Preservice Teachers' Perceptions of Mathematics: Metaphors as a Vehicle for Exploring
Wolodko, Brenda L., Willson, Katherine J., Johnson, Richard E., Teaching Children Mathematics
Many elementary preservice teachers begin our mathematics methods course anxious about learning and teaching mathematics. Students often approach us privately during the first week of class to talk about their past experiences. They explain that they dislike mathematics because they struggled in school or had poor mathematics teachers. Some express apprehension about the content of the course and ask questions such as, "Are we going to be doing much work with fractions or algebra?" Many of these students tell us that their anxiety began in elementary school. We often find that these anxious students are reluctant to participate in class, even though we model constructivist principles throughout the course by actively engaging the students in learning and encouraging oral and written discourse.
Loewenberg Ball (1990, p. 12) states that "teachers, equipped with vivid images to guide their actions, are inclined to teach just as they were taught." Our challenge is to help preservice teachers confront their past experiences and anxieties about the teaching and learning of mathematics. If these are openly dealt with during their university education, fewer teachers may be content to teach just as they have been taught.
To learn and to teach, one must have an awareness of leaving something behind while reaching toward something new (Greene 1995). This year, we tried a new approach to addressing mathematics anxiety issues. Our goal was to have students examine their past experiences as mathematics learners and begin to explore the impact of these experiences on their future teaching. This article describes the use of metaphors to explore perceptions of the learning and teaching of mathematics.
Metaphor is part of our everyday lives. The way that we think, communicate, and build knowledge is based partly on the metaphorical way in which we think. "The essence of metaphor is understanding and experiencing one thing in terms of another" (Lakoff and Johnson 1980, p. 5). Webster's New World Dictionary and Thesaurus (1997) defines metaphor as "a figure of speech containing an implied comparison, in which a word or phrase ordinarily and primarily used for one thing is applied to another (Ex.: the curtain of night, all the world is a stage)."
The metaphors that we live by have an impact on the way we view learning and teaching mathematics. For example, one metaphor for teaching views the learner as an "empty vessel," while another views the learner as a "tool box" equipped with different tools or strategies with which to solve problems. The empty vessel metaphor describes knowledge as a substance to be attained. When a student is viewed as a vessel, the teacher attempts to fill the vessel with his or her knowledge through practices such as lecturing. In this metaphor, knowledge is viewed as a substance outside the child. Learning occurs when knowledge is "put inside" the child. Common phrases such as "attaining knowledge" or "grasping an idea" are examples of this view that are used in everyday language. Principles and Standards for School Mathematics (NCTM 2000, p. 20) presents a constructivist notion of learning and teaching in which metaphors such as "empty vessel" are no longer helpful. A primary learning principle in this document is that "students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge." Most of our preservice students still talk about experiencing traditional mathematical practices in elementary school. These future teachers face the challenge of building a bridge between previous frameworks for understanding and present frameworks for learning and teaching mathematics.
Recognizing the impact of personal metaphors on perceptions of teaching and learning mathematics, we wondered if exploring these metaphors would help our university students voice their mathematics anxieties and begin a conversation of change. …