Learner Participation in AI-Assisted Introductory Calculus: A Principle of Non-Substitutive Teaching

AI assistance can produce a correct mathematical solution while leaving open what the learner has understood, checked, or become able to extend. This paper develops a proposed principle of non-substitutive teaching for introductory calculus: assistance should sustain accessible opportunities for the learner participation that a justified educational purpose requires. The principle permits direct explanation, worked solutions, and continuing tools. It also subjects question-led teaching to scrutiny where prompts conceal authority or impose avoidable difficulty. Comparisons with scaffolding, intellectual emancipation, educational purpose, and a contemporary reconstruction of buyan zhi jiao clarify the philosophical commitments. A derivative argument is developed from its domains and assumptions through algebraic and limit justifications, then used in hypothetical teaching contrasts. Two recent AI tutoring studies illustrate the importance of distinguishing instructional packages and assessment horizons. The paper separates mathematical validity, observed participation, acquired competence, and normative adequacy. Its contribution is a structured framework for criticism and instructional design; empirical validation of the proposed principle, wider applicability, and longer-term formation remain open.