Abstract

Countries are regularly upgrading K12 curricula. This is a major challenge, involving the knowledge and experience of experts on teaching and experts on the subject matters. But to teach a curriculum it is also critical to know the causal dependencies between contents during the learning process: how the students' previous performance in each content influences their future performance in each one of them. This critical empirical information is not provided in the curriculum. However, nowadays with the massive online activity of teacher and students, patterns among contents can be detected. Applying machine learning algorithms on the trace of more than half a million mathematical exercises done by 805 fourth graders from 23 courses in Chile we have identified graphs with causal dependencies among contents. These graphs emerge from the collective activity of teachers and students. They implicitly take into account logical relations, teachers' practices as they follow the curriculum, and students' learning processes.