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Article Excerpt
Abstract
Beliefs are mental representations of reality that guide peoples' thoughts and behaviors. Originally the Mathematics Beliefs Scales (MBS) was hypothesized to measure tour subscales. After administering it to 123 teachers and 54 preservice teachers, the factor analysis indicated a three-factor solution and a more parsimonious 18-item Revised Scale. This shortened version of the MBS should assist researchers in data collection by (a) shortening the time it takes to administer the scale, (b) removing seemingly redundant items, and (c) focusing on specific constructs contained within the instrument.
Introduction
Beliefs have been described and defined by different researchers in different ways. Beliefs are the bedrock and cornerstone at the heart of our actions (Corey, 1937). Beliefs are the best indicators of the decisions individuals make throughout their lives (Dewey, 1933). Beliefs are classified as instrumental and relational approaches to a situation (Carter & Yackel, 1989). Pajares (1992) proposed that beliefs are mental representations of reality that guide thought and behavior and are often initiated early in life and maintained in the lace of strong contradictions. These entrenched beliefs serve as a filter through which teachers view the world and interpret information. All teachers possess beliefs about their profession, their students, how learning takes place, and the subject areas they teach. It follows, therefore, that teacher practices should flow from these beliefs. Teacher beliefs are instrumental in defining teacher pedagogical and content tasks and for processing information relevant to those tasks (Nespor, 1987).
In the Principles and Standards for School Mathematics (NCTM, 2000), the National Council of Teachers of Mathematics state that "Effective teachers realize that the decisions they make shape students' mathematical dispositions and can create a rich setting for learning" (NCTM, 2000, p.18). These decisions are controlled and influenced by their beliefs. Thus beliefs are implicit in teacher discourse, teacher objectives, and teacher practices. Many researchers have studied teacher beliefs about mathematics. Teachers' beliefs and practices essentially mold classroom teaching, including discourse. "One's conception of what mathematics is affects one's conception of how it should be presented. One's manner of presenting it is an indication of what one believes to be the most essential in it ... The issue, then, is not, what is the best way to teach? But, what is mathematics really all about?" (Hersh, 1986, p. 13).
Researchers (Knapp & Peterson, 1995; Vacc, Bright, & Bowman, 1998) realized that changing beliefs took much time and support. Other researchers also found that substantial improvements occur in classroom achievement when teachers shift their beliefs along with their practices (Fennema, Franke, Carpenter, & Carey, 1993). Researchers (Carter & Norwood, 1997; Ford, 1994; Lubinski, 1993) have also compared teachers' and students' beliefs about mathematics. In addition researchers also revealed a definite relationship between teacher beliefs and actual classroom content, and how students learned in individual classrooms (Grant, Hiebert & Wearne, 1994; Hart, 2002). Clarke (1997) looked at how the beliefs held by teachers were reflected in the roles of the teachers--what the teachers did. Students in a research classroom studied by Carter and Norwood (1997) believed different factors such as task orientation, ego orientation, and extrinsic motivation scales were also important in mathematics success. Student responses possibly indicated that students were mirroring their teachers' beliefs. Battista (1994) stated that teachers who are presently teaching mathematics learned from teachers who used traditional curriculum depicting teachers as educators in a vicious cycle, teaching the same way that they were taught in school. These teachers held a view that was in direct contrast to the reform movement.
Constructivist teachers have beliefs and exhibit practices allowing students to construct their own knowledge through active investigation and meaningful discourse...
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