  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.
