The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.

过去十年见证了基于标准的强烈呼吁，要求改进数学知识和方法。在美国，各地区已聘请指导教练来帮助教师将其教学从基于算法的指导转变为以学生为中心且在概念上侧重于目标的指导。这项研究的目的是促进该领域对以下方面的理解：（a）帮助教师制定更多基于概念的教学形式的特定教练做法；（b）教练如何学习制定这些做法。使用基于设计的实施研究方法，我们使用特定模型对教练进行了一对一的教练培训（基于内容的教练）；然后，教练与老师一起计划与教练模型保持一致的课程。数据由课前会议的录像带组成，这些录像带根据模型进行了转录和编码。对32位教练在2年内的实践进行的分析表明，我们的教练模型的三个组成部分（关注学生的思维，教学法和数学）均显示出随着时间的推移在统计学上的显着改善。通过对一位教练的五次教练会议进行的说明性分析，我们发现，从五个计划中的进展一直到一般策略水平的计划讨论，到关于特定任务教学的更具体的对话，再到将注意力集中在数学概念，学生思维上的更深入的讨论，已超过了五个会议，以及教学方法。我们认为，对教练学习的描述是为未来教练培训的设计奠定基础的重要的第一步。