Epistemology, Ontology, and Method: Comments on Tiberghien’s and Dreyfus’ Papers

ion starts from an initial, simple, undeveloped first form, which need not be internally and externally consistent. The development of abstraction proceeds from analysis, at the initial stage of the abstraction, to synthesis. It ends with a consistent and elaborate final form. It does not lead from concrete to abstract but from an undeveloped to a developed form of abstract in which new features of the concrete are emphasized. In other words, the activity itself can be the initial, simple, undeveloped first form of the abstraction that will come. This is an appealing position because, as instructional designers, everything we ask students to do can be leveraged with regard to processes of abstraction and generaliztion. However, as I noted already, without a theory of mathematical thinking with regard to what we want students to learn, the design process will remain intuitive and unsystematized. (To be developed: DG seems to be on the verge of using activity theory in a way that confounds ONT1 and ONT2, as discussed earlier.)