Mathematical practices are everywhere: The intersections of pre-service teacher claims, non-mathematics-education faculty claims, and observable actions

Mathematics traditionally has been taught in a way that reifies the cultural belief that it is discrete in nature and, therefore, irrelevant to other content areas and the real world. National Council of Teachers of Mathematics, inclusive of mathematics teacher educators, views this belief as unproductive to learning and has stressed the need for students to make connections between mathematical content areas, to other disciplines, and to the real world. Unfortunately, many teacher-preparation programs (TPPs) structurally are organized with overt divisions between content areas, which likely perpetuates the belief that mathematics is disconnected and irrelevant. Nonetheless, this project was motivated by the hope that at the individual classroom level within such TPPs, non-mathematics teacher educators (TEs) were integrating mathematical practices and, thus, assisting in changing this unproductive belief. An analysis was completed of a three-part, data-collection process of (a) 180 pre-service teachers' assignments requiring that they align activities from non-mathematics education courses with mathematical practices; (b) 16 TEs' questionnaire data on how they use mathematical practices in their instruction; and (c) 11 full-class, video-taped observations of TEs teaching. Findings revealed that TEs do implement mathematical practices but do not claim always that this is what they are doing.