Mathematical theory of peer-instruction dynamics

A mathematical theory of peer instruction describing the increase of the normalized number of correct answers due to peer discussion is presented. A simple analytic expression is derived which agrees with class data. It is shown that our theory is connected to the mathematical learning models proposed by Pritchard et al. It is also shown that obtained theoretical lines are useful for analyzing peer-instruction efficiencies.

Figure 1

(Color) The normalized number of correct answers after discussion versus before discussion for (a) a university course of introductory mechanics and (b) high-school physics courses. The red solid lines represent the theoretical curve of Eq. (8). In (a), the blue broken line represents the best fitting curve in the second-order polynomial approximation. The four green points represent data associated with Newton’s third law. In (b) the violet and blue points correspond to the data from 2008 classes and 2009 classes, respectively. The violet and blue broken lines are corresponding best fitting curves.

Figure 2

(Color) The peer instruction efficiency (PIE) versus correct answers before discussion for (a) the university course and (b) the high-school courses. The red solid lines represent the theoretical line of Eq. (9). The broken lines represent the best fitting lines for the data. In (b) the violet (blue) points and line represent the 2008 (2009) data. The four green points in (a) represent data associated with Newton’s third law.