An Evolving Research to Tackle Teaching and Learning Challenges during Differential Equations Course: A Combination of Non-routine Problems and Teacher Training

Abstract

Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with differentiation and integration is only introduced first time at the 12th year of study or at pre-university level, and the students have no previous knowledge and understandings of this topic. Therefore, the aim of current study is to determine whether teaching and learning of DEs is a challenging task and also, to find out the ways these challenges can be tackled to develop a better understanding for differential equations problem solving. Results showed that teaching and learning of differential equation is not only a difficult part of the mathematics as compared to algebra, trigonometry but also demand high level of conceptual understanding and special efforts for solving differential equation problem. Addition of non-routine problems has been found major factor to enhance teaching and learning. Teacher should also be properly equipped and trained, so that they may educate both routine and nonroutine differential equation problem.

Predicting Non-Routine Mathematical Problem-Solving Anxiety of Ninth Graders

“…Non-routine mathematical problems are the ones challenging the solver to think and reason more and differently (Lee & Chen, 2009). Non-routine mathematical problems are encouraged to develop reasoning abilities (Bibi et al, 2019). Snyder (1998) underscored problem-solving as the core of mathematics, which requires a problem-solver to be creative to find the appropriate strategies during the problem-solving process.…”

Promoting conceptual understanding of differential equations through inqiury tasks

“…We argued that the correct formation of the concept as Vygotsky's scientific concept can be achieved only through the rigorous explanation of all relevant definitions and theoretical results, including the Existence and Uniqueness Theorems (EUTs), which meaningfully complete the definition of a solution to a DE and link all important notions. We believe that conceptual understanding of DEs can be fostered by the use of inquirybased pedagogy [12] and non-routine problems [2]; first steps in this direction were recently made by the authors [17][18][19].…”

Challenges of Mathematics Learning with Heuristic Strategies

“…Several methods to overcome this, such as give problems related to their daily life. The selection of real-world problems is one of the important pillars in constructivist teaching (Bibi et al, 2019).…”