Some limitations that affect the learning of mathematics are related to two dysfunctional issues: lack of acknowledgment of students‘ differences in the didactic designs and of the students’ awareness about their learning skills. Accessible and affective didactic designs aim to overcome such dysfunctional issues. In this direction, the document presents three contributions: first, the exploration of technological relationships that foster cognitive convergence between the student and tools; second, a revision of hypotheses that give support to accessible and affective didactic designs; and third, the documentation of the learning trajectories that some diverse Colombian populations made while they were playing the game called The Jumper. The methodologies used in the research were Design Science Research and Teaching Experiments.