CONSTRUCTION OF CONCEPTUAL KNOWLEDGE: THE CASE OF COMPUTER-AIDED EXPLORATION OF PERIOD DOUBLING

Abstract

This research focuses on students using an experimental approach with computer software to give visual meaning to symbolic ideas and to provide a basis for further generalisation. They use computer software that draws orbits of x=f(x) iteration and are encouraged to investigate the iterations of f_λ(x)=λx(1-x) as λ increases. The iterations pass through successive acts of period-doubling as λ=λ₀, λ₁, λ₂, …,. students are invited to estimate the values of λ and to compare their experimental results with the theory of geometric convergence. The supervisor acts as a mentor, using various styles of questioning to provoke links between different ideas. A variety of data is collected to give evidence for the ways in which students develop conceptual links between symbolic theory and the visual and numeric aspects of computer experiment.