However, many of these activities have broad application and the placement of activities should not be considered immutable. The numbers correspond to the list of activities attached to this paper. The basic concepts of and techniques applied to the study of dynamical systems could be introduced to young children, and certainly are appropriate for middle school students. The key concept underlying the numerical techniques is iteration. Usually this is done recursively which means that the output of one iteration is used as the input for the next iteration.
Recursion is the key element of feedback loops, a basic element of system dynamics.
Feedback loops can be either positive or negative depending on whether the effect on the output of the function is to increase the output or to decrease the output. These basics can be explored easily on a calculator or with a spreadsheet. Students can begin their analysis of the data that they collect for their dynamical systems by applying some basic tools of data analysis to tables of information. They can calculate first and second order finite differences and look for patterns. They can plot points, putting the independent quantity on one axis and the dependent quantity on the other axis.