Source-linked AI summary
Course design in the age of AI
Benjamin Davies
TL;DR
The paper asks how teachers should redesign courses when students can delegate tasks to AI. It develops a learning-by-doing model of course design and finds that AI changes optimal course structure and can widen learning differences across students.
Problem
Prior work leaves open how teachers should redesign courses to ensure students develop skill when students can delegate tasks to AI.
Method
The paper introduces a model of learning-by-doing and course design to analyze AI's impact on optimal course design and student skill development.
Results
AI changes optimal course design, while complementary AI makes high-skill students learn faster but low-skill students build skill slower.
Takeaways & Limitations
Course design must account for students' incentives to delegate to AI because AI can alter task sequencing and produce different skill-development outcomes across students.
Takeaways & Limitations
The model relies on several simplifying assumptions that could be relaxed in future research.
Abstract
from arXiv · showhide
I develop a model of learning-by-doing and course design, and use it to study the impacts of artificial intelligence (AI). A myopic student faces a sequence of tasks that he can work on or delegate to AI. Work requires costly effort but builds skill; delegation requires no effort but builds no skill. A teacher designs the task sequence ("course") to maximize the student's skill development, given his choices to work or delegate. Without AI, the teacher makes earlier tasks more effort-intensive and later tasks more skill-intensive. With AI, the teacher must redesign early tasks to induce effort, leading to less skill development. If AI complements effort, then improvements in AI quality make high-skill students learn faster but low-skill students learn slower.
1 Introduction
The paper asks how teachers should redesign courses when students can delegate tasks to AI, and develops a learning-by-doing model to analyze the resulting effects on course design and skill development. It frames courses as designable objects constrained by delegation and derives distinct designs and learning outcomes depending on students’ incentives and AI’s relationship to effort.
- Research question: The paper asks how teachers should redesign courses so students develop skill when they can delegate tasks to AI.This question takes AI access as given and changes coursework rather than banning AI.
- Model: The model features a myopic student choosing whether to work or delegate, while a teacher designs the task sequence to maximize skill development.Working requires costly effort and builds skill; delegation produces output without effort or skill gain.
- First-best design: Without delegation incentives, optimal courses become gradually less effort-intensive and more skill-intensive because effort and skill are complementary inputs.Earlier effort-intensive tasks induce effort when skill is low, while later skill-intensive tasks exploit greater skill.
- Second-best design: When students may delegate, the teacher makes earlier tasks more skill-intensive relative to first-best, producing an increasing-then-decreasing effort-intensity sequence and less overall skill.The distortion makes the course incentive-compatible and ensures some skill development, but it remains worse for learning than first-best design.
- Skill and AI productivity: Students with more initial skill gain more overall skill, whereas more productive AI tightens the teacher’s incentive constraints and requires greater course distortion.More-skilled students are less tempted to delegate and can therefore be induced to work with less distortion.
- Complementary AI: When AI complements effort, improving AI quality makes high-skill students gain skill faster but low-skill students gain skill more slowly.AI quality affects learning through both complementarity with effort and increased temptation to delegate.
2 Model
The model studies a myopic student who chooses whether to work on sequential tasks or delegate them to AI, while a forward-looking teacher designs task effort intensities to maximize skill development. Working uses costly effort and builds skill; delegation produces output without effort or skill accumulation.
- A myopic student faces sequential tasks and can either work on them or delegate them to an AI assistant.
- Work combines costly effort with skill to produce output, whereas delegation requires no effort and builds no skill.
- Effort intensity measures how much production relies on effort rather than skill: effort-intensive tasks reward applying methods, while skill-intensive tasks reward identifying them.
- The student’s myopia creates a conflict with the teacher because he values current production and effort costs, while the teacher values skill development.
- Skill accumulation is proportional to exerted effort, while AI-generated output is independent of the student’s skill and task effort intensity.
- The teacher chooses each task’s effort intensity to maximize the student’s final skill, given the student’s best responses.
3 Best-responses
The student’s best-response effort depends on motivation, skill, and task effort intensity. Skill raises effort on tasks that are not fully effort-intensive, while the relationship between effort intensity and effort can be increasing or inverted-U-shaped.
- Best-response effort is positive and increases with the motivation parameter π.
- When η < 1, higher skill increases both best-response effort and payoff; when η = 1, effort and payoff are independent of skill.
- For s = 1 and π = 1, best-response effort increases with η, whereas for s = 5 it has an inverted-U-shaped relationship with η.
- For every s > 0, a unique effort intensity maximizes best-response effort.
4 Optimal courses
The teacher chooses task effort intensities to maximize skill accumulation while respecting the student's choice between working and delegating. Without productive AI, optimal courses make early tasks more effort-intensive and later tasks more skill-intensive; with productive AI, incentive compatibility lowers effort and skill development.
- Course design: The teacher selects each task's effort intensity to maximize the student's best-response effort subject to the incentive constraint.Skill accumulation depends on whether the student works or delegates and, if working, on his best-response effort.
- First-best course: When AI generates no output, the student works on every task, so the teacher can maximize best-response effort without incentive constraints.The delegation payoff is zero, and the student's payoff from working is nonnegative.
- First-best course: ηFB(s) = 1 for s ≤ πe, while for s > πe the unique first-best effort intensity lies in (0, 1) and decreases with skill.The student's best-response effort is maximized at ηFB(s).
- First-best course: First-best courses use ηt = ηFB(st), with effort intensity equal to 1 initially and decreasing across later tasks.Because skill rises after each task and ηFB is non-increasing, later tasks become less effort-intensive and more skill-intensive.
- Second-best course: With positive AI output, the first-best course may violate incentive compatibility because the student prefers delegating the initial task.Under the stated restrictions, π/2 < y < s0, so AI out-produces the student on a fully effort-intensive task but not at the initial skill level.
- Second-best course: Second-best effort is ηSB(s) = min{ηMIC(s), ηFB(s)}, producing an increasing-then-decreasing task sequence and less skill development than first-best.The student exerts weakly less effort and receives weakly higher payoffs under second-best design, while the teacher's skill-development objective is worse.
- Implications: Overall skill gain increases with initial skill, motivation π, and accumulation rate r, but decreases with AI-generated output y.The same monotonicities hold for each task's skill increment.
5 Extension: Complementary AI
The extension models AI quality as complementing effort and shows that its effects on course design, effort, and learning depend on student skill. Higher AI quality benefits high-skill students but can reduce effort and skill gains among low-skill students.
- AI quality and incentives: AI quality q multiplies both effort productivity and delegated output, allowing AI to complement or substitute for student effort.The student can use AI either to avoid effort or to accelerate effortful subtasks.
- First-best design: The first-best effort xFB(s; q) increases with AI quality, while the first-best course assigns more effort-intensive tasks as q rises.The teacher does so because higher AI quality increases the student’s willingness to exert effort.
- Second-best design: Second-best incentive-compatible intensity ηMIC(s; q) decreases in q below s†, is constant at s†, and increases above s†.The threshold s† is equivalently characterized by ηMIC(s†; q) = 2/3.
- Heterogeneous learning: Second-best effort xSB(s; q) decreases in q for s < s‡(q) and increases in q for s > s‡(q).The threshold s‡(q) increases with AI quality.
- Heterogeneous learning: AI-quality improvements make high-skill students gain skill faster but low-skill students gain skill slower.High-skill students become more willing to work, whereas low-skill students become more tempted to delegate.
- Distributional implications: AI quality can widen the skill distribution even when it compresses performance differences, because low-skill students’ output rises without corresponding skill growth.The paper treats compression in performance and divergence in skill as joint implications of the same mechanism.
6 Discussion of modeling assumptions
The discussion examines how production, complementarity, effort costs, and skill accumulation assumptions shape the model’s course-design results. The paper reports that its qualitative conclusions are robust to arbitrary AI quality but depend on some structural assumptions.
- AI quality: The paper’s qualitative conclusions do not change when AI quality q ≥ 1 is allowed to vary arbitrarily.The baseline discussion suppresses q for notational economy.
- Production technology: CES production parameterizes complementarity between effort and skill through elasticity of substitution 1/(1 + ρ).Higher ρ makes effort and skill more complementary and makes substitution between them more difficult.
- Production technology: With CES production, first-best effort intensity is constant in ρ below the skill threshold π(1 + ρ)^(1/ρ) and decreases in ρ above it.The best-response effort is maximized at η = ηFB(s).
- Production technology: The constant-then-decreasing shape of first-best effort intensities arises from complementarity between effort and skill.Perfect substitutes would instead make best-response effort independent of skill and lead the teacher to choose η = 1.
- Effort costs: Convex effort costs are necessary for first-best courses to have gradually decreasing effort intensities.Under convex costs, the relevant expression increases in skill, so the maximizing effort intensity falls as skill rises.
- Scope boundary: If AI-generated output can exceed the payoff from working, the teacher must distort tasks away from skill intensity, producing qualitatively different courses.This is a scope boundary for the model’s predictions.
- Skill accumulation: If skill grows with output rather than effort, the teacher wants qualitatively different courses because output is maximized at boundary effort intensities.The teacher may choose ηt = 1 or let ηt approach zero depending on skill.
7 Conclusion
The paper develops a learning-by-doing model of course design and derives how delegation to AI changes optimal tasks, skill accumulation, and distributional outcomes. Its conclusions also identify limitations from myopia, single-student design, and constant motivation assumptions.
- The model analyzes how AI affects optimal course design and student skill development.
- Without delegation incentives, the teacher designs courses that become gradually less effort-intensive and more skill-intensive.
- When delegation is tempting, the teacher distorts the course toward more skill-intensive tasks, reducing the student’s overall skill gain.
- Students who start with more skill gain more overall, while greater temptation to delegate reduces skill accumulation.
- When AI complements effort, higher AI quality makes high-skill students build skill faster but low-skill students build skill slower.
- The model assumes a myopic student, a teacher designing for one student with known initial skill, and motivation constant across tasks.These assumptions differ from settings where students value future skill, courses serve heterogeneous students, or task motivation varies.
- With heterogeneous initial skill, the teacher may leave low-skill students behind to optimize for high-skill students and loosen incentive constraints.
- Allowing motivation to vary across tasks could change when the incentive constraint binds, and the optimal reward timing remains unresolved when design and delegation coexist.
A Proofs
The appendix states that the main results are extended to AI quality q greater than one.
- The appendix presents general versions of the results allowing the AI quality parameter q to exceed one.
A.1 Proof of Lemma 1
The proof establishes comparative statics for the student’s best-response effort under complementary AI.
- Lemma A.1 defines positive best-response effort x*(s, η; q) for a given skill level and effort intensity.
- Best-response effort increases with the motivation parameter π and AI quality parameter q.
- Best-response effort increases with skill when η < 1 and is constant otherwise.
A.2 Proof of Lemma 2
The appendix establishes comparative statics for the student’s best-response payoff under complementary AI.
- Lemma A.2 defines the payoff generated by the student’s best-response effort x*(s, η; q).
- Best-response payoff increases with motivation π and AI quality q, and increases with skill when η < 1.
- Payoff decreases with effort intensity when η < s/πq^2 and is non-decreasing in η otherwise.
- The proof derives these comparative statics from the effort lemma and the student’s first-order condition.
A.3 Proof of Lemma 3
Lemma 3 characterizes first-best effort intensity under complementary AI: it is uniquely determined, maximizes best-response effort, and declines with skill beyond a threshold. The intensity varies continuously with skill and AI quality and converges to zero as skill becomes large.
- A unique ηFB(s; q) ∈(0, 1] maximizes the student's best-response effort for every skill level.
- When s ≤ πeq2, first-best effort intensity equals 1; when s > πeq2, it is interior and satisfies (13).
- For s > πeq2, ηFB(s; q) decreases in s and increases in π and q.
- ηFB(s; q) is continuous in both s and q and converges to zero as s →∞.
A.4 Proof of Theorem 1
Theorem 1 derives first-best course design under complementary AI by applying the effort-intensity characterization task by task. Effort intensity is initially maximal, then decreases after a threshold task as the student's skill rises.
- The teacher's optimal effort intensity on each task equals ηFB(st; q).
- There is a threshold task tFB such that ηt = 1 before it, while ηt decreases over later tasks.
- If final skill satisfies sT ≤ πeq2, every task has ηt = 1.
- If sT > πeq2, intensity remains 1 before tFB and then satisfies ηt+1 < ηt for later tasks.
A.5 Proof of Proposition 1
Proposition 1 characterizes first-best effort and payoff under complementary AI. Both are continuous in skill, constant below a threshold, and increasing above it.
- First-best effort xFB(s; q) and payoff uFB(s; q) are continuous in skill s.
- For s ≤ πeq2, first-best effort and payoff are constant in s.Specifically, xFB(s; q) = πq and uFB(s; q) = π2q2/2.
- For s > πeq2, first-best effort and payoff increase in s.
A.6 Proof of Lemma 4
Lemma 4 establishes parameter restrictions for the complementary-AI model under the stated assumptions. The restrictions bound the delegation payoff relative to AI quality and initial skill relative to the delegation payoff.
- Under (SB; q), πq/2 < y.
- Under both (SB; q) and (ND; q), qy < s0.
- The first-best payoff satisfies uFB(s0; q) ≥ π2q2/2 independently of s0.
A.7 Proof of Lemma 5
Under complementary AI, each skill level above qy has a unique incentive-compatible effort intensity, and the second-best course’s effort is increasing early and decreasing later. Second-best effort and overall skill gain rise with initial skill, motivation, and accumulation rate, while AI-generated output reduces them in the stated cases.
- Lemma 5: For every skill level s > qy, there is a unique effort intensity satisfying the incentive condition, and incentive compatibility holds if and only if ηt ≤ ηMIC(st; q).The mapping s 7→ηMIC(s; q) is continuous and increasing on its domain.
- Theorem A.2: The second-best course sets ηt = ηSB(st; q), with effort intensity increasing through task tSB and decreasing thereafter.The maximizing task may be non-unique, but a smallest maximizer tSB exists.
- Lemma A.6: Second-best effort increases with skill level and motivation, decreases in AI-generated output when full-information effort yields utility below πqy, and is otherwise constant in y.These comparative statics characterize xSB(s; q) under the complementary-AI assumptions.
- Lemma A.7: Skill increments increase with initial skill, motivation, and the accumulation rate, but decrease with AI-generated output.For each task, the increment is Δ(st, ηt; q) ≡ st+1 − st.
- Theorem A.3: Overall skill gain sT − s0 increases with initial skill, motivation, and the accumulation rate, while decreasing with AI-generated output.This conclusion follows from the comparative statics of task-level skill increments.