Building the Foundation: Whole Numbers in the Primary Grades

Abstract

Teachers are accountable for classroom interactions and pupils’ work assessment. However, those visible actions are only a part of teachers’ work, and include also. (1) Planning not only a single lesson but also a sequence of lessons and more gener-ally thinking about and designing the entire mathematical theme (for instance, WNA as a whole). This usually depends on use of resources that are selected by the teacher. (2) Selecting the physical objects to be used during the lesson (or the sequence of lessons), the textbook which can be used by the pupils and/or by the teacher as a source of inspiration, the tasks that might be designed by others and are available (by sharing with colleagues, by browsing the Internet, etc.), the items for the assessment, etc. These aspects of teaching require teacher knowledge, which is not easily observed, since it is accessible only by means of what the teacher might say about her activity, which is always a reconstruction on her part, and what the teacher is doing in the classroom, which is subject to diverse interpretations. Various aspects of teacher knowledge have been considered within different frameworks that all take into account pedagogical content knowledge (Shulman 1986 ). This model has been refined by Deborah Ball and her colleagues (Ball et al. 2008 ), who have examined the impact mathematical knowledge for teaching on the quality of instruction (Hill et al. 2008 ). It is thus my purpose to highlight some aspects of whole number arithmetic knowledge for teaching which seem important to promote interest-dense situations (Bikner-Ahsbahs et al. 2014 ) and thus the development of pupils’ metacognitive strategies. The whole book containing this chapter is freely available on Springer web site (see DOI).