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More specifically, the review covers the literature on programming misconceptions, the cognitive theory of mental models, constructivist theory of knowledge and learning, phenomenographic research on experiencing programming, and the theory of threshold concepts. These bodies of work are examined in relation to the concept of a \u201cnotional machine\u201d\u2014an abstract computer for executing programs of a particular kind. As a whole, the literature points to notional machines as a major challenge in introductory programming education. It is argued that instructors should acknowledge the notional machine as an explicit learning objective and address it in teaching. Teaching within some programming paradigms, such as object-oriented programming, may benefit from using multiple notional machines at different levels of abstraction. 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