Exploring the Function of Teacher Beliefs in Mathematics Instruction

• In Event: The Functions of Teachers’ Beliefs: Filter, Frame, and Guide

Abstract

Purpose and Theoretical Framework

According to social cognitive theory, beliefs act as filters that influence our perceptions and interpretations of reality (Bandura, 1989; Pajares, 1992). In this perspective, teachers’ beliefs about instruction and learning are key factors in how they interpret curriculum, understand students’ behavior, plan lessons, and make instructional decisions. Beliefs, however, serve other functions, particularly framing problems and guiding actions. The purpose of this paper is to review qualitative data from four existing studies to illustrate how beliefs serve all three functions (filters, frames, and guides), with an emphasis on distinguishing between the functions of filtering and framing.

Data Sources and Analysis

Two of the four studies reviewed were mixed-method studies focused on conceptual change (Gill & Algina, 2006; Gill, Vitanova, Brice, & Chew, 2007). Thought-listings and scenario responses were reviewed to examine how beliefs filtered participants’ interpretation of the text. Two other studies were examined to understand how beliefs function as filters, frames, and guides. In one (Gregoire, 1999), a problem-solving-oriented math teacher’s interview responses provide greater insight into how beliefs function in all three contexts. In the final study (Gill & Hoffman, 2009), the discourse of a mathematics teacher team was analyzed for how beliefs serve as frames for problem solving.

Results

Results from the first two studies showed that beliefs filter how experienced teachers interpret differing pedagogies. For example, one teacher wrote that she would “strongly recommend” a scenario depicting traditional instruction because the teacher used “visual learning materials” and because different students “have different learning styles” (Gill et al., 2007). So her prior belief in the value of using math manipulatives and in learning styles allowed her to interpret a traditional math lesson in a very positive light.

Gregoire’s (1999) ethnographic study presents an interesting example of beliefs acting in all three contexts because of the disconnect between the teacher’s beliefs about problem solving, math educators views on problem solving (e.g., Hiebert et al., 1996), and what actually took place in her classroom (she told them how to solve the problem). The math teacher’s deeply held belief in an instrumentalist view of math (Ernest, 1989) filtered what she learned about problem solving during her summer workshops. Her belief in the importance of problem solving framed her lesson planning, with her allotting a portion of time at the start of each class dedicated to problem solving, and her self-efficacy beliefs for math and math teaching influenced how she presented the problems to students.

The final paper, which focused on teachers’ discourse during planning time, yields rich data about framing beliefs. Teachers, for example, uniformly expressed a belief in ability tracking, which framed their lesson planning such that pre-Algebra students were to copy the strategies from the overhead; Algebra and Honors students had to summarize the strategies, and the lowest students were not even given the strategies.

Significance

Findings are reviewed to explore the tacit nature of beliefs, distinguish between the functions of filtering and framing, and discuss their significance for research and practice.

Author

• Michele Gregoire Gill, University of Central Florida