CP 90-3 With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics.
Abstract
Much current educational discourse centers on the importance of teachers' subject matter knowledge. Complementing concerns for subject matter knowledge is energetic interest in developing and studying alternative pedagogies that emphasize active learning and meaningful engagement. Both strands of the discourse are threaded with rhetoric about "understanding," "authenticity," and "genuineness"__about building bridges between the experiences of the child and the knowledge of the expert. Teaching and learning would be improved, so the argument goes, if classrooms were organized to engage students in authentic tasks, guided by teachers with deep disciplinary understandings. Students would conjecture, experiment, and make arguments; they would frame and solve problems; they would read, write, and create things that mattered to them. This paper examines the challenge of creating classroom practices in the spirit of these ideals. With a window on her own teaching, the author presents three dilemmas__of content, discourse, and community__that arise in trying to teach mathematics to third graders in ways that are, in Bruner's (1960) terms, "intellectually honest." These dilemmas arise reasonably from competing and worthwhile aims and from the uncertainties and complexities inherent in striving to attain them. The paper traces and explores the author's framing of and response to these dilemmas, providing a view of the pedagogical complexities that underlie current educational discourse and raising questions about the conditions necessary to support teachers' efforts to link students with mathematics in intellectually honest ways.