Levels of introspection in mathematics instruction

Abstract

Case studies of five teachers who participated in a three-year staff-development project formed the basis for this grounded study which focused on primary factors that dominated teachers' instructional decision making. As the analysis progressed, qualitatively different levels of introspection, rank ordered by the degree to which children's thinking was utilised in the decision-making process, were identified. These distinct levels were robust in that they consistently reappeared across all coded categories of decisions made by these teachers. Moreover, these levels were positively correlated with the quality of students' thinking based on what they said or did during instruction (p = .60). Further, wheri all project teachers were categorisation the basis of their dominant level of introspection, a positive correlation was found between these levels and their belief scores on a mathematics teaching and learning survey (p = .61).

Head mathematics teachers’ beliefs about the learning and teaching of mathematics

“…Sosniak et al (1991) comment as follows: Jackson (1986) labels these orientations "the mimetic and the transformative," terms which he says encompass the differences expressed in long-standing debates between "traditional" and "progressive" educators, over "subjectcentred" and "child-centred" practices .... One of the traditions is concerned primarily with the transmission of factual and procedural knowledge while the other emphasises qualitative transformations in the character and outlook of the learner. (p. 121) Stipek & Byler (1997), in their study of early childhood teachers' "beliefs about appropriate education for young children" (p. 312), designated two similar factors as "child-centred beliefs" and "basic skills beliefs," while Lubinski, Thornton, Heyl, & Klass (1994) described factors which can be compared with those introduced above as the ends of a continuum of teachers' beliefs. The analysis reported in this paper considers the two factors as being separate rather than two extremes of one beliefs factor.…”