2013 Conference Proceedings - University of Nevada, Las Vegas

METAPHORS AS A MEDIUM FOR HERMENEUTIC LISTENING FOR TEACHERSSean YeeCalifornia State University, FullertonSyee@Fullerton.EduMetaphors span language in many forms. Mathematics educators regularly use metaphors torelate one mathematical concept in terms of another. Embedded within these concepts are a setof shared experiences that educators use to communicate new ideas to students. However,students also use metaphors to convey their experiences, perceptions, and understanding. Thispaper reports on a large mixed-methods study that discovered a coherent set of metaphors thathigh school students and teachers associated with mathematical problem solving. Moreover,this methodology helps teachers learn how to listen hermeneutically for student experiences.This methodology is being developed for teacher professional development.This study began with a pilot study that identified that high school students are capable ofusing complex metaphors (Lakoff, 1993) to describe their perceptions of mathematical problemsolving while solving problems. This allowed for a larger study to determine the existence of acoherent system of conceptual metaphors (Kovecses & Benczes, 2010) related to problemsolving used between teachers and their students. The results of this larger study are presented inthis paper. As with all good studies, the results have raised more questions than answers. Onesuch question was, “How are teachers listening to the students’ metaphors/experiences?”Surprisingly, the application of this study’s novel methodology (Conceptual Metaphor Theory,CMT) has demonstrated a means to listening in the classroom. Specifically, the researcheridentified that CMT analysis can move teachers from a constructivist paradigm of interpretivelistening to a hermeneutic model of listening for conceptual understanding (Davis, 1997).Related LiteratureThe Greek word, metaphora, means to transfer or carry over (Presmeg, 1997).Metaphors are currently defined as denoting one figure of speech as another (Merriam-Webster,2011). However, their use spans far beyond speech. Over the last 30 years, metaphors havebeen identified in language not only for communication, but for cognition and education (Sfard,1997; Lakoff & Johnson, 1980; Ortony, 1993). This advancement can be implemented in theclassroom to help improve student learning through teacher listening.Students bring significant experiences to the classroom that happen outside of school, yetteachers lack a means to access such experiences under a sociocultural theory (Cobb, 2007). Adistributed cognition theory (Cobb, 2007) allows such experiences to embed themselves on theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 171