ABSTRACT

Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students’ mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students’ written work. In interviews, participants solved mathematical tasks and the analyzed student written work in order to make assertions about student understanding. Analysis of participants’ assertions revealed three primary reasoning strategies: mathematical reasoning, pedagogical reasoning, and reasoning through self-comparison. Self-comparison involved participants comparing the student work directly with their own work on the task. This strategy showed promise, as it could be used to help make inferential assertions about student understanding. It also highlighted areas of caution around how beginning pre-service teachers might make use of evidence. This study contributes to the existing literature around noticing student thinking in written work by highlighting the significance of reasoning through self-comparison.

摘要

通过书面工作来分析和解释学生的思维是一种关键的，常常是挑战性的教学实践。它需要注意学生的数学思维并利用数学知识进行教学。这项研究调查了职前中学教师在他们的写作准备工作初期是如何进行写作的。在访谈中，参与者解决了数学任务，并分析了学生的书面作业，以便对学生的理解力做出断言。对参与者的主张的分析揭示了三种主要的推理策略：数学推理，教学论推理和通过自我比较的推理。自我比较涉及参与者将学生的工作与自己在任务上的工作直接进行比较。这个策略显示出希望，因为它可以用来帮助对学生的理解作出推断。它还强调了有关岗前教师如何利用证据的注意事项。这项研究通过强调通过自我比较进行推理的重要性，为围绕写作中注意学生思维的现有文献做出了贡献。