Distinct targeting of multiple mathematical proficiencies in first-year service teaching

Abstract

Mathematics students need to develop several distinct proficiencies simultaneously. These include procedural fluency, strategic competence, adaptive reasoning, conceptual understanding and a productive disposition towards the subject. These distinctions can be made explicit to students and they are given differentiated learning outcomes, activities and assessments. Procedural fluency requires repetition and immediate and personalised feedback; this is provided through online formative assessment tasks. Valuable tutorial time can then be devoted to strategic competence and adaptive reasoning with extended problems drawn from different domains. Conceptual understanding is aided by drawing analogies between concrete examples from different disciplines and subsequently abstracting key concepts. A productive disposition is inculcated by embedding all activities in an authentic context and using contemporary and thought provoking applications.