Teachers’ Mathematical Beliefs And Instructional Practice

Studies on the relationship between pedagogical beliefs and instructional behavior have reported different degrees of consistency (Frykholm, 1995; Thompson, 1992). While the nature of this relationship seems to be dialectical in nature (Wood et al., 1991) it is not clear whether beliefs influence practice or practice influences beliefs (McGalliard, 1983). It is in fact a complex relationship (Thompson, 1992) where many mediating factors determine the direction and magnitude of the relationship. This section reports a number of studies that have explored the relationship between teachers’ mathematical beliefs and instructional practice.

Benbow (1995) conducted an intervention program to deliberately modify the beliefs and instructional  practices of 25 preservice mathematics elementary teachers. Findings showed that there was no change in teachers’ mathematical beliefs at the end of the program. However, the researcher stated that instructional behaviour in terms of selection of curriculum content and learning activities, teacher’s role, and teachers’ beliefs on self-efficacy were modified as a result of the program. Lack of pedagogical knowledge and subject-based content were found in some cases to be an obstacle to transfer progressive oriented beliefs into practice.

Brown and Rose (1995) conducted an interview study with 10 elementary mathematics teachers in order to determine their theoretical orientations. Teachers’ responses showed a varied range of theories of teaching and learning mathematics. Teachers also said that these orientations influenced their instructional behavior. The analysis of data revealed that teachers do not implement fully their ideal conceptions of mathematics education because of perceived pressure from parents and school administrators to implement traditional teaching. Other identified mediating factors were the need for more preparation time to satisfy instructional and curricular demands, and the challenges of mixed ability classes. Erickson (1993), in a study with two experienced middle school mathematics teachers, concluded that teachers’ ideal beliefs have a strong influence on their instructional practice. However, obstacles to fully implement their ideals included lack of preparation time and lack of collaboration among peers; size of room; availability of technology, materials, and money; non-supportive administration and parents; need for lengthened class periods; and personal opportunity for growth. Foss and Kleinsasser (1996) studied the behavior and instructional practice of 20 elementary mathematics pre service teachers. At the end of a one semester methods course participants had not changed their beliefs about teaching and learning mathematics, which were found to be traditional oriented and heavily influenced by previous traditional learning experiences in diverse educational settings. Participants’ instructional behaviour replicated or modelled activities learned in the methods course, but not to the extent that reflected an adoption of innovative approaches to teaching and learning mathematics in an articulated and consistent way.

 In addition, Cooney (1985) studied a beginning mathematics teacher who was committed in belief and in practice to problem solving instruction. The author described the conflict between the teacher’s struggle to teach problem solving and students who preferred a more content-based instruction, a friction that sometimes led to classroom management problems. Perry et al. (1999) studied the beliefs of Australian head secondary mathematics teachers and classroom secondary mathematics teachers as independent samples. Head teachers said that curriculum demands were an obstacle to implementing innovative teaching. In the respondents’ words: 

We try to make the work relevant but we are constrained by the syllabus. Sometimes, I feel, pressure of the syllabus tends to force us to cut corners with the kids…If I sound cheesed off, it’s just that I may be a disillusioned mathematics teacher. (p. 14)

Raymond (1993) investigated beliefs and practices of six beginning elementary mathematics teachers and found diverse degrees of consistency. Two teachers displayed a high degree of correspondence between belief and practice, two teachers showed a moderate level, while the other two showed a low level. Reasons

for the inconsistencies were found to be lack of resources, time limitations, discipline, and pressure to conform to standardized testing. The author concluded that there is a dialectical relationship between beliefs and practice. According to the researcher, teachers’ mathematical beliefs influenced their practice more than their instructional practices influence their mathematical beliefs. The researcher also found that previous school experiences, teachers’ current practice, and, importantly, teacher education courses also influence teachers’ mathematical beliefs. Teachers also identified their own mathematical beliefs, students’ abilities, the particular topic to be taught, the school culture, as well as the mathematics curriculum as factors that influenced their instructional practice. Taylor (1990) attempted to assist a high school teacher to modify his beliefs through a process of conceptual change. However, there were conflicting beliefs, such as the teacher’s belief that he had to teach for constant assessment and for covering the syllabus given that he did not want to jeopardize students’ learning with alternative strategies. Consequently, change in instructional behaviour was restricted. 

Van Zoest, Jones, and Thornton (1994) interviewed and observed six elementary preservice mathematics teachers participating as students in an intervention program to enhance their teachers’ mathematical beliefs. The authors found that participants acquired beliefs consistent with socioconstructivist views of learning and teaching mathematics, although they were not able to translate these views into practice in the early stages of instructional episodes. The reason for this inconsistency was found in teachers’ lack of pedagogical skill to guide students through the whole problem solving process, time needed to go through a task, teachers’ and students’ tension on how to go about a problem solving situation, and teachers’ concerns about students’ ability to solve the problem. 

Other studies not showing consistency include Grant (1984) studying secondary mathematics teachers, Kessler (1985) investigating four senior high school mathematics teachers, Brosnan, Edwards, and Erickson

(1996) researching four middle school mathematics preservice teachers, and Desforges and Cockburn (1987) studying seven experienced mathematics primary school teachers.

Thompson (1985) studied two relatively experienced mathematics teachers in their teaching of problem solving and found a high level of consistency between their beliefs and instructional practice. Phillip, Flores, Sowder, and Schapelle (1994) reached the same conclusion while studying four “extraordinary” mathematics teachers. Other studies reporting a strong relationship between teachers’ beliefs and practices have been conducted by McGalliard (1983) investigating senior high school mathematics teachers, and Steinberg, Haymore, and Marks (1985) studying novice teachers. Shirk (1973) working with preservice elementary teachers and Stonewater and Oprea (1988) working with inservice teachers also reported similar consistencies. 

In general, inconsistencies between teachers’ beliefs and practices are due to constraining forces out of a teachers’ control, such as parental and administrative pressure to follow traditional oriented methods of instruction. Other factors include the traditional oriented mathematical learning style of the students as well as a lack of time and materials. These factors seem to act as major barriers for some teachers in implementing their progressive beliefs, constraints that current approaches in mathematics education do not take into account (Nolder, 1990).