INTRODUCTION

This paper reports on the beliefs that ninth and tenth grade students have about mathematics. These beliefs were revealed using contemporary metaphor theory. An analysis of the students' metaphors for mathematics indicated that students had well developed and complex views about mathematics including math as: an Interconnected Structure, a Hierarchical Structure, a Journey of Discovery, an Uncertain Journey, and a Tool. The other common themes that were revealed were that perseverance is needed for success in mathematics and that some students view their role in learning math as active while others view their role as passive. Introduction Students have broad views about the nature of mathematics and about their role in the learning of mathematics. These views are linked to interpretations of how mathematics is played out in their own lives, both within and outside of school. Contemporary metaphor theory provides a means of unpacking the beliefs that students have about mathematics. Identifying and understanding students’ metaphors for mathematics will provide mathematics professionals with a window into students’ internalized views about mathematics. Such understanding informs how beliefs influence students’ acquisition and practice of mathematics (see Leder, Pehkonen, & Torner, G., 2002; Pajares, 1992; Posner et. al., 1982). The purpose of this study is to determine students’ beliefs about mathematics using metaphor theory. The study was guided by two main research questions: What metaphors do ninth and tenth grade students use to describe mathematics? What do these metaphors reveal about students' beliefs about mathematics? Literature Review Metaphors allow students to work with novel or abstract ideas by mapping them into strong, meaningful images that were originally developed in a different context (Davis, 1984). Ashton (1994) stated that: “An essential feature of metaphor is that it demands the interpreter becomes actively involved in searching for meaning. This is done by seeking for elements that the two parts of the metaphor have in common in order to share insight.”(p. 358) Metaphors are “very private, personal, and ripe with meaning for an individual (Presmeg, 1997, p. 277). According to Lakoff and Johnson (1980), metaphor is of fundamental importance to meaning making. That is, how we think is fundamentally metaphorical. Creating metaphors helps us to structure our experiences. Contemporary metaphor theory is situated within the psychology of embodied cognition, which emphasizes the social context and origins of knowledge and thus critiques mathematical absolutism (i.e. denies the independent existence of mathematics). In the subjectivist embodied cognition framework, the main question of interest is: “What does each student think mathematics is really about?” With contemporary metaphor theory, poetic metaphors such as “Death is the mother of beauty” (Stevens, 1954) are considered specific cases of the ordinary, everyday metaphors that are pervasive in our daily lives (Lakoff, 1993). Within this framework “...the locus of metaphor is not in language at all, but in the way we conceptualize one mental domain in terms of another” (Lakoff, 1993, p. 203). In this study, we will use the following operational definition of metaphor. A metaphor is the recursive movement between a source and a target that are structurally similar, both changing through the dynamic process of learning (Lakoff & Johnson, 1980, Lakoff & Nunez, 1997).