Teachers’ knowledge of students’ mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers’ mathematical knowledge and their knowledge of students’ mathematical thinking. The present study builds on this body of work to explain how such interplays occur. Over a semester, I worked in partnership with a secondary school mathematics teacher on cycles of task design, interactions with a student, and in-depth reflection on the student’s thinking about linear programming. Adopting and extending Piagetian constructs of assimilation and accommodation, I describe several key mental processes that illuminate the teacher’s learning of mathematics and of the student’s mathematical thinking. I conclude with a discussion of the study’s empirical and theoretical contributions to understanding teachers’ mathematical learning in relation to student thinking.

教师对学生数学思维的了解是数学教育中日益增长的研究领域。文献报道了大量证据表明教师的数学知识与学生的数学思维知识之间存在相互作用。本研究以这些工作为基础来解释这种相互作用是如何发生的。在一个学期的时间里，我与一位中学数学老师合作，​​进行任务设计、与学生互动以及深入反思学生对线性规划的思考。我采用并扩展了皮亚杰的同化和顺应结构，描述了几个关键的心理过程，这些过程阐明了教师的数学学习和学生的数学思维。最后，我讨论了该研究对理解教师数学学习与学生思维关系的实证和理论贡献。