Exploring a Diverse Learner’s Equipartitioning Learning Trajectory

ABSTRACT Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this teaching experiment was to explore a diverse learner’s understandings about equipartitioning and relational reasoning. Across eleven 45-min individualized sessions, the equipartitioning learning trajectory (EPLT) served as the framework for investigating the student’s thinking and learning. Findings illustrate how a student’s actual trajectory can be focused on developing a many-to-one meaning for fractions and relational reasoning, rather than strictly adhering to the sequence of proficiencies hypothesized by the EPLT. Further, the student’s engagement with cognitive elements which characterize mental activity reveals ways instruction might be tailored to support a student’s relational reasoning. Implications include a more nuanced perspective on individual learning of equipartitioning and important considerations for educators who support relational reasoning in diverse learners.