for the learning of mathematics

an international journal of mathematics education

Marcy B. Wood - Vol. 30 Num. 3 (2010)
 Not understanding Andy: a metaphorical analysis of students’ resistance to learning


Metaphors are a fundamental mechanism we use to make sense of our world. They structure our interpretations of and interactions with ideas, including mathematical ideas. Thus, the sense students make out of mathematical ideas depends upon the metaphor they use to structure their thinking. This paper examines the metaphors used in one fourth-grade classroom as students engage with ideas about fractions. Most of the students in the classroom used 'fraction as container' and 'fraction as piece metaphors,' while one student, Andy, used a conceptual blend of two metaphors: 'fraction as piece' and 'fraction as number.' Because Andy’s use of metaphors did not match that of his classmates, his talk and reasoning about fractions were not well understood by most of the other students. This finding suggests that metaphorical analysis may be a productive tool for making sense of differences in communication and understanding across various constituents of mathematics classrooms.