Relating computational cartesian graphs to a real motion

an analysis of high school students' activity

Ulises Salinas-Hernández

Isaias Miranda

pp. 55-71

in: Norma Presmeg, Luis Radford, Wolff-Michael Roth, Gert Kadunz (eds), Signs of signification, Berlin, Springer, 2018

Abstract

In this chapter we apply the recent findings of the Theory of Objectification (TO) to analyze grade 12 students' processes of interpretation of Cartesian graphs that are displayed by software—that manages real time video and reproduces it frame by frame in a computer—and are related to an experiment of a free falling tennis ball's motion across an inclined plane. We specifically are interested in analyzing how students' understanding of the mathematical relationships of the physical variables (space and time) precedes students' understanding of how real motion occurs. Our data analysis shows that students firstly associated the Cartesian graphs with the linear trajectory of the motion; secondly, with the researcher's intervention, students focused their attention on the software to deal with the shape of the Cartesian graph and the physical phenomena; thirdly, by simulating the experiment with artifacts and gestures, they established a functional relationship between the spatial (vertical and horizontal) and time variables. By doing so, they were able to describe the trajectory of the tennis ball in terms of various mathematical relations (vertical position and time, horizontal position and time, vertical position and horizontal position). We conclude that the opportunity the students have to manipulate (more or less on a whim) the software, is what affords students' processes of interpretation of a specific characteristic.