A Tool-Invariant Framework for Teaching and Assessing Computational Methods in the Age of Agentic AI

Created: 2026-07-19 | Tags: agentic-aiai-literacyassessmentauthentic-assessmentcomputational-thinkinggenerative-aihigher-edoral-defenseover-relianceverification

Larry Engelhardt (Francis Marion University) โ€” arXiv:2607.15518 [physics.ed-ph], submitted 17 Jul 2026. CC BY 4.0. doi:10.48550/arXiv.2607.15518.

๐Ÿ“„ arXiv full text (HTML) โ€” open access; supplement tables (task-by-task progression, oral-defense rubric) as ancillary PDF.

Note on type: This is a framework / position essay (first-person, draws on the author's teaching practice), not a controlled empirical study. Its claims are argued and illustrated, with open questions explicitly flagged as untested. It is tagged confidence: high for fidelity to the source and internal rigor, but the design prescriptions are the author's and largely await validation (Fall 2026 cohort).

Summary

Agentic AI โ€” systems that write, run, and revise simulation code from natural-language specs โ€” is the latest step in a centuries-long migration of mechanical work from human to tool. Engelhardt argues that what a learner must know is tool-invariant: across tools (fingers โ†’ pencil โ†’ calculator โ†’ Python โ†’ agent), the requirements are stable; only their content and weight shift. The paper organizes these into five pillars, argues that sensemaking/verification is now the load-bearing skill (because AI-generated artifacts are bespoke and unvalidated, unlike socially-validated libraries), and draws the assessment consequence: when artifacts can be generated on demand, the artifact no longer certifies the student. The proposed response: AI-free in-class coding quizzes (measure white-box residue) + oral defenses of comment-stripped, AI-assisted work (measure orchestration), with a verification gate that must pass regardless of total score.

The five pillars (tool-invariant)

1. Inputs and outputs โ€” what goes in, what comes out, conditions of validity; problem posing. 2. Method concept โ€” a working model of what the method does, including its knobs (step size, tolerance) and characteristic failure modes (instability, divergence, overfitting, aliasing). 3. Terminology โ€” precise disciplinary vocabulary; now an input channel, since vague natural-language specs silently cede choices to the tool. 4. Sensemaking โ€” judging whether outputs make sense and establishing correctness (verification/validation). Always present; becomes load-bearing under agentic AI. 5. Operating the tool โ€” the actuation skill: once penmanship, now directing an agent (broad, shallow "interactional expertise" rather than narrow deep syntax).

The pillars organize into a workflow: Specify โ†’ Predict โ†’ Delegate โ†’ Verify โ†’ Interpret; Iterate, threaded by calibrated reliance (how much verification is owed, given tool + task).

Why verification is newly load-bearing (the core argument)

Opacity was never the problem โ€” validation is. A library routine (FFT, linear algebra) is opaque but socially validated (published algorithms, decades of testing, millions of users). An AI-generated simulation is opaque and bespoke: a population-of-one artifact from a stochastic process whose competence frontier is "jagged and invisible," whose failures arrive disguised as successes (running code, smooth plots, confident prose). The verification burden that ecosystems amortized across a community now lands on each student, for each artifact, every time.

Principle of validation authority: delegation is safe exactly where the delegator retains the ability to validate the outputs. A computational-physics course now exists to train validation authority. Corollary: "anyone can build software with AI" holds only where correctness is observable in use (dashboards, apps); a physics simulation's correctness must be established by disciplinary checks.

What must remain human (non-delegables)

Posing the problem ยท choosing & owning the physical model/assumptions ยท the pre-execution prediction ยท specifying the checks ยท final epistemic responsibility ("the AI said so" is never a justification). Items 1, 2, 5 are constitutive of doing science, not claims about current AI capability, and do not weaken as models improve.

Assessment design (the constructive response)

Teaching practices

Connections to the wiki

Related Pages

Citation

APA: Engelhardt, L. (2026). A Tool-Invariant Framework for Teaching and Assessing Computational Methods in the Age of Agentic AI. arXiv:2607.15518 [physics.ed-ph]. https://doi.org/10.48550/arXiv.2607.15518