Kazemi, Franke & Lampert (2009) defined ambitious teaching as teaching that “requires that teachers teach in response to what students do (emphasis in original) as they engage in problem solving performances, all while holding students accountable to learning goals that include procedural fluency, strategic competence, adaptive reasoning, and productive dispositions” (p. 1).
In an effort to prepare their preservice teachers to engage in these ambitious practices, the researchers chose a set of instructional activities that would enable their preservice teachers to learn the work of teaching, with the mathematics teacher educators teaching the work of teaching. This teaching and learning occurred across three dimensions: 1) principles of high quality teaching, 2) essential teaching practices which embody those principles and 3) mathematical concepts and processes to be learned that provide direction for teaching practices.
The instructional activities the researchers used in their study were 1) counting, 2) strategy sharing, 3) posing a sequence of related computational problems and 4) solving word problems (Kazemi, et al., 2009). The researchers worked in schools with children and experienced teachers to develop their instructional activities. They used the instructional activities with preservice teachers and then had them publically rehearse the instructional activities with their peers as the mathematics teacher educators coached them through the rehearsal.
What instructional activities do preservice teachers need to have opportunities to learn during their mathematics methods courses? By nature, these would vary across grade levels.