# AGS Math: A Pedagogy of Non-Offloading **Status:** Foundational document. Any feature decision in the AGS Math app must be consistent with this paper. When in doubt, this document wins over convenience, engagement metrics, or user requests. **Author:** Pamela Lim **Last updated:** 10 May 2026 --- ## 1. The principle The AGS Math app exists to develop mathematical reasoning in children. It is not a homework-completion tool. It is not an answer-generator. It is not an AI tutor that solves problems on request. Its purpose is to make the student think — and to make handing thinking off to the machine *harder* than doing the thinking themselves. This is the operating principle of the entire app. Every feature, every screen, every interaction must be tested against it. Features that violate it, however clever, however technically impressive, however well-reviewed by users, do not ship. --- ## 2. Why math is the most vulnerable subject Math is the subject where AI offloading is most tempting and most damaging. It is most tempting because mathematical problems have well-defined answers. A child can paste a problem into any large language model and receive a complete, formatted, correct solution in seconds. The artifact — a finished problem set, a homework page, a worksheet — looks identical whether the child solved it or pasted it. It is most damaging because mathematical reasoning is built by repetition of struggle. The child who never struggles with a problem never builds the neural patterns that recognise its structure next time. They acquire a portfolio of solved problems with no underlying competence. When the test or the next-level problem arrives, they have nothing to draw on. This is not a hypothetical risk. It is the dominant outcome in classrooms where AI access is unrestricted and the assessment is the artifact. We see it already in essay writing across schools. Math is next, and math is worse, because math compounds: the child who skips Grade 4 fractions cannot do Grade 6 algebra. There is no faking forward. The AGS Math app, deployed to children with internet access and ChatGPT subscriptions, sits at the centre of this risk. We must therefore design the app such that the path of least resistance is the path of learning. --- ## 3. What "understanding is the deliverable" means in practice In a traditional homework system, the deliverable is the answer. The answer is what the teacher grades, the parent checks, the platform records. AI-offloading is the optimal strategy when the answer is the deliverable — it produces the answer faster, more accurately, and with less effort than the child can. The AGS Math app must invert this. The deliverable is the **process of arriving at the answer**, not the answer itself. The cascade — `correct_streak`, `wrong_streak`, `difficulty_passed`, `total_correct_attempts`, `total_incorrect_attempts` — is not bureaucratic record-keeping. It is the unit of progress. A child who pastes problems into an LLM and submits answers cannot pass the AGS Math system, because the cascade requires sustained performance at the top difficulty tier with consecutive correct answers. The system can be cheated only if every answer in a streak is correct — which means the child who is offloading is learning to be a reliable LLM operator, which is itself a skill, but is not the skill the system is designed to certify. More directly: the system rewards a child who answers seven questions, gets four wrong, recovers, and reaches the top tier through genuine struggle, more than it rewards a child who answers seven questions correctly through paste-and-submit. The first child is producing process. The second child is producing artifact. The Maxile and `skill_passed` reflect the first. This is not an accident of design. This is the design. --- ## 4. What this rules out The following patterns are forbidden in the AGS Math app. They violate the operating principle. They do not ship. **Hint buttons that approach the answer.** A hint that says "the answer is around 40" or "use the formula a² + b² = c²" is not a hint, it is a reduction of the problem space toward triviality. Hints that ship in AGS Math must scaffold *reasoning*, not deliver it. They must be questions, not statements: "what do you know about this triangle?" not "this is a Pythagorean problem." **An AI tutor that solves problems on request.** No tutor feature in AGS Math may compute and display the answer to the problem the student is working on. The tutor's job is to push back, ask, redirect — never to compute. If a tutor feature ships, it must be configured to refuse direct answers and to require the student to make the next inferential step themselves. **"Show solution" buttons that are easy to press.** A child who has not attempted the problem must not see the solution. The solution must be gated behind sufficient genuine attempts (or an explicit "I give up" that costs kudos and triggers a difficulty step-down). Looking up the answer must be more expensive than trying again. **Adaptive difficulty that drifts toward easy to maintain engagement.** The temptation in adaptive systems is to lower difficulty when the user struggles, to keep them clicking. AGS Math must not. The difficulty must adapt to the child's *demonstrated capacity*, not to their comfort. A child whose `wrong_streak` reaches `no_wrongs_to_fail` drops a tier — but the system continues to challenge them. It does not collapse to triviality. **Bulk question generation that produces formulaic problems.** AI-assisted question generation is permitted, but the output must be reviewed by a human pedagogue before reaching students. Pattern-matchable questions produce pattern-matching students. Questions must demand reasoning, not recognition. **Engagement-optimisation features that reward time-on-app over learning.** Streaks, daily goals, and reward systems are permitted only when they reward *demonstrated competence*. A streak of "logged in seven days" is not a learning streak. A streak of "passed three new skills this week" is. --- ## 5. What this requires The same principle, stated as positive requirements: **Hints must be Socratic and tiered.** Tier 1: a question that surfaces what the child already knows ("what's the relationship between these two numbers?"). Tier 2: a hint about method ("try drawing a diagram"). Tier 3: a worked example of a *similar* problem with different numbers. The actual problem's answer is never given. **Wrong-answer feedback must reveal reasoning failure, not the right answer.** A child who answers 47 to a problem whose answer is 53 should not see "incorrect — the answer is 53." They should see something like "you got 47. Check your second step — what did you assume about the order of operations?" The child must do the work of locating their own error. **Kudos must reward attempt and recovery, not just correctness.** A child who attempts a hard problem and gets it wrong should earn more kudos than a child who skips it. A child who fails three times then succeeds should earn more than a child who succeeds first time on an easier version. The reward structure must value the process of reasoning under difficulty. **The interface must demand commitment before revealing information.** No information about the problem (hints, related skills, difficulty, worked examples) is shown until the child has committed to an attempt. Commitment-first, information-second. This mirrors classroom pedagogy: the teacher does not show the worked example before the student has tried. **The cascade must be visible to parents and teachers.** Process metrics — streaks, attempts, recovery rates — must be the headline data on parent and teacher dashboards. Not "completed 12 questions." Not "scored 80%." Process. This redirects parental attention away from artifact and toward learning. **Curated curriculum, not infinite content.** The question bank must be finite, ordered, and pedagogically structured. Infinite content tempts skipping. Finite content forces engagement with what is in front of the child. --- ## 6. The seven mechanisms, applied to the math app The seven mechanisms that make AI-offloading harder than doing the work, mapped onto a digital adaptive math app: **Oral examination and Socratic viva** — partially available. A digital app cannot conduct viva at scale. But the AI tutor, properly constrained, can perform a constrained version: asking follow-up questions in real time, demanding the child articulate their reasoning, refusing to accept answers without justification. This is the core of any future tutor feature. **Branching mid-task work** — fully available. The cascade already implements this in primitive form: the next question's difficulty depends on the answer to the last. Future versions can branch on *method* — if the child solves a problem one way, the next question requires a different approach. AI cannot pre-cache an entire branching tree of responses to a child's specific reasoning path. **Personal-data tasks** — partially available. Word problems can be parameterised by the child's stated context (their family size, their school's location, their birthday). The student's lived data resists fabrication. This is a future feature; the curriculum team should design problem types that draw on the student's own context. **Process artifacts, not product artifacts** — fully implemented. The cascade is the canonical example. We grade the streaks, the recovery, the difficulty progression — not the artifact of a finished worksheet. This is the foundation; everything else builds on it. **Adversarial sparring** — partially available. The current app does not have a sparring mode. A future feature: an AI opponent that proposes a reasoning step and asks the child to find the flaw. The child's job is to be the critic, not the producer. AI excels at producing flawed reasoning; the child's job is to detect it. **Performance and demonstration** — not available in a digital app. This belongs to the wider AGS school programme. Math performance — explaining a solution to a class, demonstrating a method, defending a result — happens in the live AGS classroom, not the app. **Local, embodied tasks** — not available in a digital app. Belongs to the school programme. The app supports the school by providing the abstract reasoning practice that grounds embodied math work. The math app is responsible for mechanisms 2, 3, 4, and 5. Mechanisms 1, 6, and 7 belong to the wider AGS programme. This is the correct division of labour. --- ## 7. What AI legitimately does for us The non-offloading principle does not mean AI has no place in the app. It means AI's role is constrained. The legitimate uses are: **Diagnosis.** AI infers the child's level, identifies weak skills, and chooses the next question. The child does not see this happening. The AI's output is "what to ask next," not "the answer to what we asked." This is the role the picker, the cascade, and the diagnostic IRT walk play. **Scaffolding.** AI generates Socratic hints, alternative phrasings, related practice problems. AI never delivers the answer; AI delivers the question that helps the child arrive at the answer themselves. This is a future feature. **Adversarial sparring.** AI plays the role of the flawed reasoner, the unreliable source, the questioner. The child's job is to push back. This is a future feature. **Personalisation of context.** AI generates word problems set in the child's stated context — their school, their hobbies, their family. The mathematics is unchanged; the wrapper is personal. **Pattern detection in the child's process.** AI looks at the child's streak patterns, error types, time-on-question, and surfaces patterns to the parent or teacher: "your child consistently fails problems of this type — here's what I notice." The pattern is the deliverable to the adult. The child is not told the pattern; they continue to encounter problems of that type until the pattern resolves. What AI does not do: **AI does not solve the child's problem for them.** Ever. Not as a hint, not as a worked example, not as a tutor response, not as a "let me show you." **AI does not reduce the difficulty of a problem set to maintain engagement.** The difficulty is set by the cascade, which is set by demonstrated competence. AI does not override this for emotional comfort. **AI does not produce the artifact the child is being asked to produce.** If the child is asked to write out the steps of solving a quadratic, the AI does not write them. The child writes them; the AI evaluates whether the steps are sound. --- ## 8. Operational rules Concrete feature-level rules, derived from the above: 1. No feature in the AGS Math app may, on student input, return the answer to the problem the student is working on. The answer is the artifact the student is producing; the system never produces it for them. 2. Every hint is tiered. Hints earlier in the tier are questions; hints later in the tier are method suggestions; the final tier is a worked example with different numbers. Hints never give the answer. 3. Solutions are gated behind genuine attempt. A child must reach the `no_wrongs_to_fail` threshold (currently 2) before the solution becomes available. Even then, accessing the solution costs kudos and triggers a difficulty step-down on the next question. 4. No `skill_passed` flag flips on a streak that includes pasted answers. (Practical implementation: monitor for paste events, time-on-question outliers, copy-from-clipboard activity. Anomalous patterns invalidate the streak. This is detection-via-side-channel, since we cannot inspect what the child is doing in another tab. The signal is imperfect, but the principle is: a pass that the system cannot verify as genuine is not a pass.) 5. Process metrics (streaks, attempts, recovery rates, difficulty progression) are the headline data on parent and teacher dashboards. Score and completion are secondary. This is a UI rule, not just a backend rule. 6. AI tutor features, when built, default to refusal. The tutor is configured to refuse direct answers and require the student to articulate next steps. The tutor cannot be jailbroken into producing the answer; if it is, the feature is broken and must be fixed. 7. Question generation by AI is reviewed by a human pedagogue before deployment. AI does not write directly into the production question bank. 8. Feature proposals that violate any of the above are rejected at design review, regardless of engagement projections, parent demand, or competitive pressure. --- ## 9. Implications for the roadmap This principle has direct consequences for upcoming AGS Math features. **The unified `QuestionPickerService` (post-beta sprint)** must be designed against the spec, not against engagement. The picker must demand sustained performance at top tier. It must not collapse to easy questions to keep the child clicking. **The hint feature (currently in `Question.hints` relationship, not yet wired to UI)** must be tiered before launch. A flat list of hints with the last one being the answer is unacceptable. **The solution feature (currently in `Question.solutions` relationship)** must be gated behind genuine attempt with a kudos cost. A "show solution" button accessible at any time is unacceptable. **Future AI tutor** must be designed with refusal as the default behaviour. Procurement of any third-party tutor (e.g. an LLM-backed chat feature) must be evaluated against this constraint. A tutor that defaults to "let me solve this for you" is not a tutor that ships in AGS Math. **Future adversarial sparring features** are a strategic priority. The school that pioneers these features in a digital math app captures a teaching surface no competitor currently occupies. **Personalised word problems** are a strategic priority for the same reason. The child's own data is the cheapest available defence against fabrication. --- ## 10. The strategic position This principle is also a strategic position. The mainstream educational technology industry is moving toward AI integration as a feature: AI tutors, AI homework helpers, AI essay assistants. These products optimise for engagement, parental willingness to pay, and time-on-app. They are, in aggregate, accelerating the deskilling of children. Many parents now intuit this and are looking for an alternative they can trust. AGS Math's position is the alternative. Not "AGS uses AI well in the classroom." A stronger claim: **AGS designs curriculum such that AI cannot be used badly — because the only use available to a student is the use that returns thinking to the student.** This positions AGS as a curriculum operator rather than a curriculum consumer of AI. It is a defensible position because it requires actual curriculum-design work, which competitors will find expensive to copy. It is a parent-facing position because it answers the question parents are increasingly asking: *will my child still be able to think after using this?* The pedagogy of non-offloading is not a constraint on what AGS Math can be. It is what AGS Math is for. --- ## 11. Change log | Date | Author | Change | |---|---|---| | 10 May 2026 | Pamela Lim | Initial draft. Principle established. Operational rules locked. |