Academic journal article Education

How Innovative Middle School Mathematics Can Change Prospective Elementary Teachers' Conceptions

Academic journal article Education

How Innovative Middle School Mathematics Can Change Prospective Elementary Teachers' Conceptions

Article excerpt

Over the past decade, mathematics education reforms have challenged teachers to expand their pedagogical repertoire to include classroom activities that allow students to pose and solve rich problems and reason mathematically (Mathematical Sciences Education Board [MSEB] & National Research Council [NRC], 1989; National Council of Teachers of Mathematics [NCTM], 1989). These specific reform recommendations have resulted in, among other things, a flourish of curriculum development activity across the grade levels. Reform-oriented curriculum materials differ from traditional mathematics textbooks in that they emphasize student explorations of real-world mathematical situations and discussions of problem-solving activities. Another important distinction is that reform-oriented materials offer more extensive information for teachers than do traditional texts. For example, the materials include details about different representations of content, historical information about mathematical and pedagogical ideas, examples of what students might do with or think about particular activities and content, potentially fruitful questions for eliciting discussion, and so on. This second distinction reflects tinction reflects an increasing recognition that it is teachers, not texts alone, who determine how the innovations envisioned by reformers and curriculum designers become implemented in the classroom.

What issues do curricular reforms raise for those involved with the preparation of future teachers? In light of the differences in the instructional methods prospective teachers will be expected to use in schools and those they likely experienced as students of mathematics, teacher education programs are faced with the task of creating opportunities for prospective teachers to critically consider important mathematical and pedagogical ideas. As the MSEB and NRC (1989) state, "Teachers themselves need experiences in doing mathematics--in exploring, guessing, testing, estimating, arguing, and proving ... they should learn mathematics in a manner that encourages active engagement with mathematical ideas" (p. 65). Many prospective teachers possess weak knowledge and narrow views of mathematics and mathematics pedagogy that include conceptions of mathematics as a closed set of procedures, teaching as telling, and learning as the accumulation of information (Brown, Cooney, & Jones, 1990; Thompson, 1992). If reform themes are to be enacted in the mathematics classrooms of future teachers, these conceptions need to be challenged and developed in ways that will support meaningful and lasting change.

This paper reports about a project that was designed to challenge and re-develop preservice elementary teachers' conceptions of mathematics by engaging them in the use of middle school reform-oriented curriculum materials. Recognizing that current reforms expect these teachers to teach unfamiliar mathematics using pedagogical methods that they have not experienced personally, this report focuses on the teachers' perceptions of the opportunities afforded by the curriculum materials to engage them as both learners and teachers of mathematics.

Description of the Project

Our project took place between January and May of 1998 in a one-semester mathematics course, titled Geometry for Teachers, for which the authors were the instructors of two sections. Of the approximately 50 teachers enrolled in the Geometry course, most were sophomores (10 juniors), female (3 males), and European-American (1 African-American).

The examples presented in this paper emerge from teachers' written comments on various course assignments. The preservice teachers wrote three papers in which they analyzed their experiences as former elementary students, reflected on their studies in the Geometry course, and presented visions of themselves as future teachers. Teachers had opportunities to learn or revisit geometric concepts and mathematical processes, as well as pedagogical issues and practices, as they engaged with three types of text materials: (1) student editions of curriculum materials, (2) teachers' guides of curriculum materials, and (3) a reform document for elementary mathematics curriculum. …

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