2013 Conference Proceedings - University of Nevada, Las Vegas

for 10-15 minute interviews about specific problems from one of three recent commonassessments designed and determined by the teachers. The researcher chose problems that wouldrequire students and teachers to express their perceptions of problem solving. The researchwould first interview the honors geometry teachers and have them explain how they wouldexpect students to approach the problem. From the population of honors geometry students, theresearcher methodically randomized volunteers of the study by their teacher’s assessment of theirperformance. The study included 22 independent student interviews and 6 independent teacherinterviews.Novel MethodologyThe uniqueness of the methodology for this study stems from the two-step process ofidentifying the metaphors via a modified Interpretive Phenomenological Inquiry (IPA) (Eatough& Smith, 2008) that uses CMT analysis to identify conceptual metaphors, followed by aquantitative analysis of the frequency and popularity of conceptual metaphors to identify acoherent subset that are commonly used for the classroom. In the former step, IPA is morecomplicated than classical phenomenological studies because coding the data is not performedby identifying identical words used by the participants. Conceptual metaphors are identified byrelationships and association, thus two students could use the same source domain for the targetdomain of mathematical problem solving without using similar words: “I was thinking it would be the easiest way.” “I just go right into it because I know how to solve these.”Both of these literal metaphors from participants of the study create the same conceptualmetaphor, PROBLEM SOLVING IS A JOURNEY, without using similar words. The codingoccurs with the shared experience, the source domain. These source domains were notpreviously categorized as this was a phenomenological design. Often, the coding requirescorroboration by context and student elaboration. Thus the interviews with students were semistructuredso as to allow the researcher to ask the participant to elaborate on their understanding.After completing the qualitative stage via CMT analysis, this study focused on understandingstudents’ metaphors for mathematical problem solving, and thus the source domains associatedwith the target domain of problem solving. Results were tallied quantitatively within twodimensions: popularity and frequency. Frequency tallied all of the source domains and brokedown, by percentage, which source domains were most frequented by students and teachers.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 173