Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10–11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants’ ability to evaluate and attend to the cognitive demand of problems.

应对数学问题是课堂上的一项核心活动。教师选择的问题决定了教室中发生的数学内容，过程和数学探究的性质，从而有助于数学技能和性格的发展。因此，对于准和实践的教师来说，选择，设计或重新定义数学问题是一项关键技能。这项研究探讨了数学写信倡议对发展28位准小学教师的问题提出技巧的影响。我们检查了由准教师设计的数学问题的特征，以及他们对10-11岁的孩子完成为期12周的信函写作计划之前和之后对构成良好数学问题的理解。对数据的分析揭示了参与该计划的好处，这在几个问题特征的改善中得到了证明。多种方法和多种解决方案问题的数量以及所提出问题的认知需求水平都在增加。提出非传统问题的挑战，以及为成功提供机会的竞争要求，可能已经削弱了参与者评估和关注问题的认知需求的能力。