Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

Examines strategies used by preschool children to subdivide items and focuses on how counting and sharing relate to one another. Indicates that children exhibited alternative strategies--suggesting use of a recipient as a mental cycle-marker and an adjacent recipient strategy--with pauses between allocations suggesting a re-presentation of lots…

Examined the effects of intervention in the instruction of 12 male seventh-grade students for the purpose of developing number sense. Results indicate that after instruction students were more likely to use strategies to solve number magnitude, mental computation, and computational estimation problems that reflected number sense. (Contains 50…

Investigates possibilities for and manifestations of collaborative work with pairs of kindergarten students as they worked on tasks designed to promote early number development. Students generated four strategies, and three themes emerged from the analysis of the cooperative solutions. Contains 34 references. (Author/ASK)

Mathematics educators frequently recommend that students use strategies for measurement estimation, such as the reference point or benchmark strategy; however, little is known about the effects of using this strategy on estimation accuracy or representations of standard measurement units. One reason for the paucity of research in this area is that…

Report provides new data concerning children's accuracy as measured by previous studies and clarifies progress of first graders during entire year on difficult single-digit addition and subtraction problems. Discussion focuses on advantages of an adding on interpretation of subtraction and the importance of emphasizing conceptual understanding…