Levels of participatory conception of fractional quantity along a purposefully sequenced series of equal sharing tasks: Stu's trajectory

•We present key understandings of fractional quantity, evidenced through problem solving strategies, observable operations, and naming/quantification of one fifth grader with learning disabilities.•Data analysis uncovered four distinct points of understanding within the child's understanding that is reflective of a conceptual trajectory.•Results of this work suggests that, when intervention is employed that engages children with LD in solving problems within their mathematical activity and responds to their ideas and ways of thinking, children with LD can and do advance their conceptions. Further, instruction for any child, including those labeled LD, should focus on what the child is able to understand, learn, and ultimately do mindfully.