When the mathematics gets lost in didactics

This study shows how six elementary teachers, construed locally as effective, interpreted and were observed to enact the same curricular and didactical language very differently. One group of three provided high-level cognitively challenging tasks to engage children in mathematics. A second group of three, ensuring their children enjoy mathematics, subordinated mathematical learning to an emphasis on didactics. The actions of this second group made mathematics invisible. Introduction The theme of this conference, asking us to reflect upon the development of mathematics teaching through design, scale and effect, led me to reanalyse data from a larger recent study of English elementary teachers’ beliefs and practice. The study looked in-depth not only at how six teachers taught mathematics but, more importantly, justified the ways in which they presented the subject. The results were both surprising and cautionary. All teachers espoused a rich problem-solving environment, but in reality, the manifestations of their beliefs varied greatly. Why? This paper reports on how the mathematical learning intentions of a teacher can get lost in the attention paid to didactics. The paper that follows is a consequence of a constant comparative analysis that yielded five categories of mathematics-related didactics common to all six teachers. However, despite their explicit mathematical focus, the extent to which mathematical learning was evident in their practice varied considerably. These categories were: the role of prior knowledge; the creation of mathematical connections; mathematical vocabulary; mathematical reasoning and rich mathematical tasks. Drawing on the traditions of grounded theory from which the constant comparison process derives (Glaser and Strauss, 1967), the following discusses briefly, and atypically for a research paper, the literature pertaining to these categories prior to a more lengthy discussion of the methodology adopted in the study. Prior Knowledge The activation of students’ prior knowledge has long been associated with constructivist perspectives on learning whereby “information is retained and understood through elaboration and construction of connections between prior