2013 Conference Proceedings - University of Nevada, Las Vegas

Popularity tallied whether or not a student or teacher used a given metaphor. The need for bothquantitative analyses was necessary to verify that one students’ abundant use of one sourcedomain did not bias the results. For example, what if a student used the source domain ofJOURNEY associated with the target domain PROBLEM SOLVING 100 times in the interviewwhile another student frequented the term only once? This may skew the data if frequency alonewas studied. Thus popularity was a means to verify internal validity for this methodology.ResultsThe CMT analysis discovered some surprising relationships (and lack thereof) betweenteacher and student thinking. Table 1 is a list of source domains used by students, and sourcedomains used by teachers related to problem solving.Table 1Teacher and Student Source Domains Associated with Mathematical Problem SolvingStudent(22)Teacher(22)ABILITIES, ACQUISITION, APPROXIMATING, BUILDING, CALCULATING,COMPARING, CONDITIONAL, CONTEST, CONVINCING, DISCOVERY,EXPERIMENTING, IMAGINING, JOURNEY, PARTITIONING, PROCESS,PROVING, REVIEWING, SEARCHING, THINKING, VISUALIZATION,VOCALIZATION, WARACQUISITION, BUILDING, CHANGE OF STATES, CONFLICT, DISCOVERY,DOING BUSINESS, FAMILIARITY, GENERALIZING, HABITS, IMAGINING,JOURNEY, PARTITIONING, PROCESS, REVIEWING, RACE, RULES,SEARCHING, SETS OF SKILLS, TOOLBOX, VISUALIZATION, UP, WARThere is a significant overlap between student and teacher source domains. Students used a totalof 22 source domains while teachers used 22 source domains. There were significantly morestudent interviews than teacher interviews, so it is natural that the diversity in metaphors usedwere in the students’ favor.There were source domains used by the teacher which were lacking in the student’s sourcedomains. For example, one teacher used the conceptual metaphor of PROBLEM SOLVING ISDISSECTING.“They’ve been taking these shapes and breaking them up and dissecting them intovarious more familiar shapes…. because the triangle ends up being the right triangle,they’ll look at that and dissect into those two triangles . . . We’ve talked about dissectingthe problem. I think they will see this as being easier to dissect than it will be so surroundthe shape with a rectangle and subtract the triangle…”Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 174