The doctrine of normal tendency in active learning teaching methodology: investigations into probability distributions and averages

Traditional lecture and active learning methods of teaching a university course are compared. The particular course is university calculus. The lecture method was applied to two sections of calculus. The active learning method was applied to two other sections. In all cases students were given an examination near the beginning of the course and a final examination at the end of the course. The score averages for the active learning method were higher than for the lecture method. The distribution of scores for the lecture method were non-normal multimodal in the first and final examinations. The distribution for the active learning method went from non-normal multimodal in the first examination to unimodal normal in the final examination. A new undeceivable nature evidence-based method is presented for measuring teaching efficacy by probability distribution.