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On-the-fly computations are apparent in all levels of the CS studies. Yet, textbooks do not underline their characterizing design features. One of their primary features is the non-modular composition of design patterns. Additional design features involve insightful observations and the perspective of state transitions. Unfortunately, novices demonstrate limited competence with these features, even after repeatedly seeing on-the-fly designs. The objective of this paper is to shed light on the novice difficulties, and to elaborate on the above features, in advocating the importance of their explicit presentation to students.