Just what conceptualizations are students forming? Hamide Dogan-Dunlap UTEP

Metaphors and Reasoning in Mathematics “A figure of speech in which a word or phrase literally denoting one kind of object or idea is used in place of another to suggest a likeness or analogy between them” (Mish, 1991). Any metaphor one constructs will have both ground (similar) and tension (dissimilar) (Presmeg, 1998). Similarities between the objects involved in a metaphor constitute the ground, while dissimilarities constitute the tension (Presmeg, 1998).

Metaphors are implicit analogies Consisted of “Tenor/Target” and “vehicle/Source.” (English, ????chapter 6). “Graph is increasing” Target Source Graph is Increasing Similar elements (Sfard, 1994, p. 47)

“Function is getting closer to…” Target Source Function is getting closer Similar elements

the metaphor thinking of “function as a machine” includes the aspect that both objects allow one; to observe phenomena that might otherwise remain unseen. The tension of the metaphor includes the aspect that a machine is a physical object, while a metaphor is not.

Metaphor plays a prominent role in mathematical thinking. metaphors include thinking of a function as a machine (Cuevas & Yeatts, 2001). Limit as “end of an object.” Continouity as “a car (pencil) moving along a graph.”

Results from one mathematical domain applied to another (Geometry, Algebra…). Lakoff and Nunez (2000) have gone so far as to argue that the very substance of mathematical thinking is metaphorical in nature.

Metaphors used in conceptualization of mathematical function concept Target: Function in mathematics Source ?????? Similar elements ????

Students do use metaphors to make sense of mathematical information provided. Some however may not be able to determine the relevant similar elements between target and source. May form, as a result, misconceptions.

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