The article describes the history of the knowledge popularization in Russia and the current situation in this domain with the impact of rapidly developing computer technologies. The article also introduces the Construct, Test, Explore (CTE) contest aimed to take students into the scientific phenomena through the game laboratories illustrating the unsolved and difficult problems of mathematics, informatics, and physics. The CTE School project based on the contest ideas is devoted to learning basic algorithms from the theory of information or discrete mathematics through training experiments.