As one of the core skills of the 21st century, computational thinking has received increasing attention from educators and researchers. Although some research has been conducted on computational thinking, few studies examined the impact of learning activities on students' computation thinking skills from the perspective of cognitive development. Based on the theory of scaffolding instruction, a progressive thinking training approach with flowcharts was proposed to cultivate students' computational thinking skills. A quasi-experiment was designed to evaluate the effectiveness of the training. Forty-nine Chinese tertiary students undertaking a programming course were randomly assigned into two groups -- the experimental and control groups. During the course, the experimental group received progressive training, and the control group received non-progressive training. The results showed that the experimental group gained a significantly higher level of academic achievement than the control group. Meanwhile, the experimental group showed a remarkable improvement in programming self-efficacy. Furthermore, the participants in the experimental group showed a higher level of computational thinking skills, including cooperative learning, critical thinking, and problem solving skills. In summary, the progressive thinking training approach with flowcharts could not only improve the participants' computational thinking skills and programming self-efficacy, but also help them to achieve better academic outcomes.