Alba Gonzalez Thompson
Case studies were conducted to investigate the conceptions of mathematics and mathematics teaching held by three junior high school teachers. Examination of the relationship between conceptions and practice showed that the teachers' beliefs, views, and preferences about mathematics and its teaching played a significant, albeit subtle, role in shaping their instructional behaviour. Differences among the teachers in their conceptions and practices are explained followed by a discussion of properties of their conceptual systems.
Most research on the relationship between the effectiveness of mathematics teachers and their knowledge has focused on the teachers' knowledge of mathematics (Begle, 1972, 1978; Eisenberg, 1977). The questions of how teachers integrate their knowledge of mathematics into instructional practice and what role their conception of mathematics might play in teaching have largely been ignored. With regard to research on teaching in general, Shavelson and Stern (1981) noted:
Very little attention has been paid to how knowledge of a subject matter is integrated into teachers' instructional planning and the conduct of teaching. Nevertheless, the structure of the subject matter and the manner in which it is taught (e.g., with integrity or improbability, contempt or respect; see Fenstermacher, 1980) is extremely important to what the students learn and their attitudes toward learning and the subject matter.
Teachers develop patterns of behaviour that are characteristic of their instructional practice. In some cases, these patterns may be manifestations of consciously held notions, beliefs, and preferences that act as 'driving forces' in shaping the teacher's behaviour. In other cases, the driving forces may be unconsciously held beliefs or intuitions that may have evolved out of the teacher's experience.
There is strong reason to believe that in mathematics, teachers' conceptions (their beliefs, views, and preferences) about the subject matter and its teaching play an