According to classical republicans the main purpose of education is to prepare children for their future a citizens, i.e. full members of society. Lateral and critical thinking is the most important aspect of republican education, far more important than learning plain facts by heart. Without these skills a democratic republic cannot survive in the long run.
In order to train children in these skills, I propose that solving situational puzzles should be a regular event at schools. The idea is that the teacher will tell the students a short story. However, this story contain a small riddle and the students have to solve it by asking questions. The teacher then answer those questions, until one of the students manages to solve the puzzle.
To assist teachers giving these lessons in critical and lateral thinking, they should be given a book with such puzzles, some clues and the solutions. Also teachers should be trained to lead the game. Possibly there should be different books for different ages and development levels. The inclusion of general knowledge children are supposed to learn at school anyway, seems to be advisable either.