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Developing good responses to students' errors.

Article Excerpt
Abstract

This paper describes an activity involving pre-service elementary teachers. The exercise explored in this activity required pre-service teachers to reflect upon their own K-12 mathematics experiences and to determine what made them uncomfortable as mathematics learners. While the exercise revealed common negative mathematics experiences among this group, the brainstorming activity aimed at generating newer ways of correcting mathematics errors proved to be more difficult than first imagined by these pre-service teachers. What can be said about this activity is that it raised the level of awareness about the importance of teacher responses on the part of pre-service teachers.

Introduction

Among school subjects, mathematics is particularly associated with anxiety. In fact, mathematics anxiety has been a significant research topic for a long time. Although the research subjects vary from elementary school students to pre-service teachers (e.g., Newstead, 1998; Taylor & Fraser, 2003; Trujillo & Hadfield, 1999), the body of research mainly focuses on identifying possible causes and strategies to prevent or reduce high levels of mathematics angst. One of the repeatedly reported causes of mathematics anxiety is the pressure to find 'one correct answer using one correct procedure' (e.g., Baroody, 1987; Greenwood, 1984). This pressure prevents students from actively participating in class discussion and leads to drill-driven instruction and emotional tensions. Consequently, research studies suggest that teachers need to provide a safe environment conducive to learning by accepting multiple ways of solving a problem and encouraging students to focus on their thinking process rather than on a final answer (Faivilling, 2001; Hackworth, 1992; Hembree, 1990). This suggestion is also in line with the National Council of Teachers of Mathematics' (2000) emphasis on effective teaching, which urges teachers to "establish and nurture an environment conducive to learning mathematics" by encouraging discussion and collaboration (p.17).

The purpose of this paper is to describe an action research activity conducted in a pre-service elementary mathematics methods course. First, the instructor asked students to reflect upon their own K-12 experience in mathematics classrooms and to provide statements that outlined both positive and negative events. Each student then shared his or her set of former experiences, with special attention paid to those pre-service teachers considered to be negative. This information formed the basis for an in-depth classroom discussion on how teachers can reduce mathematics anxiety and create a classroom climate that helps to promote mathematics learning. The classroom discussion contained two instructional objectives: 1) For pre-service teachers to view their earlier K-12 mathematics experiences through the adult lens of a teacher. In other words, now that these pre-service teachers are about to embark on their own professional journey, how do they view their childhood mathematics experience from an adult perspective? 2) Once these pre-service teachers identified their own...

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