Thesis for the degree Doctor of Philosophy

In this paper we investigate task design in an unusual professionaldevelopment course for elementary school teachers, conceived and taught byresearch mathematicians. Prior analysis singled out relevance for teaching as acritical design issue for engaging teachers in effective learning. The aim of thecurrent research is to uncover how relevance for teaching was achieved withoutcompromising mathematical rigor and depth. Findings are based on an analysisof three representative cases of task designing in which the authors whereinvolved – one as instructor and task designer, the other as participant observer.Our analysis reveals a designing model that first addresses purely mathematicalconcerns and then refines tasks, taking into consideration a series of constraintsimposed by the requirement of relevance for teaching. Using Schoenfeld'sResources-Orientations-Goals framework for decision making, we show howthe mathematicians drew on their special knowledge of mathematical content toachieve such relevance in ingenious ways. We find that tasks are best alignedwith Knowles's principles of Adult Learning in cases where the designersappropriated the teachers' point of view, no longer seeing the need for relevanceas a constraining imposition, but rather as an opportunity to combine and mergeknowledge specific for teaching and purely mathematical knowledge.