TEACHING AND LEARNING

TEACHERS’ ATTITUDES AND PERCEPTIONS ABOUT MATHEMATICS TEACHING AND LEARNING

Teachers’ own beliefs about mathematics, how children learn mathematics, and what constitutes good teaching affect the way teachers choose to teach mathematics and what they choose to teach. Research has shown us that many graduates of teacher education programs still end up teaching the way they were taught as students (usually in a traditional manner) despite the quality of their teacher education program. This must change in light of our changing society and the current research on effective mathematics teaching and learning. It is a major challenge for school administrators if a teacher does not believe that change is necessary in the mathematics program.

Teacher beliefs, and the choices teachers make, can have a major impact on how students view mathematics and their learning of it. According to research, it is suggested that teachers’ beliefs about mathematics are often limited and may be dualistic, in the sense of having a traditional right/wrong orientation and using mostly single procedures to arrive at the correct answer. A consistent theme found in Cooney, Wilson, Albright, and Chauvots (1998) RADIATE study was that teachers equated good teaching with good telling. In other words, students should understand mathematics step by step and should not be confused. A second  theme that was found was that of “caring.” Because teachers cared about their students’ success in mathematics class, they felt that caring meant enabling students tomaster basic skills, often putting aside challenging tasks on assessments for those that mimicked the traditional skill-based lessons done in class. This is a reductionist

orientation that is counter to reform efforts in mathematics.

Baroody (1998) provides a summary of research on three different views of mathematics that have been identified among teachers:

1. Mathematics as a collection of unrelated basic skills

2. Mathematics as a coherent network of skills and concepts (mathematics as a static body of knowledge)

3. Mathematics as away of thinking (inquiry process,mathematics as a dynamic field)

Knowledge and beliefs are inextricably intertwined. Our beliefs are like a filter through which new phenomena are interpreted. A teacher’s sense of purpose as a mathematics teacher, philosophy of learning and teaching, and sense of responsibility in terms of the community in which he or she teaches are all fused with what the teacher “knows.” As well, it is important for teachers to be reflective practitioners. In the case of mathematics, teachers need to see mathematics as a creation of knowledge rooted in rationality. Mathematics knowledge is not static; it is fluid. Context and reflection play an important role in allowing the knowledge required by reform to be fluid and flexible. Both “what the teacher knows” and the way the knowledge is acquired are important issues.

Administrators can push teachers to change their classroom activities, but we also need to change their fundamental beliefs and attitudes about teaching and learning, the roles of teachers and students, and how teaching and learning should be carried out. For change to be successful, teachers’ beliefs, attitudes, and practices need to be aligned. It seems logical that influencing teachers’ beliefs may be essential to changing teachers’ classroom practices. At one end of the beliefs continuum are traditional beliefs. Stipek, Givvin, Salmon, and MacGyvers (2001) found that teachers who scored high on these more traditional beliefs were less self-confident about teaching mathematics and enjoyed it less. In their data analysis, five dimensions of beliefs (more traditional beliefs linked to teachers’ being less confident about teaching mathematics) were strongly associated with each other:

1. Mathematics is a set of operations to be learned.

2. Students’ goal is to get correct solutions.

3. The teacher needs to exercise complete control over mathematics activities.

4. Mathematics ability is fixed and stable.

5. Extrinsic rewards and grades are effective strategies for motivating students to engage in mathematics.

If one looks at the opposite end of the dimensions (reform based beliefs linked to teachers’ being more confident about teaching mathematics), there was consistency in the following beliefs:

1. Mathematics is a tool for thought.

2. Students’ goal is to understand.

3. Students should have some autonomy.

4. Mathematics ability is amenable to change.

5. Students will want to engage in mathematics tasks if the tasks are interesting and challenging (not for extrinsic rewards).

The authors speculate that building teachers’ self-confidence in mathematics (which requires building their mathematical understanding) could be an important and perhaps necessary criterion in moving teachers toward more inquiry-oriented beliefs and practices. If this suggestion is valid, the school administrator’s challenge in this area is to be able to provide the intensive, sustainable professional development required to improve teacher understanding of mathematics, to improve confidence in the subject area, and to change beliefs and attitudes about teaching and learning mathematics.