Top-Down Decomposition vs Bottom-Up Composition for Teaching Functions to Lower-Secondary Learners: A Pedagogical Synthesis

The introductory programming literature carries a long, partly implicit, partly explicit, debate over how to introduce functions to novice learners: top-down (state the problem, name a top-level procedure, refine it stepwise into sub-procedures, descend until each sub-procedure is primitive, in the style of Wirth 1971 stepwise refinement and the Polya 1957 decomposition heritage) versus bottom-up (write small concrete functions on concrete data, drill the function-as-named-reusable-unit chunk, then compose larger procedures, in the style of Caspersen 2007 function-teaching pedagogy and the Cunningham-Beck test-first compositional tradition). For lower-secondary (THCS, age 11– 15) learners, the question is not academic. The same chapter of the same textbook can take either pedagogy and produce very different competence profiles. This paper synthesises five decades of cognitive-science and computing-education literature and reaches three contributions. First, a literature verdict: topdown stepwise refinement, as classically operationalised, exceeds the working-memory and prerequisite-skills budget of THCS novices because it requires the learner to hold an unbounded abstract plan in working memory before any concrete function has been written, and the expertise-reversal effect predicts (and the McCracken 2001 / Lister 2004 / Lopez-Whalley 2008 line empirically supports) that top-down strategies favour learners who already hold the chunks. Second, bottom-up composition produces running concrete functions immediately and allows the abstraction-intent chunk (B1.1 candidate 4) to be built from felt repetition. Third, a mixed-strategy recommendation operationalised for the Python Pathway Volume 2 chapter on functions: bottom-up dominant introduction followed by explicit decomposition modelling once the chunk is held. Per the elixresearches no-cohort scope, the recommendation is theoretical; deployment validation is deferred to B1.4 (Python-first cohort) and C2.1 (PRIMM cohort).