This study explores narratives about critical moments in mathematics learning written by K-8 pre-service teachers’ (PSTs) in the United States over a 20-year period. These critical moments, such as a single memorable task, course, test, or comment from a teacher, had a powerful and sustained impact on PSTs’ mathematics identities, which they carried with them as they entered the teaching profession. We classified narratives using McCulloch et al. (Sch Sci Math 113(8):380–389, 2013) and Drake’s (J Math Teach Educ 9(6):579–608, 2006) categories and found a potentially new category, Taking the Reins. We also classified PSTs’ mathematics orientations as either relational (oriented toward creative problem solving and conceptual understanding) or instrumental (enacting rote procedures without meaning) (Skemp in Math Teach 77(1):20–26, 1976). Many PSTs identified a causal relationship between their mathematics orientations and narrative arcs: relational learning opportunities encouraged positive narratives, while instrumental learning opportunities either resulted in negative narrative arcs or positive but fragile mathematics identities that crumbled under minor stress. We found little variation over time in the nature and prevalence of the narrative arcs and mathematics orientations, suggesting that any changes in mathematics teaching practices over time were not reflected in students’ learning experiences.

这项研究探讨了由美国K-8职前教师（PST）撰写的有关数学学习中关键时刻的叙事，历时20年。这些关键时刻，例如单个难忘的任务，课程，测试或老师的评论，对PST的数学身份产生了强大而持续的影响，这些身份在他们进入教学行业时就随身携带。我们使用McCulloch等人对叙事进行分类。（Sch Sci Math 113（8）：380–389，2013）和Drake's（J Math Teach Educ 9（6）：579–608，2006）类别，发现了一个潜在的新类别，即“ Taking绳”。我们还将PST的数学方向分为关系型（面向创造性的问题解决和概念理解）或工具性（实施无意义的死记硬背程序）（Skemp in Math Teach 77（1）：20-26，1976）。许多PST都确定了他们的数学取向和叙述弧之间的因果关系：关系学习机会鼓励积极的叙述，而工具学习机会要么导致负面的叙述弧，要么产生积极但脆弱的数学身份，在很小的压力下就崩溃了。我们发现叙事弧和数学取向的性质和普遍程度随时间变化不大，这表明数学教学实践随时间的任何变化都不会反映在学生的学习经历中。工具学习的机会要么导致负面的叙述弧，要么产生积极但脆弱的数学身份，这些身份在较小的压力下崩溃。我们发现叙事弧和数学取向的性质和普遍程度随时间变化不大，这表明数学教学实践随时间的任何变化都不会反映在学生的学习经历中。工具学习的机会要么导致负面的叙述弧，要么产生积极但脆弱的数学身份，这些身份在较小的压力下崩溃。我们发现叙事弧和数学取向的性质和普遍程度随时间变化不大，这表明数学教学实践随时间的任何变化都不会反映在学生的学习经历中。