5: Concentric Task Sequences: A Model for Advancing Instruction Based on Student Thinking

There is wide agreement about the complexity of teaching mathematics and the difficulty of learning to do it well (e.g., Ball & Cohen, 1999; Borko & Putnam, 1996; National Council of Teachers of Mathematics [NCTM], 2000). Most secondary mathematics teacher education programs have at least one course dedicated to mathematics-specific methodology and some have as many as three or four such courses. A study of syllabi for these courses, however, showed little consistency in the content they contain or even in their goals (Ronau & Taylor, 2006). In the interest of contributing to dialogue about what could, and perhaps should, be in a secondary mathematics methods course, we describe a particular approach we have used in our course—what we call concentric task sequences—and share some thinking behind this approach and ways it has supported preservice teachers’ development. We conclude by reflecting on how our collaboration has served as professional development for us as teacher educators.