Supporting Generative Thinking About the Integer Number Line in Elementary Mathematics

This report provides evidence of the influence of a tutorial "communication game" on fifth graders' generative understanding of the integer number line. Students matched for classroom and pretest score were randomly assigned to a tutorial (n = 19) and control group (n = 19). The tutorial group students played a 13-problem game in which student and tutor each were required to mark the same position on a number line but could not see one another's activities. To resolve discrepant solutions, tutor and student constructed agreements about number line principles and conventions to guide subsequent placements. Pre-/posttest contrasts showed that (a) tutorial students gained more than controls and (b) agreement use predicted gain. Analyses of micro-constructions during play revealed properties of student learning trajectories.