Teaching Scalability Reasoning through a Complexity-First Approach to Algorithms and Data Structures

Algorithms and Data Structures (ADS) courses centrally incorporate complexity analysis, yet formal exposure to asymptotic concepts does not by itself ensure robust and transferable scalability reasoning. This paper introduces a complexity-first pedagogical framework , termed ADSC (Algorithms, Data Structures, and Complexity) , that integrates computational-cost reasoning and algorithmic auditing as continuous learning practices in algorithms education.

The framework introduces Scalability Literacy as the ability to anticipate feasibility limits, critically evaluate efficiency claims, and identify hidden computational costs in both human-written and AI-generated code. ADSC distinguishes among asymptotic growth, implementation- and architecture-dependent effects, and paradigm-specific execution costs, and operationalizes these distinctions through empirical experimentation, comparative implementation analysis, and resource indicators including comparison counts, data movements, peak memory usage, and scale-sensitive execution behavior.

Sorting algorithms serve as a primary pedagogical laboratory for connecting formal complexity models with observable computational behavior across quadratic and \(\Theta(n\log n)\) regimes, while multi-language and multi-paradigm comparisons expose implementation- and abstraction-dependent costs. The framework is grounded in sustained university-level teaching practice and is complemented by exploratory, retrospective evidence from multiple instructional cohorts. Archived assessment artifacts were interpreted using four pedagogical categories of Scalability Literacy : asymptotic recognition, empirical validation, architectural awareness, and algorithmic auditing.

The resulting evidence provides descriptive support for the instructional plausibility of ADSC but is not intended to establish causal learning gains, measurement stability, or longitudinal invariance across cohorts. By making computational cost and scalability behavior explicit and empirically inspectable, ADSC offers an adaptable instructional structure for supporting complexity-aware algorithmic judgment, particularly in educational environments increasingly shaped by AI-assisted programming.