Just Tell Us the Rule: Learning to Teach Elementary Mathematics

Abstract

In this article, I address a major problem in the education of elementary teachers; namely, that teacher education programs constitute a relatively weak intervention (Ball, 1988; Borko et al., 1992; Evans, 1987; Speedy, Fensham, & Annise, 1989). Preservice teacher education in mathematics, for example, often has a limited effect on student teachers' willingness to learn and teach mathematics for relational understanding. Relational understanding, in Skemp's (1989) terms, is knowing both what to do and why (p. 2) and may be distinguished from instrumental understanding--the application of rules without reason. Initial surveys of student teachers entering the present undergraduate teacher education course demonstrate that most student teachers view the task of teaching mathematics instrumentally; they see mathematics as a set of rules not readily understood that must be memorized (Hill, 1994). The present mathematics methods program aims to achieve significant change in this attitude despite the daunting body of evidence indicating that such long-held attitudes are notoriously resilient (Ball, 1990). I investigated whether the mathematics methods program significantly facilitates preservice elementary teachers' willingness to learn and teach mathematics for relational understanding. The central aim of the methods program is to encourage student teachers to value this type of understanding. Only if student teachers value it will they want to teach in a way that facilitates children's relational understanding. The findings indicate that engaging in a continuous cycle of putting theory into practice by teaching children and reflecting on the results leads student teachers to value relational understanding. These findings are relevant to elementary teacher educators in mathematics and other discipline areas in which student teachers experience anxiety; they may also be relevant to educators in any discipline area in which conceptual change is a pertinent issue, for example, where student teachers must adopt teaching approaches different from those familiar to them from their schooling. The Mathematics Methods Program The mathematics methods program is a collaborative university-elementary school initiative and is designed to provide student teachers with the opportunity to form meaningful and effective connections among practice, theory, and reflection. Student teachers spend one day per week for 22 weeks in an elementary school where they attend a mathematics methods class taught by their university tutor. They also teach mathematics to small groups of children, under their tutor's supervision. After working with the children, student teachers and tutor regroup to discuss and reflect on their experiences of teaching. Student teachers then incorporate their new discoveries into their planning for the following week's session with the children. This weekly cycle of theory, action, and reflection continues throughout the academic year. According to psychodynamic theories of learning, the emotional component of learning, stemming from powerful emotional experiences, provokes significant attitudinal and behavioral change (Goldfried, 1979). The present mathematics methods program is based on the philosophy that productive change in learning and teaching practices will more likely flow from emotionally powerful experiences, part of the reality shock that Koetsier and Wubbels (1995) describe. In this approach, individuals consistently and repeatedly experience theory, practice, and reflection in an integrated way. If teachers are to practice effective methods, they must have the challenge and the opportunities to experiment with these methods (Lauriala & Syrjala, 1995). For meaningful and lasting change in attitudes and practices to occur, I believe that student teachers must experience the responses of children to their teaching and discuss and reflect on these experiences. …