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Anne K. Morris

The author presents a procedure for learning from variations that occur when instructors implement lesson plans designed by others. This kind of variation, occurring in many classrooms every day, can provide a source of information for improving curriculum, both in terms of instructional activities for students and especially in terms of clarifications for instructors to support more effective implementation. The author provides detailed descriptions, in the context of a mathematics course for preservice K-8 teachers, for using implementation variations in a practical, research-based way to study and improve teaching. The goal is to build an accumulating knowledge base for teacher education. Examples are presented to illustrate how increasingly rich lesson plans, based on observing implementation variations, can move toward achieving this goal.

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Anne K. Morris and James Hiebert

Two studies were conducted to identify the conditions under which instructors teaching the same mathematics teacher preparation course would continuously improve their shared instructional products (lesson plans for class sessions) using small amounts of data on preservice teacher performance. Findings indicated that when lesson-level student performance data were simply collected, by course section, the instructors could make important changes to the lessons but did not often do so. However, when the instructors were encouraged to compare data across semesters, they generated hypotheses that guided instructional improvements, which then were tested through multiple cycles. The cycles of hypothesis testing helped instructors clarify the goals for improvement, use the performance data to test whether changes were actually improvements, and reduce their tolerance for marginal student performance.

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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.