This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors’ beliefs associated with teaching philosophies influence both the content that prospective teachers have the opportunity to learn (what) and the nature of the prospective teachers’ opportunities to learn (how). Through analytic induction, three assertions were developed to understand and explicate: similarities in opportunities to learn, differences in opportunities to learn, and perceptions about the purpose of the methods courses across the three cases. Specifically, the first assertion examines how all three methods instructors focused on developing conceptual understanding and combating mathematical misconceptions for which prospective teachers most often experience opportunities to learn through representations and approximations. The second and third assertions place more emphasis on differences across the cases based upon observed instructor actions and their beliefs. This study is significant because it helps us gain a deeper understanding about prospective teachers’ opportunities to learn within one teacher education program, and therefore, may point toward what can be done in the future to better prepare teachers in elementary mathematics education and the development of ambitious instruction. Additionally, this study unpacks how prospective teachers in the same teacher education program may have varying experiences and thus varied access to opportunities to learn.

这项多案例研究研究了三种基本数学方法的讲师如何在同一个教师教育计划中为他们的准教师提供学习机会。通过访谈，课堂观察和人工制品收集定性数据。研究结果表明，教师与教学理念相关的信念既影响准教师有机会学习的内容（什么），也影响准教师学习机会的性质（如何）。通过分析归纳，提出了三个主张来理解和说明：在三个案例中学习机会的相似性，学习机会的差异以及对方法课程目的的看法。具体而言，第一个断言考察了这三种方法的讲师如何集中精力发展概念性理解并消除数学上的误解，因为准教师最常通过表述和近似来体验学习的机会。第二和第三断言更加强调了基于观察到的教师行为及其信念的案例之间的差异。这项研究意义重大，因为它可以帮助我们更深入地了解准教师在一个教师教育计划中的学习机会，因此，可能会指出将来可以做些什么，以更好地为基础数学教育的老师和发展雄心勃勃的教学做准备。此外，本研究还揭示了在同一教师教育计划中的准教师可能会有不同的经历，从而获得学习机会的途径也有所不同。