As Bass (2017) observed, there has been much attention in education on problemsolving and substantially less on theory building.Moreover, as Bass demonstrated,without some analysis of commonalities, it would be hard to connect problemsolving in one area to another.We see this chapter as highlighting where boththeory building and problem solving contribute to articulating connections amongtransformations at the secondary level and abstract algebra;and demonstrate thatGHOMs can be used to make those connections.We now turn to our three situations.Reconciling Definitions for CongruenceEven among materials presenting geometry from a transformational approach,definitions for congruence appear to differ:
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