Abstract:

A significant challenge in computing education is that many foundational problem-solving concepts remain implicit in introductory curricula, creating hidden stumbling blocks that hinder student development. Concepts such as state, scope, binding, composition, and correctness are often introduced through the idiosyncrasies of a specific programming language's syntax, rather than as first-class, abstract ideas. This paper argues for a pedagogical approach that uses the formal systems of Logic and Abstract Mathematics to make these critical concepts explicit, tangible, and manageable for learners.

We posit that Predicate Logic provides the essential framework for formally defining program state, invariants, and correctness, moving students beyond vague intuition. Simultaneously, Lambda Calculus offers a minimal and rigorous model for understanding functional abstraction, parameter binding, and composition, disentangling these core operations from the syntactic noise of industrial languages.

By teaching these formal systems not as advanced topics but as primary explanatory tools, we equip students with a conceptual toolkit to deconstruct and master the implicit building blocks of computation. This foundation is crucial in an evolving landscape where the proliferation of AI-assisted coding elevates the human role to that of a precise specifier and validator. We present a unified framework and discuss classroom strategies for using logic and mathematics to expose and clarify these conceptual hurdles, thereby fostering the deep, transferable abstract thinking required for modern software development and effective human-AI collaboration.

Keywords:

Computing Education, Formal Foundations, Conceptual Hurdles, Abstract Thinking, AI Collaboration.