XP System BrainLift

• Owner
  • Serban Petrescu
• Purpose
  • To establish a definitive, research-backed knowledge base on XP (eXperience Points) systems for educational games, specifically for designing TrashCat's XP system.
  • This document will analyze and synthesize insights from three established XP systems: Math Academy (research-backed adaptive learning platform), Alpha Andy M / TimeBack (mastery-focused multi-app ecosystem), and LearnWithAI / Athena (content-specific assessment-heavy approach).
  • It will serve as the authoritative reference for making XP design decisions in TrashCat, ensuring our system incentivizes genuine learning, prevents gaming behaviors, and aligns with our dual-mode (Speedrun + Practice) pedagogical model.
  • The goal is to extract universal principles and identify context-specific adaptations needed for a game-controlled speed, fact-level progression system where students cannot control pacing.

Sources

• LearnWithAI XP Brainlift
• Andy M's XP Brainlift
• Math Academy's Way

DOK4: Spiky Points of View

• We use effort-intrinsic XP (time-based) instead of content-intrinsic XP (milestone-based), directly contradicting universal best practice.

  • Why it's controversial: Every examined system (Math Academy, Alpha Andy M, LearnWithAI) explicitly rejects time-based XP. Alpha Andy M states: "Expected XP belongs on each piece of course content and is student independent." The research consensus is that time-based XP punishes efficiency, rewards dawdling, and enables gaming. Content-intrinsic XP (fixed per task) is considered the only viable approach.
  • Our Bet: We bet on the sophistication of our learning algorithm to prevent gaming behaviors architecturally, making time-based XP viable where it would fail in other systems. Our algorithm controls: (1) which facts are eligible for practice (spaced repetition cooldowns), (2) when practice sessions end (completion caps, cooldown exhaustion), (3) how fast students can answer (game-controlled speed), and (4) daily diagnostic frequency (Speedrun caps). These constraints ensure that "active play time" is always productive learning time - students cannot dawdle, farm, or game the system because the algorithm controls pacing and availability. Given this architectural protection, "1 minute of work = 1 XP" becomes maximally simple and understandable for third graders without sacrificing integrity. We accept that XP becomes a time metric rather than an achievement signal, but rely on Progress % to track actual learning outcomes.

• We award zero XP for intervention time, even though students spend real effort on error correction.

  • Why it's controversial: In a time-based XP system (1 minute = 1 XP), excluding intervention time creates complexity. Students are actively engaged during interventions (TurnWheels, DragDrop, CueFading), spending ~30 seconds of real effort per intervention. Why does this time not count when all other active time counts?
  • Our Bet: XP tracks run time only - when the cat is moving and students are answering math facts. Interventions pause the run, creating a natural time penalty for errors. This architectural decision aligns XP with forward progress (facts answered) rather than total engagement time. The simplicity of "run time = XP time" is clearer than "active time = XP time," and it preserves the pedagogical principle that interventions are corrective work, not rewarded work. Students understand: mistakes cost you time (paused XP accumulation) plus effort (completing the intervention).

• We award XP for Speedrun despite it being purely diagnostic assessment.

  • Why it's controversial: Alpha Andy M explicitly states "Do NOT award XP for passive activities... Wait until learning is verified." Speedrun is assessment (showing what you know), not practice (building what you don't). Traditional thinking says assessment shouldn't earn XP unless tied to performance thresholds.
  • Our Bet: Speedrun is active work requiring focus and effort. It's the critical daily ritual that drives Practice mode targeting. In our time-based system, the daily cap (only the first Speedrun per skill awards XP) prevents farming while ensuring students are incentivized to complete the diagnostic properly. The fixed time-based reward doesn't create sandbagging incentives (poor performance doesn't extend the run) or answer-lookup incentives (performance doesn't affect XP earned).

• We stop awarding XP when skills reach 100% completion in both Practice and Competition modes, hard-capping progression despite unlimited available practice.

  • Why it's controversial: Math Academy allows unlimited XP earning per day. Their system uses pace-based efficiency adjustments but doesn't cap absolute XP. Alpha Andy M sets daily targets rather than caps. Preventing students from earning XP for continued practice on mastered material could feel punishing to motivated students who want to keep playing.
  • Our Bet: Without this cap, our time-based system enables trivial XP farming: students could grind completed skills indefinitely, earning 60 XP/hour with zero cognitive load. This would corrupt XP as a learning metric entirely. The cap ensures XP tracks genuine learning effort, not mindless repetition. Students can still practice completed skills for maintenance (pedagogically valuable), they just don't earn XP for it. This applies to both Practice mode and Competition mode - completed skills award zero XP regardless of game mode. This forces students to engage with new, challenging content to earn XP, maintaining integrity of the reward signal.

• We award no bonuses for exceptional performance, creating zero quality-based multipliers.

  • Why it's controversial: All examined systems award 20-25% bonus XP for exceptional performance (>95% accuracy). Research (Egram, 1979) empirically validates that performance-contingent bonuses increase future performance. Math Academy states "quality impacts efficiency 50x more than pace." Flat-rate XP regardless of accuracy ignores quality entirely as a factor in earning rewards.
  • Our Bet: In our time-based system, quality already affects XP rate indirectly: accurate students avoid slowdown penalties and intervention time, completing more questions per minute. Adding explicit bonuses would reintroduce complexity that the executive decision explicitly rejected. We accept that our XP system provides weaker incentives for careful work than research-backed alternatives, prioritizing "embarrassingly simple" over "pedagogically optimal." Game-controlled speed provides some quality signaling; we rely on that rather than XP multipliers.

• Game-controlled speed is our anti-gaming advantage that eliminates rush-farming exploits architecturally.

  • Why it's controversial: Most educational games and apps must invest heavily in detecting rush/gaming behaviors (answer time analysis, pattern detection, anti-cheat systems). We're claiming we don't need most of this despite having a time-based XP system, which is traditionally the most gameable approach.
  • Our Bet: By removing player control over running speed, we architecturally eliminate the "rush to farm XP" exploit despite using time-based XP. Students physically cannot answer faster than the game allows. Combined with (1) daily Speedrun caps, and (2) completed-skill caps, we prevent the main gaming vectors that make time-based XP problematic in other systems. Time-based XP in a player-controlled environment is terrible; time-based XP in a game-controlled environment is merely mediocre. Our architectural advantage lets us use a simpler system that would fail elsewhere.

• Progress percentage counts all stage advancements holistically, not just final Mastery, keeping Progress and XP fully decoupled.

  • Why it's controversial: Math Academy can count only completed lessons as progress because lessons are daily-completable units. TrashCat's Mastered stage requires 11+ days of spaced repetition. Counting only Mastered facts would show 0% progress for the first 11 days, making the system feel broken. With time-based XP showing constant accumulation regardless of learning milestones, Progress % becomes the only metric tracking actual curriculum advancement.
  • Our Bet: Progress should reflect visible forward movement through the learning pipeline. We weight all stages (Assessment=0%, Practice=20%, Review=40%, Repetition=70%, Mastered=100%) and average across all facts. This creates an honest progress metric that moves daily while still emphasizing durable achievement. Progress % measures current knowledge state; XP measures time invested. These are intentionally decoupled: a student can earn 60 XP on a skill while Progress increases from 35% to 45%, or earn 60 XP while Progress stays at 95% (grinding late-stage repetitions). Different metrics for different purposes.

• We gate time-based XP on 80% accuracy per minute in Practice mode only, keeping Competition mode purely time-based.

  • Why it's controversial: Our time-based XP system (1 minute = 1 XP) was designed to be "embarrassingly simple." Adding an accuracy threshold reintroduces complexity and creates a scenario where students can play for a minute but earn zero XP if their accuracy is below 80%. This contradicts our stated goal of simplicity and could feel punishing to struggling students.
  • Our Bet: Pure time-based XP without any quality signal creates a gaming vector in Practice mode: students could randomly guess answers, maintaining active session time while learning nothing. The 80% accuracy threshold (aligned with Alpha Andy M's mastery threshold) ensures XP represents productive learning time, not just time spent. We measure accuracy using active session time (excluding paused time, interventions) in 60-second windows matching our 1 XP = 1 minute baseline. This preserves the time-based simplicity while adding a minimal quality gate. Students who are genuinely trying will naturally exceed 80% accuracy; only deliberate gaming or severe struggle triggers the gate. For struggling students, the algorithm's difficulty adjustment and intervention system should bring them above 80% naturally. Competition mode remains purely time-based (1 minute = 1 XP) without accuracy gating, as the competitive context and different question selection logic provide sufficient anti-gaming protection.

DOK3: Insights

• Never decrement XP retroactively for knowledge decay or fact demotions. XP is a permanent record of effort expended. Progress/Mastery tracks current knowledge and can decrease. When facts demote from forgetting, XP earned during the original promotion stays. Award negative XP only at task completion for detected gaming, never later.

• Never track actual time spent. Always use a fixed expected XP per task. Effort-intrinsic XP is fundamentally broken: punishes efficiency, rewards dawdling, and enables gaming. Content-intrinsic XP (fixed per task) is the only viable approach. Calibrate by speed-running competent users.

• Mastery thresholds gate when to award XP, not whether intermediate milestones deserve XP. Math Academy's 60% floor allows partial XP (50-75%) for partial lesson completion. Alpha Andy M's 80% floor awards zero below, full above for complete lesson mastery. The threshold determines the performance bar for earning XP on a specific learning event (lesson completion, stage transition, assessment). Higher thresholds enforce rigor but increase frustration; lower thresholds allow progression while struggling. For fluency apps, intermediate stage transitions (Slow→Fast Practice) are genuine milestones deserving XP, unlike comprehensive learning apps, where intermediate understanding isn't sufficient.

• Negative XP targets gaming patterns only, never individual mistakes or poor performance. Detect patterns across multiple events: systematic rapid guessing, idle timeouts, obvious cheating. Calibrate so genuine students rarely see penalties.

• Prevent gaming architecturally first, detect behaviorally second. Individualized paths, randomized questions, and changed reattempts eliminate cheating vectors structurally. Build architectural defenses first. Add behavioral detection as a secondary layer.

• Daily cap diagnostics. Never cap practice. Fixed-XP diagnostics can be farmed; cap to once per day per skill. Variable-XP practice self-limits (you run out of content to progress). Caps prevent farming; targets drive consistency. Use appropriately.

• Display expected XP upfront. Hide calculation details. Show what's earnable ("Up to 10 XP"). Hide how it's calculated (multipliers, penalties). Transparency for goal-setting, opacity for anti-gaming.

• Award 20-25% bonus XP for exceptional performance. Egram (1979) empirically validates performance-contingent bonuses increase future performance. Meaningful bonus (20%+) incentivizes careful work without creating risk-aversion. The threshold for "exceptional" depends on assessment noise: traditional UIs can require 100% (pure knowledge signal), game-based environments should use 95%+ (allows margin for game-induced errors like obstacle interference or navigation mistakes). Low-hanging motivational fruit.

• Pace-efficiency gains require deep prerequisite graphs with implicit review credit. Math Academy achieves efficiency ∝ pace^0.1 because its knowledge graph has "encompassings" - advanced topics that implicitly practice many simpler prerequisites. Fast students learn advanced topics before reviews are due on prerequisites, so one advanced task knocks out multiple reviews, reducing total XP needed. TrashCat's structure is flat: facts within a skill have minimal dependencies (only fact families). A student learning 8×7 doesn't implicitly practice 8×6. Conclusion: expect a weak pace-efficiency relationship in TrashCat. Doubling pace doubles speed, but doesn't reduce total XP needed.

• Award fixed XP for diagnostics with a minimum completion threshold. Performance-based diagnostic XP creates perverse incentives (sandbagging for easier placement or answer-lookup for harder placement). Fixed XP + ≥50% completion requirement + daily cap prevents all gaming vectors.

• Never award XP for automated placement consequences. Assessment effort earns XP once. Placement promotions from that assessment earn zero. This prevents double-dipping and maintains XP time-equivalence. Use cosmetics for placement celebration.

• Optimize quality first, pace second. Quality is the dominant factor. Math Academy states, "the quality of your work is the single greatest factor that affects your learning efficiency," while pace changes efficiency by only 1.07x per doubling. Invest in pedagogy and behavioral coaching before motivational systems. Careful work >> fast work.

• Measure accuracy using active session time, not wall-clock time. When calculating per-minute accuracy for XP gating, use the actual active session duration (excluding paused time, interventions, app backgrounding) rather than wall-clock timestamps. This ensures accuracy windows reflect genuine active time and prevents clock manipulation or pause-related edge cases. Each answer should record the active session time at submission, enabling precise time-window calculations on the backend.

• Educate about session length; don't restrict. Show diminishing returns data. Don't cap total daily XP. Students grinding for hours are still learning. Respect the user’s agency while providing guidance.

• XP works best as part of a comprehensive motivational ecosystem, not in isolation. Math Academy's success comes from combining XP with weekly leagues, student choice, social leaderboards, fun emphasis, and optional opt-outs. Focusing only on XP calibration (thresholds, bonuses, penalties) without considering the broader motivational architecture may miss why gamification succeeds. The whole system must balance extrinsic rewards (XP, leagues) with intrinsic motivation (autonomy, mastery, curiosity) and provide escape valves for students who find gamification demotivating.

• Beware the dark side of XP gamification. While effective for many students, XP systems can create unhealthy addiction patterns, feel punishing rather than rewarding, and force rigid progressions that frustrate curious learners. Design with awareness that gamification is a powerful tool that can backfire if not carefully balanced with genuine learning goals and student agency. Include opt-outs and escape valves for students whose learning styles clash with points-based systems.

DOK1-2: Facts

Core XP Philosophy Across Systems

• All three systems use a 1 XP = 1 minute baseline. Math Academy, Alpha Andy M, and LearnWithAI all calibrate XP so that 1 XP represents approximately 1 minute of focused, productive effort from an average serious student. This baseline provides intuitive time-equivalence for goal-setting and progress tracking.

• XP is content-intrinsic (fixed per task), not effort-intrinsic (actual time tracked). Each piece of content (lesson, quiz, test) has a fixed "expected XP" value that is the same for all students, determined by speed-running a competent person through the content. Students don't earn more XP by spending more time on a task. If a slow learner takes 2 hours to complete a 10 XP lesson and a fast learner completes it in 20 minutes, both earn the same 10 XP (plus any performance bonuses). The slow learner is simply working at 0.08 XP/minute while the fast learner is working at 0.5 XP/minute. Alpha Andy M explicitly states: "Expected XP belongs on each piece of course content and is student independent. Expected XP is the same no matter which student is engaging with the content."

• XP is explicitly decoupled from progress percentage. Math Academy and LearnWithAI explicitly separate XP (effort + quality metric) from Progress % (curriculum completion metric). Math Academy states that "a student's progress (percent of topics completed) in a course is highly correlated with, but fundamentally different from, the amount of XP that they have earned." Alpha Andy M conflates these less clearly but recognizes XP includes time spent on tests/quizzes that don't directly advance the curriculum.

• XP is cumulative and monotonically increasing; knowledge state can regress. Across all systems, XP functions as a permanent, ever-increasing record of learning effort over time. Knowledge/mastery state, however, can decrease when students forget material or fail to demonstrate retained knowledge. The two metrics serve different purposes: XP tracks historical effort, while progress/mastery tracks current capability.

• XP serves as both a measurement tool and an incentive. All systems recognize XP's dual role: (1) measuring learning effort/quality objectively, and (2) incentivizing desired behaviors through gamification. Math Academy uses XP for weekly leagues, Alpha Andy M ties it directly to daily time goals and rewards, LearnWithAI uses XP for daily/weekly tracking.

Quality-Based XP Scaling

• Math Academy awards graduated XP below mastery. Math Academy awards XP on a sliding scale: 100% accuracy gets bonus XP (+2-3 points), 90-99% gets full (100%) XP, 67-89% gets most (75%) XP, 60-66% gets little (50%) XP, and <60% gets zero or negative XP. The cutoff for earning any XP is 60% accuracy.

• Alpha Andy M uses a binary threshold at 80% for mastery. Alpha Andy M awards XP only when students demonstrate mastery at 80%+ accuracy (90%+ for assessments). Below this threshold, students receive 0 XP if effort was sincere, or negative XP if effort was insincere (cheating/gaming). No partial credit is awarded below the mastery threshold because "we don't believe the student has learned at the rigor necessary for a mastery-based system."

• LearnWithAI varies XP thresholds by activity type. LearnWithAI varies its approach by activity type: lessons require 100% mastery of MCQ assessments to award XP, writing skills award XP on each correct attempt even if not first-try, and tests award XP proportional to score (2 XP per correct MCQ question, variable XP per FRQ point).

• Awarding bonus XP for perfect performance is standard practice. All three systems award bonus XP for 100% accuracy: Math Academy gives +2-3 points on tasks, Alpha Andy M gives +20-25% bonus, and LearnWithAI awards bonus XP for 100% on tests. Research (Egram, 1979) shows that awarding bonus points for high performance increases future performance.

Reattempt and Retry Policies

• Math Academy delays reattempts but doesn't explicitly reduce XP. When students fail tasks, Math Academy changes questions and requires a delay period before reattempt. The system allows students to continue on other learning paths while waiting. No explicit XP reduction for reattempts is documented in the analyzed materials, though the system does halt failed lessons temporarily.

• Alpha Andy M implements steep XP reductions on reattempts. Alpha Andy M implements strict reattempt penalties: 50% of expected XP on the first redo, 25% on the second redo, and 0% on the third attempt. This discourages reliance on multiple attempts and incentivizes careful, focused work on the first try.

• LearnWithAI allows XP to be earned on multiple attempts, but with safeguards. LearnWithAI awards XP each time students correctly answer writing skill assessments, even after incorrect attempts. However, they acknowledge the gaming risk and plan to use TimeBack's anti-pattern detection. They intentionally don't cap this in MVP to observe student behavior first.

Demotions, Forgetting, and Knowledge Regression

• Knowledge state can regress without affecting cumulative XP. When students forget material or fail reviews, their internal knowledge state (which topics are mastered, stage positions, etc.) can be demoted or regressed. However, this state change does not trigger XP decrements. The XP they earned when originally learning the material remains in their total.

• Math Academy explicitly discusses knowledge profile "peel backs" without mentioning XP loss. Their FAQ asks, "Why doesn't it just peel back their knowledge profile immediately?" when students fail. The answer discusses carefully removing topic credit from knowledge profiles based on failure patterns, but never mentions removing the XP that was earned when those topics were learned initially. This confirms XP is a permanent effort record, not a knowledge state indicator.

• Systems award XP for reattempts even though the knowledge was supposedly already learned. When a student has to re-learn material they forgot, they can earn new XP for the reattempt (though often at reduced rates per Alpha Andy M's policy). This further confirms that XP represents effort expended, not unique knowledge acquired.

Negative XP and Gaming Prevention

• All systems penalize gaming behaviors with negative XP. Math Academy, Alpha Andy M, and LearnWithAI all implement negative XP penalties for detected gaming, cheating, or deliberately poor effort. The penalty ranges from -2 to -5 XP depending on severity.

• Negative XP is awarded for specific completion events, not retroactively for knowledge decay. When students complete a task with gaming/cheating behaviors, the system awards negative XP at the moment of completion. XP is never decremented retroactively because a student later forgot material or regressed in their knowledge. XP represents effort expended (good or bad), not current knowledge state.

• XP penalties are calibrated to avoid punishing genuine students. Alpha Andy M explicitly states: "The system must be calibrated to ensure that well-intentioned learners are rarely penalized." LearnWithAI echoes this by saying penalties should "reflect the level of frustration a teacher would feel toward poor effort."

• Systems use pattern recognition to detect gaming, not individual mistakes. Systems look for patterns (multiple rapid answers, systematic wrong answers, idling) rather than penalizing individual mistakes. Math Academy's XP penalty system is designed so that "students who used the system properly and truly gave their best effort rarely (if ever) experienced penalties."

Daily Caps and Frequency Limits

• Math Academy does not enforce daily XP caps. Math Academy allows unlimited XP earning per day. Their system uses pace-based efficiency adjustments (efficiency ∝ pace^0.1) but doesn't cap absolute XP. Students can work multiple hours and continue earning XP, though long sessions trigger efficiency warnings after 45+ minutes.

• Alpha Andy M sets daily XP targets rather than caps. Alpha Andy M requires 120 XP daily (2 hours), divided into 4 subject blocks of 25 minutes each, plus 20 minutes buffer. This is a target/requirement rather than a cap - students need to earn this minimum to meet their daily goal.

• LearnWithAI uses activity-specific daily XP caps. LearnWithAI caps placement tests to once (fixed XP regardless of retakes) and only awards XP for unit test retakes when "this is their recommended activity." This prevents farming through repeated test-taking.

Assessment and Diagnostic XP

• Math Academy awards XP for diagnostic exams. Students earn XP during placement diagnostics based on their performance answering questions. The diagnostic is treated as active learning work that deserves XP, even though it's assessing existing knowledge rather than building new knowledge.

• Alpha Andy M only awards XP for passive activities after verification. Alpha Andy M explicitly states: "Do NOT award XP for passive activities alone (e.g. articles, videos). Wait until a lesson quiz verifies the learning or test to award XP." They award XP retroactively for reading/video time once learning is verified through assessment.

• LearnWithAI awards a fixed XP amount for placement tests. LearnWithAI gives fixed XP for placement test completion (30 XP for MCQ placement, variable for FRQ placements) regardless of performance. This recognizes the time/effort of the assessment without creating incentives to perform poorly to retake.

Transparency and Display

• Math Academy shows XP values upfront to students. Students see XP values on tasks before attempting them. This transparency helps with goal-setting and creates clear expectations. The system also shows XP earned immediately after task completion.

• Alpha Andy M displays the expected XP per lesson. Each lesson has an associated expected XP value (e.g., 10 XP or 15 XP) that students see before starting. This helps students plan how many lessons they need to complete to reach their daily 120 XP goal.

• LearnWithAI shows available XP at task entry points. Their system displays "XP to earn" for lessons (on 100% mastery), "Up to X XP" for tests (if full marks are achieved), and fixed XP for placement tests. This gives students clear expectations about potential XP gains.

• Detailed XP calculation rules are not shown to users. LearnWithAI explicitly states: "The detailed rules and calculation of XP is intentionally hidden to maintain simplicity." This transparency-without-complexity approach prevents students from gaming the system while keeping the experience understandable.

Progress Metrics and Reporting

• Math Academy's progress metric is nonlinear and slows over time. Math Academy explains that "Progress is nonlinear. Students make progress very quickly at the beginning of a course because they can focus primarily on learning new topics... But the more they learn, the more there is to review – so progress slows down." Progress % is deliberately kept separate from XP to avoid confusion.

• Math Academy's progress percentage can decrease, but XP earned never decreases. When students fail tasks on "conditionally completed" topics (low-confidence diagnostic placements), Math Academy "peels back" the student's knowledge profile, removing credit for those topics and decreasing the progress percentage. However, XP already earned is never taken away - it remains as a permanent record of effort expended. Math Academy FAQ explicitly states that they will "peel back their knowledge profile" in response to failures, but there is no mention anywhere of retroactively removing earned XP.

• Progress decrease happens only for low-confidence placements, and is intentionally slow. Math Academy is deliberately slow to peel back knowledge profiles to prevent gaming: "If we peeled back a student's knowledge profile quickly in response to failing a task, even when there is strong evidence that a student knows the prerequisite content, then it would create an exploit: whenever tasks begin to feel challenging, an adversarial student could intentionally fail a number of tasks to peel back their knowledge profile until they reach the point where they have days of super easy work ahead of them."

• Math Academy enforces a minimum for new content exposure. The system ensures that "on average, students have the opportunity to work on a lesson at least ~25% of the time or so at a minimum." This prevents students from getting stuck in pure review mode.

• Alpha Andy M uses XP as the main progress metric. While they acknowledge lessons are useful for tracking progress, XP is the primary metric students, guides, and parents use to understand daily/weekly learning effort. The 120 XP daily requirement provides a clear, simple target.

Competitive and Motivational Features

• Math Academy keeps motivation high with a weekly league system. Students are grouped into leagues based on XP earning speed. Weekly promotions/demotions occur based on league position. Each week provides a fresh start while maintaining cumulative XP. This creates ongoing competitive motivation without permanent discouragement. Students can opt out if leagues aren't motivating for them. Math Academy states: "What we have seen in the performance of hundreds of kids using the system is that they really enjoy gaining points, getting in higher and higher leagues and racing against each other on the leaderboard. They are excited about the learning process."

• Math Academy structures quizzes as recurring assessment gates. A quiz is assigned every 150 XP covering recent topics. Quizzes are timed (though timing can be adjusted for accommodations) and students cannot refer back to examples during quizzes. Topics missed on quizzes trigger immediate review assignments. After adequate review, the quiz becomes available for optional retake earning additional XP. This creates low-stakes, frequent assessment with immediate feedback and opportunities for improvement.

• Math Academy emphasizes fun and avoiding burnout explicitly. Their stated goal is to "be as efficient as possible and have fun. We never want to push students too far or burn them out." This balances rigor with enjoyment as a design principle, not an afterthought.

• Math Academy provides student choice within structured progression. Students are given "an array of diverse, non-overlapping learning tasks" to choose from at any time. This autonomy allows students to select between shorter vs. longer lessons based on their current state, creating a sense of agency while the algorithm ensures all choices are pedagogically sound.

• LearnWithAI encourages consistency with streak bonuses. TeachTales awards +10% XP multiplier for maintaining a 5-day streak (at least 1 quiz completed each day with 80%+ accuracy). This incentivizes consistency and daily engagement.

XP Enforces Good Math Habits Beyond Pure Accuracy

• Math Academy gates XP on both correctness and good math habits. The system doesn't just check answers—it enforces "diligent efforts such as reading example problems carefully, using pencil and paper, and checking incorrect answers alongside fully worked out solutions." XP is withheld or reduced when students exhibit rush patterns, skip steps, or show other indicators of poor learning behaviors. This architectural coupling makes it impossible to earn high XP through shortcuts.

• Math Academy can cut lessons short when detecting struggle. If the system detects a student is struggling to comprehend a new concept, it will "cut the lesson short and save it for another time. The student will not get any XP for this lesson." Students almost always earn full XP on the second attempt. This prevents students from grinding through material they're not ready for.

• On rare occasions, Math Academy assigns negative XP for rushing and guessing. When the system detects clear patterns of rushing through tasks without genuine engagement, it can assign negative XP to discourage the behavior. This is described as rare, indicating the threshold is calibrated to avoid false positives on genuine students.

Critical User Feedback on XP Gamification

• Not all users find Math Academy's XP system motivating. Some users report the XP system feels "non-rewarding when I get points and it feels like I get punished when I answer something wrong." Others describe it as "the forever unimpressed tutor—quick to penalize and very light on encouragement." Competitors like Brilliant are cited as having more engaging gamification despite being less pedagogically efficient.

• XP systems can create unhealthy addiction patterns. Some users report feeling "hooked" on earning XP in ways that concerned them, comparing it to Duolingo's addictive but shallow engagement. The numerical feedback loop can capture attention in ways that don't necessarily align with deep learning goals. One reviewer was asked by a stranger "Are you hooked?" after noticing their high XP accumulation rate.

• The rigidity of XP-gated progression frustrates some learners. Users report frustration that Math Academy "doesn't let you skip anything, and forces you down a rigid, unchangeable path." While mastery learning has benefits, the strict dependency graph can prevent students from exploring topics they're curious about if prerequisites aren't yet satisfied.

• XP systems work better for some personality types than others. Math Academy explicitly allows students to opt out of leagues if competitive gamification isn't motivating for them. This acknowledges that extrinsic motivation through points and competition doesn't universally drive engagement across all learners.

XP Source Attribution and Tracking

• Systems track the source of XP for analytics. Math Academy tracks XP from lessons vs. reviews vs. quizzes. LearnWithAI plans to show XP source breakdown. This allows students to understand where their effort is going and enables coaches to identify issues (e.g., student spending too much time on reattempts).

• Daily and weekly XP total breakdowns are standard. All systems show daily XP totals and weekly XP totals. Alpha Andy M resets daily at midnight local time and weekly at Sunday/Monday. This creates natural goal-setting periods and fresh starts.

Expected XP Setting Methodology

• Expected XP is set by timing expert completion, not by tracking student time. Systems do not measure how long individual students actually spend on tasks. Instead, each task is assigned a fixed "expected XP" value upfront by having a competent person complete it and timing them. This expected XP becomes the baseline that all students can earn for that task, regardless of how long it actually takes them to complete it.

• Alpha Andy M uses speed-running to calibrate expected XP for lessons. They state: "Manually 'speed running' (timing a motivated human as they complete material correctly) is the best way to set expected XP for each lesson." They explicitly reject using averages or student actuals because "Using student actuals to set expected XP always overstates because it includes students who aren't using the app correctly."

• Math Academy benchmarks courses based on a 40 XP per weekday pace. Math Academy models their average student on "a serious (but imperfect) student who works an average of 40 XP per weekday." Their courses are benchmarked assuming this pace. For example, AP Calculus BC is 6,000 XP, which would take 150 weekdays at 40 XP/day.

• Total XP required for a course is always an estimate, not a fixed number. LearnWithAI explicitly states: "An important implication... is that the total number of XP for a student to complete a course is an estimate, not a fixed value." This is because spaced repetition requirements vary by student performance.

Learning Efficiency and Pace Relationships

• Math Academy defines "pace" as the average XP earned per weekday. Pace is simply a measure of how much focused learning time a student puts in each day. For example, a student earning 40 XP per weekday has a "pace of 40," meaning they spend about 40 minutes of productive learning time each weekday on average.

• Math Academy defines "learning efficiency" as curriculum progress per XP spent. Learning efficiency is a multiplier that determines how much curriculum completion (e.g., topics mastered) a student achieves for each XP they earn. Higher efficiency means less total XP is needed to complete a course. Efficiency is primarily determined by the quality of a student's work (accuracy and pass rates on tasks).

• Higher pace leads to higher learning efficiency through a mathematical relationship. Math Academy discovered that learning efficiency ∝ pace^0.1. This means if you double your daily pace (e.g., from 20 to 40 XP/weekday), your learning efficiency increases by approximately 7%. The mechanism is that faster-paced students build new knowledge ahead of their review schedule, which allows the system to find more opportunities to "knock out" multiple reviews implicitly through single advanced tasks, reducing total XP needed.

• The pace-efficiency relationship makes course completion time non-linear. A 3000 XP course takes 15 weeks at 40 XP/weekday (baseline), but only 7 weeks at 80 XP/weekday (not 7.5 weeks as simple division would suggest), because the efficiency multiplier reduces total XP needed. Conversely, at 20 XP/weekday it takes 32 weeks (not 30 weeks), due to efficiency loss from the system being unable to optimize reviews as effectively.

• Quality of work has a much larger impact on efficiency than pace. Math Academy states that "the quality of your work is the single greatest factor that affects your learning efficiency." Poor performance (low accuracy, many failures) forces the adaptive system to assign more remediation and reattempts, substantially increasing total XP needed to complete a course. This qualitative impact dwarfs the quantified ~7% efficiency gain from doubling pace.

Anti-Cheating Through Individualization

• Math Academy individualizes learning paths to reduce cheating opportunities. They state: "Math Academy customizes its learning path to each individual student, so it's unusual for classmates to have the opportunity to work on the same topic at the same time – and even if they do, then they are served different questions." This architectural approach to anti-cheating is more robust than behavioral detection alone.

• Use of question banks and randomization is a common anti-cheating measure. Math Academy uses "a large bank of questions for each topic" and assessments are "fully individualized and even randomized." This prevents students from gaining an edge by seeing classmates' work.

• Math Academy changes reattempt questions to discourage memorization, not just repetition. Math Academy changes questions when students reattempt failed tasks and waits for a delay period. This prevents students from memorizing specific question answers rather than learning the underlying concept.

XP for Placement and Credit-by-Exam

• Math Academy does not award extra XP for topics placed out of via diagnostics. While students earn XP for answering diagnostic questions during the exam, they don't receive additional "placement XP" for topics that are automatically marked as mastered based on their diagnostic performance. The XP was already earned during the assessment itself.

• LearnWithAI prevents double-dipping by not awarding XP for bypassed material. They state: "Students are only awarded XP for the learning progress they make in Athena, so we don't award them XP for the 70% of the material they have already mastered" (if they place out of it). This prevents awarding XP both for the placement test and for the bypassed content.

Typical XP Benchmarks Across Systems

• Math Academy courses generally total around 3000 XP. Most Math Academy courses contain about 3000 XP assuming prerequisite mastery (ranges from 2000 XP for Pre-Algebra to 4000 XP for Pre-Calculus). AP Calculus BC is 6000 XP, about twice an average course.

• Alpha Andy M has a 120 XP per day requirement. Their system requires 120 XP daily (2 hours), structured as 4 subjects × 25 min each + 20 min buffer. Over a school year (180 days), this totals 21,600 XP.

• Math Academy finds that 50-60 XP per day is the maximum sustainable rate. Based on their analysis, "Maximum sustainable rate is approximately 50-60 XP per day" for long-term consistency. The highest recorded monthly total was 5,728 XP (about 200 XP/day), but this is not sustainable long-term.

Session Length and Efficiency Considerations

• Math Academy signals that efficiency may decline after 45+ minute sessions. They don't cap sessions but note efficiency may decline: "there is room for us to more precisely calibrate our spaced repetition system in the future, and it's on our to-do list." Long sessions can reduce retention effectiveness.

• Alpha Andy M structures daily learning into 25-minute subject blocks. Their 120 XP daily requirement is broken into 4 subjects of 25 minutes each. This structured approach aligns with attention span research and Pomodoro-style focused work blocks.

• Short, frequent study sessions result in better retention than long, infrequent ones. LearnWithAI's FAQ asks: "If I have a limited amount of time to devote each week, should I allocate that time into longer, less-frequent sessions or shorter, more-frequent sessions?" The research-backed answer consistently favors shorter, more-frequent sessions for better retention.