Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors. Twenty-two high-school student and six teacher interviews demonstrated a rich foundation for these shared experiences by identifying the conceptual metaphors. This mixed-methods approach qualitatively identified conceptual metaphors via interpretive phenomenology and then quantitatively analyzed the frequency and popularity of the metaphors to explore whether a coherent metaphorical system exists with teachers and students. This study identified the existence of a set of metaphors that describe how multiple classrooms of geometry students and teachers make sense of mathematical problem solving. Moreover, this study determined that the most popular metaphors for problem solving were shared by both students and teachers. The existence of a coherent set of metaphors for problem solving creates a discursive space for teachers to converse with students about problem solving concretely. Moreover, the methodology provides a means to address other complex concepts in STEM education fields that revolve around experiential understanding.

中文翻译：

---

学生和教师解决数学问题的概念隐喻

数学教师经常使用隐喻来将课堂中困难或复杂的概念联系起来。数学教育和大多数基于 STEM 的教育课程中关注的一个复杂主题是解决问题。这项研究确定了学生和教师如何通过他们选择的隐喻将数学问题解决置于情境中。通过识别概念隐喻，对 22 名高中生和 6 名教师的采访展示了这些共享经验的丰富基础。这种混合方法通过解释现象学定性地识别概念隐喻，然后定量分析隐喻的频率和流行度，以探索是否存在与教师和学生一致的隐喻系统。这项研究确定了一组隐喻的存在，这些隐喻描述了几何学生和教师的多个课堂如何理解数学问题的解决。此外，这项研究确定了最流行的问题解决隐喻是学生和教师共享的。一套连贯的问题解决隐喻的存在为教师与学生具体讨论问题解决创造了一个话语空间。此外，该方法论提供了一种方法来解决 STEM 教育领域中围绕经验理解的其他复杂概念。一套连贯的问题解决隐喻的存在为教师与学生具体讨论问题解决创造了一个话语空间。此外，该方法提供了一种方法来解决 STEM 教育领域中围绕经验理解的其他复杂概念。一套连贯的问题解决隐喻的存在为教师与学生具体讨论问题解决创造了一个话语空间。此外，该方法提供了一种方法来解决 STEM 教育领域中围绕经验理解的其他复杂概念。