PISA is a large international educational assessment activity coordinated by the "Organization for Economic Co-operation and Development" (OECD). PISA's "Functional Literacy" emphasizes the theoretical concept of mathematics as a human activity. From this pedagogical point of view, PISA's "mathematization cycle"…

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…