This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth.

这篇研究文章为越来越多的文献做出了贡献，这些文献强调了通过涉及创造性冒险和基于失败的学习的设计周期来实现数学教育创新的潜力。具体来说，我们探讨了故事圈（一种以教师协作为中心的基于实践的专业发展方法）的“失败”周期如何有效地促进了项目内的创新。我们的重点是在故事圈内启用反馈机制的努力中出现的挑战该系统支持教师在协作开发课程并扩展数学教学的集体知识库时质疑自己的教学实践。通过三个挑战的例子，我们说明了各种课程工件，包括教师在预期实施时构建的课程工件和从实际实施中提取的课程工件，如何未能成为支持教师成长的唯一反馈来源。