The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children's understanding of missing-value proportional situations, (b) investigating how children transition…

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

Examines the map-making process of middle-school students to determine which actions influence their accuracy, how prior knowledge helps their map construction, and what lessons can be learned from map making. Indicates that instruction that focuses on recognition of interconnections between map elements can promote map reasoning skills. (DSK)