Current conditions limit the direct observation of learning processes useful for teachers to design the hypothetical learning trajectories. Fortunately, technology makes it possible to complement direct observation through cognitive and emotional monitoring of students during problem-solving processes. Monitoring the learning process open opportunities for tools can do scaffolding, teacher knowledge about the student’s learning process, teacher knowledge about the results of their scaffolding process, and self-knowledge of subjects about their learning processes. In order to develop technologies that engage learning through learning analytics, this document presents three mathematical games: Towers of Hanoi, Four Knights, and The Jumper, with the respective graphs that represent the problem space and a theoretical proposal to analyze the hypothetical learning trajectories generated in the solution of mathematical games. The theoretical proposal is composed of four hypotheses results from analyzing the students’ behavior while solving the game of the towers of Hanoi. All resources are free and available at git-hub.