CDIO-CT collaborative strategy for solving complex STEM problems in system modeling and simulation: an illustration of solving the period of mathematical pendulum
Hong-Yan Zhang, Yu Zhou, Yu-Tao Li, Fu-Yun Li, Yong-Hui Jiang
TL;DR
This paper addresses the lack of a unified framework for solving complex STEM problems by integrating CDIO (conceive-design-implement-operate) with computational thinking (CT) in a problem-project-oriented setting. It proposes a CDIO-CT collaborative strategy and illustrates it through solving the period of a mathematical pendulum, reframing difficulty around the computation of the complete elliptic integral of the first kind $K(k)$. Four numerical approaches—Infinite Series, AGM, Gauss-Chebyshev, and Gauss-Legendre—are developed and implemented in C to compute $K(k)$, with a robust framework for problem decomposition, abstraction, verification, and testing. The paper also presents a generalized PPOL framework for problem-based learning in complex modeling and simulation, highlighting data collection, teamwork, and the reuse of algorithms across R&D contexts. Overall, the work demonstrates how integrating CDIO and CT facilitates multi-solution exploration, practical software-oriented skills, and scalable education in STEM.
Abstract
The problem-project-oriented STEM education plays a significant role in training students' ability of innovation. Although the conceive-design-implement-operate (CDIO) approach and the computational thinking (CT) are hot topics in recent decade, there are still two deficiencies: the CDIO approach and CT are discussed separately and a general framework of coping with complex STEM problems in system modeling and simulation is missing. In this paper, a collaborative strategy based on the CDIO and CT is proposed for solving complex STEM problems in system modeling and simulation with a general framework, in which the CDIO is about ``how to do", CT is about ``how to think", and the project means ``what to do". As an illustration, the problem of solving the period of mathematical pendulum (MP) is discussed in detail. The most challenging task involved in the problem is to compute the complete elliptic integral of the first kind (CEI-1). In the philosophy of STEM education, all problems have more than one solutions. For computing the CEI-1, four methods are discussed with a top-down strategy, which includes the infinite series method, arithmetic-geometric mean (AGM) method, Gauss-Chebyshev method and Gauss-Legendre method. The algorithms involved can be utilized for R & D projects of interest and be reused according to the requirements encountered. The general framework for solving complex STEM problem in system modeling and simulation is worth recommending to the college students and instructors.