Impact of Calculus Teaching with a Blend of Traditional and Computational Techniques - Muhammad Atif Idrees; Muhammad Arif Hussain; Myong Ri (JCTE, 2025)
Challenges in learning mathematics can diminish students' interest in understanding mathematical concepts. With advancements in communication technology, a hybrid learning environment offers a promising solution to enhance the education system. Combining face-to-face classroom teaching with the use of application tools and systems proves beneficial in this context, fostering improved engagement and comprehension in education of Mathematics. Students frequently make mistakes when solving limit problems in calculus and are required to identify errors in attempts of their solutions. Even those proficient in performing specific procedures often have a limited understanding of the concepts and become confused when the problem context changes slightly. In addition, computer algebra systems (CAS) have been a topic of interest among educators for many years, eliciting both positive and negative feedback from researchers. This study employed a dual approach to research methods, involving both manual calculations obtained by different approaches and computational verification using Python, Maple, Mathematica, and Matlab. This methodology ensured the accuracy and reliability of the solutions, combining traditional problem-solving techniques with advanced software tools for comprehensive validation in finding solutions to single variable and multivariable limit problems undertaken in undergraduate calculus course.