Cognitive modelling is one of the representative research methods in cognitive science. It is believed that creating cognitive models promotes learners' meta-cognitive activities such as self-monitoring and reflecting on their own cognitive processing. Preceding studies have confirmed that such meta-cognitive activities actually promote learning effects. However, there are some difficulties in bringing about learning by creating cognitive models in an educational context. To overcome the difficulties, we propose an innovative learning design, "learning through intermediate problems" and also developed a web-based production system called DoCoPro that can be used anywhere and anytime in an environment connected to the Internet. We performed three introductory cognitive science classes in which the participants learned cognitive modelling and constructed running computer models using our system. In the first and second classes, the participants were required to construct production system models that solve pulley problems. They also posed their original pulley problems that their own models were subsequently able to solve. These generated problems were distributed to the other members. The participants were able to find incompleteness in their cognitive models, revise them to remove the incompleteness, and improve their models while solving the given problems. The participants, by successfully creating sophisticated models, acquired a deeper knowledge of the learning domain. The class practices confirmed the utility of "learning through intermediate problems" when constructing an educational environment for learning creating cognitive models. In the third class, the participants constructed cognitive models solving addition and subtraction problems using DoCoPro. The cognitive processing underlying such problem solving is automated, therefore it may be difficult to verbalize and externalize such cognitive processes. The post-questionnaire showed evidence that the participants actually performed meta-cognitive activities while monitoring their own internal information processing.