2013 Conference Proceedings - University of Nevada, Las Vegas

curriculum locally, within individual classrooms. Distributed cognition allows students’ externalexperiences to aid their learning within the classroom, if the teacher is willing to let the studentexpress re-presentations(Glasersfeld, 1991) of those experiences. Metaphors are naturalexpressions of shared experience. Often within education, the purpose of metaphors are to shareone person’s experiences through common experiences (or experiences believed to be common)(Ortony, 1993).A conceptual metaphor is a mapping, an identification of the experience to be expressed (thetarget domain) and the experience to be shared (the source domain) (Lakoff & Johnson, 1980).For example, a student said during my interviews, “to solve it for me, it meant that I had to findit somehow.” Thus the student used the conceptual metaphor: PROBLEM SOLVING ISSEARCHING. Thus the student was sharing how their understanding of problem solving (targetdomain) is perceived as searching (source domain) (Kövecses & Benczes, 2010). The studentcommunicates this because they believe the researcher has shared the experience of searchingand so relates this perception to the researcher. Due to the specifics of each domain, it isimportant to note that this is a unilateral relation: TARGET DOMAIN SOURCE DOMAIN.The method of identifying conceptual metaphors and interpreting their purpose and meaningwas first accomplished by Lakoff and Johnson (1980). Lakoff and Nunez (2000) expanded onthis idea to create Conceptual Metaphor Theory (CMT) and Danesi (2007) applied it to middleschool mathematics teachers. Kovecses and Benczes (2010) offered the first technique oflooking for coherency concretely using CMT analysis in linguistics by identifying a conceptualmetaphorical system. However, these methods were always narrative, interpretive, andqualitative methodologies. Moreover, there was a lacking of quantitative analysis from a postpositivistperspective allowing probability of metaphors to solidify the validity of a givenmetaphorical system. This is where my study takes shape and has generated a uniquemethodology that is replicable, but more importantly, a practical means to aid teachers inlistening to their students meaning.ParticipantsParticipants for this study included students from multiple honors geometry classes and allhonors geometry teachers in a suburban high school. Honors geometry was chosen due to thestudy being volunteer-based and due to the proclivity for proof to have students express theirproblem solving ability (Lakatos, 1976). The students and teachers both met with the researchProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 172