Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.
Both oral and written communication play an important role in teaching and learning mathematics (NCTM 2000). Students and teachers exchange ideas about their understanding of, and thinking about, mathematics by communicating with one another. An important part of this communication process is the choice of symbols used to represent that thinking (Hiebert 1989). The process of representing mathematical ideas using symbols and expressions should begin at the earliest stages of mathematics instruction and appear in the context of ideas to which young students can relate (Carey 1992).
The changing applications of mathematics have contributed to a shift from the perception that mathematics is a fixed body of arbitrary rules to the realization that the discipline is “a vigorous active science of patterns” (National Research Council 1989, p. 13). NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends using patterns to promote mathematical understanding and, in particular, algebraic reasoning. A number of other mathematics education reform documents make similar recommendations (e.g., AAAS [1989]; National Research Council [1990]; Steen [1990]; NCTM [2000]). Researchers have begun to identify different approaches that students use to reason about patterns (Bishop 1997; MacGregor and Stacey 1993; Orton and Orton 1996; Stacey 1989). Research also shows that using students' thinking about patterns can help them develop a better understanding of mathematical concepts and the representations that reflect those concepts (Carey 1992; Fennema, Carpenter, and Peterson 1989). This article illustrates how students' thinking about geometric patterns can be used to help them develop algebraic reasoning and to make sense of mathematical notation and symbols.
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