The research results we present in this paper reveal that properly calibrated e-learning tools have potential to effectively promote the algorithmic thinking of both science-oriented and humanities-oriented students. After students had watched an illustration (by a folk dance choreography) and an animation of the studied sorting algorithm (bubble sort), they were invited to predict and perform [(1) to reconstruct on the same input; (2) to orchestrate on a random sequence stored in a white array; (3) to orchestrate on a black-box sequence] the entire step sequence of the algorithm (using the interactive visual learning environment we developed). The results of the experiment show that while science-oriented students' performance proved superior to those of their humanities-oriented colleagues, the differences were observed to diminish as both groups advanced with their e-learning tasks. Although drawing general conclusions would be premature, we can conclude that there are no unbridgeable differences in the way these two groups relate to e-learning processes that aim to promote algorithmic thinking. Our findings also emphasize the key importance of some motivational principles in facilitating algorithmic thinking: the principle of moderate and progressive challenge, the principle of gradual shift from concrete to abstract and the principle of genuine active involvement.