The research corpus: 51 studies, published whole
Math Challenge published 51 studies, 168,355 words, with numbered sources and declared limitations — whole, including the passages where the evidence contradicts the product.
The corpus in numbers
- Studies
- 51
- Words
- 168,355
- External links
- 838
- Distinct domains
- 369
- [unverified] marks
- 17
- Themes
- 5
Every number here is counted at build time by reading the research folder in the repository. None is typed into a translation file, so none can quietly go stale. Two precisions, because similar commands give different answers. Listing every Markdown file in that folder returns 53, not 51: it counts the index, which is not a study. And this page counts words the way wc -w does, markup included, while each study page counts the text with the Markdown stripped — 9 fewer across the whole corpus.
How each study is built
All 51 have the same shape, and that was checked rather than assumed: an executive summary in Spanish and one in English, numbered findings with their citations, and design implications at the end. Together they carry 838 external links to 369 distinct domains.
The studies themselves are not translated
This index exists in seven locales; the corpus does not. 47 of the documents are written in English and 4 in Spanish, and each opens with an executive summary in both. Claiming a translated corpus would be the first false statement on a site whose argument is that it makes none.
Why the studies that contradict the product are published too
Publishing only the research that agrees with you is marketing with footnotes. What makes a corpus worth reading is the part that cost something, and several of these studies argued the owner out of what he had asked for. Those passages go out whole, at the same size as everything else.
- The original brief asked for the product to be as addictive as possible. Study mc-17 catalogued the engagement mechanics that carry real regulatory exposure, and what came out of it is a blacklist naming them one by one: no purchasable currency, no paid random rewards, no hearts that lock a child out of practising.
- The owner asked for gRPC by name. Study mc-47 found three independent reasons it cannot work here — Workers cannot make outbound gRPC calls, the browser does not speak the protocol, HTTP trailers are barely supported at the edge — and any one of them was enough. It was dropped.
- The global leaderboard sorts by points. Studies mc-18 and mc-44 both recommend sorting by estimated ability instead, and mc-18 warns that adding up points rewards whoever solves many easy items quickly. The decision goes against them anyway, says so in its own text, and records the condition for revisiting it.
- The screen-time table looks like science and mostly is not. Study mc-26 found that past the age of five no authority publishes a figure at all, so the rest of that table is labelled as our judgement rather than as evidence.
None of this is confession. A claim you can check is worth more than one you cannot, and publishing the ones that went against us, at the same size as the rest, is what makes the rest checkable.
What [unverified] means
17 claims carry an explicit [unverified] mark, all of them inside 2 of the 51 studies, and 13 studies use the word somewhere without the brackets. The mark means one thing: the agent that wrote the line could not reach a primary source. Several government sites block automated fetching, so some legal statements could not be checked at all. They stay in the text, marked, instead of being quietly deleted.
None of those passages is legal advice, and none can be a basis for compliance without a lawyer. That warning is written inside the documents, not bolted on afterwards.
How the research was actually done
The session's web-search quota ran out halfway through. The agents that followed fetched primary sources directly — MDN, WebKit, W3C, EUR-Lex, pricing pages, paper PDFs — and used a plain HTML search endpoint. Every document declares its own limitations at the end. This paragraph is uncomfortable, and it is the reason the marks above are believable.
Math Challenge research corpus
51 studies on mathematics education, child privacy, gamification and platform engineering, dated 2026-07-31 and published in full, under the AGPL-3.0, in the project's public repository.
Pedagogy — how mathematics is taught
- mc-01 Japanese Mathematics Education: Lesson Study, Structured Problem Solving, Bansho, Neriage, and Soroban/Anzan
Four-phase Japanese lessons, the TIMSS video study, and the real abacus evidence.
- mc-02 Chinese Mathematics Education: Variation Theory, Mastery, and the Evidence Behind the Reputation
Building exercise series by systematic variation instead of random numbers.
- mc-03 Singapore Math: CPA Progression, Bar Modelling, and the MOE Framework
Concrete to pictorial to abstract, and bar models mapped onto difficulty levels.
- mc-04 Cognitive Load Theory and Worked Examples in Mathematics
When to show the worked solution, when to make them solve, and how to fade support.
- mc-05 Spacing, Retrieval Practice, and Interleaving Applied to Mathematics
The review algorithm itself: parameters, intervals and the mastery threshold.
- mc-06 Early Numeracy and Number Sense for Ages 3–7 (Pre-K, Kinder, Grade 1)
The learning trajectory for ages three to seven, in order.
- mc-07 Learning fractions, decimals, ratio, and proportional reasoning (ages ~8–14)
Thirteen named errors, the wrong answer each produces, and what the tutor says.
- mc-08 Algebra Learning Ages 12–17: The Arithmetic-to-Algebra Transition, Equals-Sign Misconceptions, Error Taxonomies, and Procedural Flexibility
Nine mis-learned rules of the arithmetic-to-algebra transition, and their repair.
- mc-09 Geometry, Measurement, and Spatial Reasoning Across Ages
Which geometry formats a browser can grade, and which still need a human.
- mc-10 Math anxiety, timed testing, growth mindset, and productive struggle: what the evidence actually supports
Read before deciding anything about a timer. The evidence pushes back hardest here.
- mc-11 Feedback and Formative Assessment in Mathematics — Evidence for an AI Tutor
Feedback templates by age band, and the feedback that makes performance worse.
- mc-12 Beyond High School: Proof, Olympiad Training, and PhD-Level Mathematics — What "PhD Mode" Could Realistically Contain
Fourteen bands above school, each with grading that works without a human.
- mc-35 What the research actually says about teaching over the internet
Do-to-watch ratio, video length, and how we would measure whether this teaches.
- mc-39 Drill, Mental Arithmetic, and "Eastern" Method Traditions: What the Evidence Actually Supports
Kumon, abacus, Vedic, Russian, Hungarian, Finnish: evidence versus marketing.
Product, engine and content
- mc-13 Intelligent Tutoring Systems and Learner Modelling: BKT, DKT, PFA, and the Math Garden Elo Approach
The formula that folds accuracy and time into one score, already validated.
- mc-14 Competitive and Design Research: Leading Math Learning Products
Khan, Brilliant, Kumon, IXL, Prodigy: what to copy, what to avoid, where the gap is.
- mc-15 School grades and math curricula across countries — toward one internal ladder
Grade systems across countries, and the country-neutral ladder that came out.
- mc-36 Designing Engaging, Pedagogically Sound Math Challenges: Rich Task Traditions, Item Formats, and Standards
Twenty item formats rated for solver resistance, and the order to build them in.
- mc-37 Larry Profe — porting Larry to Math Challenge
What already exists in code, file and line, model routing, and cost per explanation.
- mc-40 Building and Operating a 2,500-Item Math Bank: What Real Learning Products Do
A 2,500-item bank: templates, hand-writing or AI, with schema, effort and cost.
- mc-44 Adaptive Placement Testing and Computerized Adaptive Testing (CAT): IRT, Cold-Start Calibration, and Knowledge Spaces
The placement algorithm buildable in version one, with no calibrated bank.
Gamification, competition and identity
- mc-16 Duolingo's Gamification System and the Research Behind Engagement Mechanics
Engagement mechanics one by one, with evidence and risk when the user is a child.
- mc-17 Ethical gamification, intrinsic motivation, and dark patterns aimed at children: the counterweight to "as addictive as possible"
The counterweight to as addictive as possible: red lines with regulatory exposure.
- mc-18 Leaderboards and Competition Design: Psychological Effects, Rating Systems, and Fair Cross-Difficulty Comparison
Rating systems, leagues of thirty, and comparing a child with a doctoral student.
- mc-19 Habit Loops, Retention Mechanics and Push Notifications for a Children's Math PWA
Notifications that are not built on guilt, and the reality of push on iOS.
- mc-42 Audio, Music, Haptics, Motion and "Juice" in Learning Games
Sound by age band, and iOS Safari has no Vibration API, in any version.
- mc-43 Avatars, Identity and Progression for Children's Products Under Strict Privacy
Safe aliases in five languages, and which cosmetics are not a loot box.
Interface by age band and device
- mc-20 UI and interaction design for children aged 3-6 (KINDER band)
Touch targets near 88 px, with the source, and why dragging fails at this age.
- mc-21 UI/UX design for children aged 7-11 (PRIMARY / ELEMENTARY band)
The middle ground: no longer a toddler's interface, not yet a teenager's.
- mc-22 UI/UX Design for Teenagers (Ages 12–17): Research for the Math Challenge SECONDARY/TEEN Theme
What makes an app read as for little kids, and how to avoid it. Dark by default.
- mc-23 Interface Design for Serious Adult Mathematics: Rendering, Input, and the Adult/Expert Theme
KaTeX, MathJax and MathLive on licence and accessibility; maths input by device.
- mc-34 Internationalizing Math Notation: Numbers, Symbols, and Long Division Across Five Languages
Mexico writes a decimal point, the rest a comma, and long division four ways.
- mc-38 Accessibility and learning differences in a global, all-ages math game
How a timed game can still meet WCAG 2.2, and what a dyscalculia mode contains.
- mc-49 Navigation Patterns for a PWA-First Site: Installed App, Mobile Browser Tab, and Desktop
One primary navigation at a time; the bottom bar exists only when installed.
- mc-50 Navigation for the Authenticated App Area: Parent Dashboard and Future Child/Adult Play Surfaces
The signed-in area never inherits the public layout; its tabs derive from the real account.
- mc-51 Clasificación de las ramas de las matemáticas y su estructura de prerrequisitos — de MSC 2020 a los planes universitarios y los currículos escolares del mundo
The 63 areas of MSC 2020, arXiv and the ICM; the universal school spine and university prerequisite chains verified at ten institutions; a 26-branch map with gates.
- mc-52 Lógica para niños: booleana, tablas de verdad y acertijos — cómo se enseña en el mundo y cómo se convierte en retos de 7 años en adelante
Bebras and its verified age bands; Smullyan as the bridge to proof (MAA); the LOGI ladder N4-N12: attributes, puzzles, truth tables, predicates.
Platform, safety and business
- mc-25 Children's Privacy and Data Protection Law for Math Challenge
COPPA, GDPR article 8, the Children's Code, Brazil's LGPD, and Mexico after INAI.
- mc-26 Screen time guidance and healthy digital habits for children: setting evidence-based bounds on a parent-adjustable daily limit
Daily limits by age, and the note that past five no authority publishes one.
- mc-27 Family Account Architecture and Consent UX — How the Best Products Do It
The family-account entity model, and signing in a five-year-old without reading.
- mc-28 Teacher/Classroom Mode: Roster Design, the FERPA/COPPA Consent Gap for a Non-School Teacher, and Safe Competition
The legal hole: a teacher with no school cannot invoke the school exception.
- mc-29 Online Assessment Integrity and Anti-Cheating: A Progressive Model for a Consumer Math App
Six progressive tiers of integrity, and what is never done to a child.
- mc-30 Behavioral/Process Data in Learning Systems: What Hesitation and Timing Mean, and Where Child Privacy Law Draws the Line
Changing an answer improves the grade 79% of the time: penalising erasure is wrong.
- mc-31 The Solver Threat: AI Math Assistance in 2026 and What Actually Resists It
Which formats survive a photo solver and a frontier model, and which cannot.
- mc-32 Cloudflare Architecture for Math Challenge
The Cloudflare inventory with name, type, purpose and binding, and its real limits.
- mc-33 PWA-First Reality in 2026: Installability, iOS Safari, Offline, and the Store Question for Math Challenge
iOS, Android and desktop capabilities; iOS push needs home-screen installation.
- mc-41 Monetization and Pricing for Family Math Edtech — What Comparables Actually Charge, and What Regulators Actually Require
What comparable products charge, payment by market, VAT and right of withdrawal.
- mc-45 Onboarding, registro y activación: cuántos campos, y por qué los tours casi nunca sirven
What each registration field costs, and why the welcome carousel is advised against.
- mc-46 Clubs, retos de grupo y prendas: cómo tener apuestas sin perdedor y sin exposición regulatoria
The three elements of illegal gambling, and a group wager with no loser.
- mc-47 Stack, protocolos y rendimiento real: qué está de verdad a la vanguardia sobre Cloudflare
Why gRPC is out: Workers cannot call it and the browser cannot speak it.
- mc-48 El sitio abierto: por qué publicar la investigación es la estrategia orgánica
The case for publishing the research, and its own note that no source is primary.
Check it yourself
Clone the repository and run these. Every figure here comes out of one of them at build time; none was written from memory.
- The 51 studies
ls docs/research/2026-07-31-mc-*.md | wc -l- The 168,355 words
cat docs/research/2026-07-31-mc-*.md | wc -w- The 17 bracketed marks
grep -o "\[unverified\]" docs/research/2026-07-31-mc-*.md | wc -l- That all 51 carry a numbered sources section
grep -l "^## Sources" docs/research/2026-07-31-mc-*.md | wc -l- The licence: AGPL-3.0
gh repo view kilowatto/math-challenge --json licenseInfo
What is not here yet
- There is no search box and no filter. {docs} studies fit in one list, and a page that works with JavaScript off is worth more than a filter that does not.
- The bodies are not translated. Only this index exists in seven locales.
- The corpus is dated {fecha} and has not been revised since. It is not peer-reviewed, and it was produced with AI assistance under human direction — which is why every document names its own limits.
The whole corpus, unedited, lives in the public repository: the research folder on GitHub