This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

Art-based reading instruction and interventions for elementary and middle school students are growing in popularity despite scant theoretical rationale and empirical research support. This study explored the degree to which painting comprehension processes map onto text comprehension processes in this population. In particular, we used think aloud…

Reasoning about mechanisms is one of the hallmarks of disciplined inquiry in science and engineering, but comparatively little is known about its precursors and development. Children at grades 2 and 5 predicted and explained the motion of simple mechanical systems composed entirely of visible linkages (levers). Students' explanations of device…