2013 Conference Proceedings - University of Nevada, Las Vegas

Notice, there is no other experiential reference to dissection. The teacher never refers to cuttinginside or slicing or any surgical operation language. This is a demonstration of what Max Black(1962) referred to as dead metaphors due to their lack of interaction with other aspects of thecurrent experience and the rote use by the participant. Moreover, the source domain ofDISSECTING was never used by any students (including his).Additionally, different teachers used different source domains but to the same end. Teacher1said “hopefully one of those things that they have physically done will spark their memory”.Teacher2 states, “In my opinion that will be the first term that that jumps out at them.” Bothteachers are referring to recognizing/discovering information about the given hexagon. Whileone is referring to sparks and fire, the other is referring to “jumping out”. Both experiences ofignition of fire and jumping are actions that are perceived as sudden. Both actions are achanging of states, jumping is moving from static into motion, ignition is moving from notburning to burning quickly. Specifically, both actions do not indicate how the change of stateswas achieved, but is rather difficult to understand such a change. This leads back to the word“realize” as, again, the notion of how a student is to be aware of this transformation (spark orjump) is purposefully not described by the teachers. Thus the only coherent aspect of problemsolving that can be drawn from such complex, linking metaphors (Kövecses & Benczes, 2010) isthat PROBLEM SOLVING IS A CHANGE OF STATES.The quantitative results demonstrated a strong similarity between the most popular and mostfrequented source domains. Table 2 demonstrates these results:Table 2Comparison of Teacher and Student Source Domains for Problem SolvingStudents’ MostFrequented SourceDomainsStudents’ MostPopular SourceDomainsTeachers’ MostFrequented SourceDomainsTeachers’ MostPopular SourceDomains26% JOURNEY 95% JOURNEY 29% JOURNEY 100% JOURNEY18% SEARCHING 86% VISUALIZING 17% DISCOVERY 100% DISCOVERY13% VISUALIZING 82% SEARCHING 11% BUILDING 83% SEARCHING12% DISCOVERY 73% PROCESS 10% VISUALIZING 83% BUILDING9% PROCESS 68% BUILDING 7% PARTITIONING 67% VISUALIZING8% BUILDING 68% DISCOVERY 7% SEARCHING 50% PROCESS8% PARTITIONING 55% PARTITIONING 6% PROCESS 33% PARTITIONING33% RACE33% SETS OF SKILLSProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 175