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We consider two complementary aspects of mathematical skills, i.e. procedural fluency and conceptual understanding, from a point of view that is related to modern e-learning environments and computer-based assessment. Pedagogical background of teaching mathematics is discussed, and it is proposed that the traditional book medium has determined much of its historical development, including the classical style of presenting mathematical knowledge. Information technology is likely to be an emerging game changer in learning and teaching of mathematics, and we argue that the potential of e-learning platforms extends beyond simple drill exercises to complex problems (having several ‘right’ solutions) that are expected to improve conceptual understanding. We discuss these ideas referring to experiences and observations from a STACK-based automatic assessment system at Aalto University since 2006 …