A grand challenge in knowledge representation is building the intelligent systems for Science Technology Engineering and Math} (STEM) Education. There are various methods for knowledge representation; however, they do not meet requirements of an Intelligent Problems Solver (IPS) in STEM education. In this paper, we propose the criteria of a knowledge model for an IPS in STEM education. These criteria trend to develop a method for knowledge representation about theory and application. For proving the effectiveness of these criteria, a knowledge model is also constructed This model can satisfy these criteria and apply to build an IPS in courses of STEM education, such as mathematics and physics.