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

Abstract

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. Supplementary Information The online version contains supplementary material available at 10.1007/s43545-021-00154-1.

Economic Growth: The Log Symmetry of Collaborative Learning Populations

“…At the time when human ideas of imagination and creativity emerge, they might be normally distributed across individual human beings. There is evidence for this in normal SAT scores, multimodal AP test scores and the empirical results from Ridley, Ngnepieba and de Silva (2021). As collaboration occurs, capitalization grows.…”

“…Let us now look at a theoretical construction that will help us complete our understanding. Ridley, Ngnepieba and de Silva (2021) show how theoretical distributions of two subpopulations of normal distributions can combine into unimodal normal distributions. Then, they show how an active learning teaching method can combine subpopulations of university calculus test scores to produce unimodal normal distributions.…”

“…Such entrepreneurial activities are known to create massive wealth (Ridley, 2020a(Ridley, , 2020bde Silva, Ridley, & Green, 2020;Llaugel & Ridley, 2018;Ngnepieba et al, 2018). Ridley, Ngnepieba and de Silva (2021) show how theoretical and empirical bimodal distributions of two subpopulations of university calculus test scores can combine into a unimodal normal distribution when collaborative learning is implemented. In addition to higher test score averages, normally distributed test scores are obtained.…”

Collaboration Trumps Intelligence as a Predictor of Standard of Living

“…As an example of collaboration, Hayek (1945) depicts a market economy as a mechanism that allows people to take advantage of the knowledge others have without having to acquire the knowledge themselves. Ridley, Ngnepieba and de Silva (2021) show how university calculus test scores and their distribution improve when collaborative learning is implemented. The individual effort of a science or engineering inventor, while brilliant, requiring superior intelligence rarely succeeds without managerial collaboration with several other individuals of less illustrious intelligence.…”

Economic Growth- The Log Symmetry of Collaborative Learning Populations

“…Such entrepreneurial activities are known to create massive wealth (Ridley, 2020a, Ridley, 2020bde Silva, Ridley and Green, 2020;Llaugel and Ridley, 2018;Ngnepieba, et al, 2018). Ridley, Ngnepieba and de Silva (2021) show how theoretical and empirical bimodal distributions of two subpopulations of university calculus test scores can combine into a unimodal normal distribution when collaborative learning is implemented. In addition to higher test score averages, normally distributed test scores are obtained.…”