We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

In STEM domains, students are expected to acquire domain knowledge from visual representations that they may not yet be able to interpret. Such learning requires perceptual fluency: the ability to intuitively and rapidly see which concepts visuals show and to translate among multiple visuals. Instructional problems that engage students in…

The findings discussed here are a small part of a larger study entitled, "Encouraging Persistence Maintaining Challenge". The paper reports five teachers' observations of the implementation of a task which was new to them. The teachers were asked to identify aspects of the task which they perceived as challenging for the Year 6 students.…

This review of the literature on five learner control variables in computer-based instruction concludes that: (1) pacing left to learner control has been found ineffective because learners tend to procrastinate or to exit lessons prematurely; (2) sequence, or content flow, has been an ineffective variable left under learner control since…