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 naive 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 early-field 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-year-olds 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.