Embodying the convergence of the Riemann accumulation function in a technology environment. (English)

Lindmeier, Anke M. (ed.) et al., Proceedings of the 37th conference of the International Group for the Psychology of Mathematics Education “Mathematics learning across the life span", PME 37, Kiel, Germany, July 28‒August 2, 2013. Vol. 4. Kiel: IPN‒Leibniz Institute for Science and Mathematics Education at the University of Kiel (ISBN 978-3-89088-290-1). 257-264 (2013).

Summary: This case study is one in a series of studies regarding the learning of the integral concept. Its focus is on the processes involved in the convergence of Riemann accumulation function (RAF) to the accumulation function (AF). The study is guided by the objectification theory which considers learning to be a process of becoming aware of the knowledge which exists in the culture. Through a task performed with a designed technological tool, the students were asked to suggest ways to make the Riemann accumulation graph and the accumulation graph converge. A semiotic analysis of the learning process of a pair of students serves as an example of evolutionary processes of the personal meaning toward the cultural mathematical meaning consist of two successive processes: a) attention to the differences between the RAF graph and the AF graph, and b) the actions performed by the student to make the two graphs converge.