One goal in teacher education is to prepare prospective teachers (PTs) for a career of systematic re_ ection and learning from their own teaching. One important skill involved in systematic re_ ection, which has received little research attention, is linking teaching actions with their outcomes on student learning; such links have been termed hypotheses. We developed an assessment task to investigate PTs' ability to create such hypotheses, prior to instruction. PTs (N = 16) each read a mathematics lesson transcript and then responded to four question prompts. The four prompts were designed to vary along research-based criteria to examine whether different contexts in_ uenced PTs' enactment of their hypothesizing skills. Results suggest that the assessment did capture PTs' hypothesizing ability and that there is room for teacher educators to help PTs develop better hypothesis skills. Additional analysis of the assessment task showed that the type of question prompt used had only minimal effect on PTs' responses.
Christine Phelps-Gregory and Sandy M. Spitzer
Linda L. Cooper, Sandy M. Spitzer and Ming C. Tomayko
Students discover why certain regular polygons tessellate and how M. C. Escher translated and rotated modifications of polygons to create tessellations.
Anne K. Morris, James Hiebert and Sandy M. Spitzer
The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one's teaching. Thirty K–8 preservice teachers completed 4 written tasks. Each task specified a learning goal and then asked the preservice teachers to complete a teaching activity with this goal in mind. For example, preservice teachers were asked to evaluate whether a student's responses to a series of mathematics problems showed understanding of decimal number addition. The results indicate that preservice teachers can identify mathematical subconcepts of learning goals in supportive contexts but do not spontaneously apply a strategy of unpacking learning goals to plan for, or evaluate, teaching and learning. Implications for preservice education are discussed.