Design and Development of a Teaching–Learning Sequence about Deterministic Chaos Using Tracker Software

In this paper, we present the design, development, and pilot implementation of a Teaching–Learning Sequence (TLS) about the physics of deterministic chaos. The main aim of the activities is to let students become aware of two key ideas about deterministic chaos: (1) the role of initial conditions and (2) the graphical representation in a momentum–position graph. To do so, the TLS is based on the observation and analysis of the trajectory of the free end of a double pendulum through the modeling software Tracker. In particular, the Tracker-based activities help students understand that, by modifying the well-known simple pendulum dynamic system into a double pendulum, long-time-scale predictability is lost, and a completely new behavior appears. The TLS was pilot tested in a remote teaching setting with about 70 Italian high school students (16–17 years old). The pretest analysis shows that before participating in the activities, students held typical misconceptions about chaotic behavior. Analysis of the written responses collected during and after implementation shows that the proposed activities allowed students to grasp the two key ideas about nondeterministic chaos. A possible integration of the TLS with an online simulation is finally discussed.