This research study was specifically concerned with the development, testing, and revision to an instructional theory for studying the mathematical concepts of equivalence and equation solving with multiple representations and multiple tools. Following a design research approach, a collaborative teaching experiment was conducted with a ninth-grade algebra teacher in which instruction was guided by a specifically designed sequence of tasks, techniques using paper-and-pencil and computer algebra systems (CAS), and theory on a hypothesized progression of learning. Retrospective analyses of data informed revisions to a resulting progression of learning and activity sequence that are being tested with pre-service secondary mathematics teachers. [For the complete proceedings, see ED584443.]