A developmental analysis of strategies employed in solving speed problems: A post-Piagetian approach

Abstract

This thesis is a qualitative study of student concepts of speed. Previously, Piaget's (1946) work on children's understanding of speed laid a solid foundation for such a study, and has provided a basis for several other investigators (e.g., Trowbridge (1979), with tertiary students). Students in this study, whose ages ranged from twelve-to-eighteen years, were questioned about their ideas concerning speed. In understanding students' concepts of speed, three major factors were considered: strategies they employed to solve a variety of problems on speed; their descriptions of speed; and, categorising and describing these responses within a suitable theoretical framework. The strategies employed by students to solve speed problems were categorised into four levels: first, focusing on the visual aspects of the problem; second, attention was given to one variable that was provided; third, two variables were used but there was no attempt to consider constraints; fourth, all relevant variables were accounted for and the strategy was nearly always successful, aside from mechanical errors. In addition a number of issues are discussed that relate to students choice of strategy. In particular: the way students referred to variables: the methods employed in solving direct and inverse variation type problems; and, the role of intuitive thinking. To enable the responses to be better understood, a post-Piagetian framework, the SOLO Taxonomy of Biggs and Collis (1982), was employed. Students' descriptions of speed were able to be categorised by extending this taxonomy. With the aid of mapping diagrams, students' responses to speed questions were placed within two modes of functioning, namely the ikonic and the concrete symbolic mode. The ikonic mode exhibited one cycle, while, within the concrete symbolic mode two cycles were identified. In general, ikonic mode responses relied on the diagram for cues, while the concrete symbolic responses relied on the given data and different strategies were employed to arrive at an answer. In addition, first cycle responses within the concrete symbolic mode, usually employed intuitive type strategies whereas second cycle responses had overviews of all the data and used strategies that incorporated the relevant variables. Within each of these cycles responses progressing through the different levels of the SOLO Taxonomy were identified. This revised model provides clarity when exploring the details of students' understanding of speed. Profiles of students' responses, using this revised model, are presented and a diagrammatic representation of these profiles indicate an appropriate way to document the levels of responses provided by students.