Overlaps and shifts of instructional goals in the design of a set of mathematics tasks

This article presents a case study on a secondary mathematics teacher, Mary (pseudonym), and her design of a set of instructional tasks in the context of proportional reasoning. In keeping with the way Singapore teachers generally conceive of instructional planning, we investigated the connections between four comparison tasks she designed through her instructional goals. We adopt the use of an item-level lens to analyse the instructional goals of individual tasks, followed by a set-level lens to determine the movement in her instructional goals across tasks. The metaphors of overlaps and shifts describe how the movement of her instructional goals helped to advance students’ understanding of proportionality and to develop their proportional reasoning. Findings illustrate the usefulness of adopting the metaphors of overlaps and shifts and using two lenses to gain insights on teachers’ complex design processes. Additionally, they suggest that teachers’ understanding of student’s knowledge at the primary level is valuable for designing tasks that will ease students’ transition to secondary mathematics.