace may have a deleterious effect on motivation and achievement. (64 references) (MKR)