Significant progress can be made in the part of elementary school education that relies on intelligent tutoring systems (ITS), if the role of a referee and a peer advisor will be performed by a pedagogical agent that is a computer implementation of a cognitive architecture modeling the process of learning. Recent studies in cognitive architectures funded by the DARPA IPTO BICA Program have identified the key potential of feasible today artificial intelligence as bootstrapped cognitive growth (i.e., gradual acquisition of knowledge and skills using previously acquired knowledge and skills), up to a human level of intelligence in a selected domain. This approach is not limited to laboratory settings and short-term paradigms, it is intended for a long-term, open-ended learning scenario in real-world settings. Several cognitive architectures were designed for this purpose, among which is GMU BICA, a self-aware biologically inspired cognitive architecture. Here we describe a computational model of student learning based on GMU BICA and its use as an ITS called Cognitive Constructor, which has two components called a Science Microworld and a Pedagogical Agent (GMU BICA agent). Results of our analysis show that the system will be useful in elementary school education.