Sort and Search Teaching: A Trace-First vs Implement-First vs Visualize-First Synthesis

Sort and search are the consolidation-stage anchor topics of every introductory algorithm course, yet the field has not adjudicated which of three dominant teaching sequences — trace-first (tracing given algorithm code before any implementation), implement-first (the learner codes a sort or search from a specification or pseudo-code before deeply engaging with execution), or visualize-first (animated or embodied algorithm visualization is consumed before tracing or implementation) — produces the most durable competence. The published literature splits roughly into three camps anchored, respectively, by the Hundhausen-Douglas-Stasko 2002 meta-analysis and the Naps et al. 2003 engagement taxonomy (visualize-first conditioned on engagement above passive viewing), the Lopez-WhalleyLister 2008 tracing-explaining-writing hierarchy and the Lister 2004 multi-national tracing data (trace-first as prerequisite for writing), and the Parsons-Haden 2006 line, the Sedgewick Algorithms tradition, and the broader active-learning metaanalyses (scaffolded-implement-first as durable-learning act). This paper synthesises the three traditions and adjudicates the disagreement through four dimensions: cognitive-load profile, depth of understanding decomposed into operational / semantic / transfer layers, motivation and engagement, and classroom infrastructure cost. The verdict is two-part. First, no singlemodality sequence dominates across all four dimensions; the apparent disagreement is partly a function of which dimension the source camp privileges. Second, a visualize-first short → trace-second → implement-third sandwich dominates each singlemodality sequence at the consolidation stage, because visualizefirst builds the cheap operational-semantic anchor that tracefirst refines into per-step notional-machine prediction and that implement-third converts into a procedural-knowledge chunk. The paper specifies an operational deployment for the elixresearches Python Pathway Volume 3 and From-Scratch-ToPython sort and search chapters — bubble-sort dance → Python Tutor trace of insertion sort → minimal Parsons-scaffolded implementation — and supplies a constraint-indexed selection rule for when classroom time forces a single-modality choice. Per the program no-cohort scope, the deployment is described and theoretically validated; no learner data is collected.