Gomes Ferreira, Veronica Gitirana; (1997) Exploring mathematical functions through dynamic microworlds. Doctoral thesis , Institute of Education, University of London.

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Abstract

The aim of this research was to investigate students' perceptions of function as they interacted with the different dynamic representations of function made available through computer environments. Microworlds were designed comprising sequences of activities around the software, Function Probe, and two adaptations of DynaGraph, DG Parallel (with parallel axes) and DG Cartesian (using Cartesian axes). A series of case studies of four pairs of students was undertaken in Brazil in order to trace the evolution in students' perceptions of a selection of function properties; namely turning point, variation, range, symmetry and periodicity. This diversity of properties was chosen to examine different ways students analyse functions: pointwise, variational, global and pictorial. Starting with an examination of the curriculum followed by the case study students as a means to describe the origins of their perceptions, a longitudinal investigation was undertaken in order to identify the main features of each of the microworlds that appeared to contribute to students' progress. The students' perceptions were analysed by drawing attention to their origins, their usefulness and their potential limitations (from a mathematical point of view). A methodology for this longitudinal study was devised which incorporated visual presentations to capture the main characteristics of students' perceptions. The results showed that DG Parallel, a 'new' representation, prompted the development of perceptions free of previous limitations and sufficiently robust to allow revision. However, properties previously perceived pictorially were rarely identified in DG Parallel. Together with DG Cartesian, interactions with this microworld provoked the students to develop a variational view of some of the function properties. In addition, DG Cartesian served as a two-way bridge between variational and pictorial views. By way of contrast, using the tools in FP to transform graphs seemed not to shape perceptions, but to assist in the exploration of the function properties.

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