ABSTRACT. Many mathematics educators have found that prospective elementary school teachers' beliefs interfere with their learning of mathematics. Often teacher educators consider these beliefs to be wrong or naïve and seek to challenge them so prospective teachers will reject them for more generative beliefs. Because of the resilience of prospective teachers' beliefs in response to these challenges, teacher educators could consider alternative ways of thinking about and addressing beliefs, particularly the potential of building on rather than tearing down pre-existing beliefs. Data from an earlyfield experience linked to a mathematics-for-teachers course provide evidence that when prospective teachers work intimately with children, in this case trying to teach 10-yearolds about fractions, the experience has the intensity from which beliefs can grow. Most of the prospective teachers in the study were surprised that mathematics teaching was more difficult than they had anticipated. They began to consider the importance of providing children time to think when solving mathematical problems. The change described in the study is incremental rather than monumental, suggesting that building upon prospective teachers' existing beliefs will be a gradual process.

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Learning to teach is rife with challenges. Preservice teachers’ self-efficacy can potentially mitigate the stress of these challenges, and teacher education programs are fundamental in helping them build this important resource. As such, understanding the foundations of self-efficacy is important for researchers and teacher educators alike. Grounding our study in social network theory, we explored the relationship between sense of belonging to a teacher education program, network centrality, and self-efficacy. Our sample included 245 preservice teachers in three university teacher education programs. We found that sense of belonging to the program and network centrality (in-degree and out-degree) were significantly and positively related to preservice teachers’ self-efficacy beliefs. This study builds on a growing literature that explores the relationships between preservice teachers’ social networks and their beliefs and practices.

Because of the role beliefs play in the teaching

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