Abstract:
The thesis presents a novel framework (Framework for Informal Assessment Questions – FIAO) for classifying the informal questions used by secondary school mathematics teachers, in their regular classrooms. This framework classifies such questions on a five-step hierarchy that goes from questions that require recall (level 1) and procedural knowledge (level 2) to increasingly complex integration of different concepts (levels 3 & 4) and generalisation (level 5). The belief behind this hierarchy was that questions that help students to make connections lead to conceptual understanding, as argued by Hiebert and Lefevre (1986) and Skemp (1971, 1976, & 1979). The framework was built on the hierarchies of Bloom's taxonomy (1956), de Lange's levels of assessment (1995), and Kaput's four types of activities in school mathematics.
Fifteen transcripts of lessons, taken from videotapes of Sri Lankan and New Zealand secondary schools, were analysed using the FIAQ. Measures for assessing the reliability and validity of this classification were inter-rater reliability and the use of teachers' pedagogical concept maps (Liyanage & Thomas - 2002) of the lessons. From this analysis it was possible to characterise lessons as primarily procedural or conceptual. It is suggested that this framework can be of considerable help for teachers who are interested in evaluating their own practice (Liyanage, Irwin, & Thomas, 2000) and it provides another tool for teachers to improve their questioning in class.
