SMA Modelling of the Dynamics of Teaching Methods on Students’ Mathematics Achievement in Probability
Benjamin Adu Obeng
*
Department of Mathematics Education, University of Skills Training and Entrepreneurial Development Kumasi, Ghana.
Yaw Boateng
Department of Mathematics Education, University of Skills Training and Entrepreneurial Development Kumasi, Ghana.
Ebenezer Appiagyei
Department of Mathematics Education, University of Skills Training and Entrepreneurial Development Kumasi, Ghana.
Bright Asare
Department of Mathematics Education, University of Skills Training and Entrepreneurial Development Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
This study looks at the dynamics of teaching methods in senior high school classrooms. A model showing the effect of four teaching methods on students’ achievement in probability concepts. The model adapted the SIR model. Three compartments were considered: Susceptible, Teaching Method, and Achievement (SMA). The basic reproductive number is determined and analysed. The stability analysis of the equilibrium points revealed local asymptotic stability of the Concept Equilibrium Points, which means the probability of concept acquisition among students by an effective teaching method adopted by the teacher will increase. The sensitivity and numerical analyses revealed that any teaching method adopted has a significant probability of concept infection rate, that enhance an accelerated student population transitions from the susceptible compartment through to the conceptual infection compartment and the achievement compartment (mastery), while reducing dropout rates in the achievement compartment and sustaining students’ achievement. Conversely, higher dropout rates in the infection compartment also have a negative effect on the achievement compartment (mastery level). Also, Collaborative Learning produced the highest students’ achievement, followed by Problem–Based Learning, Inquiry-Based Learning, and then the Lecture Method. The findings recommend equipping teachers with training and resources to adopt learner-centered approaches, especially for applied concepts such as probability.
Keywords: Collaborative Learning (CL), Problem-Based Learning (PBL), Inquiry-Based Learning (IBL), Lecture Method (LM), Concept Free Equilibrium Point (CFEP), Concept Equilibrium Point (CEP)