Stability Analysis on the One-dimensional ODE System Based on CPTA Model
Rajat Kaushik
Department of Education in Science and Mathematics, Regional Institute of Education, NCERT, Bhopal, India.
Aji Thomas
Department of Education in Science and Mathematics, Regional Institute of Education, NCERT, Bhopal, India.
Sudhanshu Aggarwal
Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh, India.
Ram Keval *
Department of Applied Mathematics, M. J. P. Rohilkhand University, Bareilly, Uttar Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
The Concrete-Pictorial-Abstract (CPA) paradigm is a recognised method in educational strategy. This paradigm has been enhanced by integrating "Technology," a crucial element of learning. The research elaborates on the enhanced as Concrete-Pictorial-Technology-Abstract CPTA model and formulates an Ordinary Differential Equation (ODE) system to comprehend the model mathematically. To analyse the model, we identified the equilibrium solutions or critical points and examined the stability of each equilibrium point. We have constructed the phase line and direction field to augment comprehension of the topic. The analysis is corroborated by numerical simulations, justifying the incorporation of technology into the existing model to achieve more accurate findings. This paper's findings mathematically demonstrate that technology catalyses learners, facilitating their progression from concrete to abstract levels more rapidly.
Keywords: CPTA model, CPA model, local stability, bifurcation analysis, ordinary differential equation