Bob's Productive Task Engagement in Fractional Reasoning: A Case Study

Productive engagement in fractional reasoning is essential for abstracting fundamental algebraic concepts vital to college and career success. Yet, data suggest students with learning disabilities (LDs), in particular, display pervasive shortfalls in learning and mastering fraction content. We argue that shortfalls in understanding are in fact issues of access in terms of opportunities that students have to productively engage with learning objects (i.e., tasks) that meaningfully bring forward and promote students' fractions understanding. In this study, we define engagement as a state and take up a single case study methodology to illustrate behavioral, affective, and cognitive engagement of Bob, a student with a LD, as he works with a series of fraction tasks designed to support his engagement. Results reveal patterns of productive engagement as regards this student's fractional reasoning as they relate to the tasks he was given over time. Contributions of this work include insights into Bob's engagement within tasks and provide considerations for teaching practice seeking to promote productive engagement by design.