In this paper, we report an enquiry into elementary preservice teachers’ learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers’ prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective “spection” in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers’ retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices.

在本文中，我们报告了对小学学前班教师学习的一种询问，因为他们从事自己的数学学习。作为一组研究人员，他们在英语大学中从事初级教师基础教育，我们共同计划并教授了有关增长模式概括的会议。会议结束后，对两所大学的15名职前教师进行了访谈，重点是他们对数学活动方法的明确认识。还检查了职前教师在课堂上对类似活动的前瞻性计划和教学后评估。在教师学习的背景下，我们借鉴了积极主义的方面和反思性“选择”的概念，追踪了职前教师对学习的回顾和对教学的期望之间的关系。我们的分析表明，对自己的概括过程的敏感性不断提高，为新手教师提供了对不同教学方法进行有意识地回应而不是做出冲动反应的机会。本文通过研究如何对初学者进行回顾性分析，为新手小学教师的回顾性思考提供了一个新的维度。不仅是在教学上做数学，而且可以做数学，这可以促进数学教学专业知识的增长。我们认为，聘用职前数学老师来支持对他们的数学学习进行有意的回顾性分析以及对教学影响的前瞻性考虑可以实现更为关键的教学选择。