Retrieval Practice
The act of remembering is the act of learning.
Roediger & Karpicke (2006)
Pulling a fact out of memory strengthens it more than putting it in. Luna's loop is built around spaced retrieval surfaced inside meaningful problems.
Private-School Pilot
The science behind thinking made visible.
Luna is currently being shaped inside one private-school deployment. The product is built on a single conviction: learning accelerates when a student's thinking is captured the moment it happens — and the teacher can see it.
Foundations
Four findings, fifty years of evidence, one platform.
Luna isn't built on novelty — it's built on the parts of cognitive science that have replicated for half a century. Here is the spine of the research, and what each finding becomes in software.
Desirable Difficulty
Effortful processing produces durable knowledge.
Bjork & Bjork (2011)
Luna deliberately introduces small struggles — interleaving, generation, delayed feedback — calibrated so that the student fights productively rather than fails.
Formative Assessment
Feedback matters most when immediate.
Black & Wiliam (1998)
Feedback during learning has massive effects. Luna turns every interaction into a formative checkpoint for both the student and the teacher in real time.
White Paper · v 1.0 · 42 References
Read the full paper.
Thinking Made Visible: The Cognitive Science of Atomized Thought-Capture, Real-Time Misconception Modeling, and Extended-Mind Pedagogy. A formal account of the research Luna is built on, with in-text citations and a complete bibliography of the cognitive-science literature behind retrieval practice, desirable difficulty, formative assessment, metacognition, free-response diagnostics, the misconception tradition, and extended cognition.
Roediger & Karpicke 2006Bjork & Bjork 2011Black & Wiliam 1998Hattie 2009Flavell 1979Ericsson & Simon 1980diSessa 1988Clark & Chalmers 1998Luhmann 1981Bloom 1984VanLehn 2011Dunlosky et al. 2013+30 more
Luna Research · 2026
Thinking Made Visible
The Cognitive Science of Atomized Thought-Capture, Real-Time Misconception Modeling, and Extended-Mind Pedagogy
§R · References [1]–[42]
The Schema
Not a curriculum of items. A scaffold for thought itself.
Luna doesn't model skills as nodes a student fills in. We model thinking as a sequence: tiny exercises, each describing one step of reasoning, threaded into chains the student walks through while we listen. The trace is stored as a zettelkasten — the student's own linked memory of every idea they have had.
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The Atom
One exercise = one thinking step.
Luna asks the student to perform one specific move of thought. The atom is the smallest unit at which a thought can be observed.
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The Chain
A directed flow of cognition.
Students traverse atoms in a chain. That thought becomes the input to the next atom, mimicking how a mathematician or close-reader actually moves.
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The Zettelkasten
Every thought becomes a linked note.
Captured thoughts are written to a zettelkasten. Notes are atomic, addressable, and densely cross-linked, building the student's personal knowledge graph.
Dual Architecture
Different subjects require different cognition.
We do not force a single interaction model across disciplines. Math and Physics demand manipulation of models—sliders, area builders, and number lines. ELA and History demand close reading, context-switching, and evidence synthesis.
Math & Science
Interactive Manipulation
The student interacts directly with the mathematical structure. The cognitive work is spatial and structural.
Grasp AtomsLive Models
ELA & Humanities
Immersive Reading Tasks
The student immerses in a primary text to identify rhetorical moves and defend claims. The cognitive work is analytical and comparative.
Prove AtomsText Evidence
The Zettelkasten
Knowledge that links to itself.
Every thought captured in a chain is written as an atomic note and linked to the notes it touches. Over a year the student accumulates their own personal knowledge graph — a zettelkasten in Luhmann's sense, mechanically maintained by Luna.
- Atomic— one idea per note, written in the student's own words.
- Addressable— every note has a permanent ID; you can cite it from any future chain.
- Linked— notes carry typed edges — supports, contradicts, exemplifies, decomposes.
- Surfaceable— when a new chain touches an old idea, Luna pulls the note back into view.
presupposition of prior knowledge
Lincoln 2nd inaugural
load-bearing assumptions
check what is "already-known"
rhetorical move: appeal to common ground
SAT anchor: identify assumption
misconception: tone = topic
Thought Capture
We give the student something to think about — and then we listen.
Luna's most important design decision: most atoms ask the student to write what they're thinking. Multiple choice still exists, but it is the minority path; freewrite is the spine.
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Present a tight prompt.
Not a worksheet. A single atom — one thinking step — chosen by the chain to land where the student's reasoning needs to do work right now.
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Capture the reasoning as it happens.
A short freewrite field, voice transcript, or scratchpad. If the draft stalls, a Cerebras-powered margin nudge offers one quiet hint. No chat loop, no answer giveaway.
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Use labs when the idea needs a picture.
Ratio Scaling, Number Line Walker, Fraction Pie, Partition Bar, Area Model, and the chemistry labs are embedded in atoms and open in /labs for reference.
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Report to the teacher in real time.
The teacher's dashboard updates the moment a student's thinking diverges from the expected path. Not at the end of the unit. Not on next week's report. Right now.
Live · Student #4 · Pre-Algebra
Prompt
Explain why 5 + (-3) feels like subtraction.
Student Freewrite — captured live
Signals Detected
names directionseparates operation from signuses number-line motionready for subtracting negatives
Modeling Misconceptions
Multiple choice tells you what. Freewriting tells you why.
Bubble tests collapse a student's thinking into one of four buttons. Luna refuses that compression. By asking students to write — even just a sentence — we recover the structure of their reasoning and can name the misconception precisely.
The Old Way
Multiple Choice
A binary signal, lossy by design.
What is the area of a circle with radius 5?
A25π
B10π
C25Selected · wrong
D50π
What we learn
Student got it wrong. That's all. Was it confusion about π? Forgetting to square? A guess? An off-by-one on the radius? We cannot tell.
The Luna Way
Freewrite
A trace of the actual reasoning.
Find the area of a circle with radius 5. Show your thinking.
area is pi times r... I think
the formula is pi r squared
so pi * 5 = 5pi
wait, squared means times itself?
no, I'll do pi * 5 = 25
What we learn
- →docs.misconceptions.lunaWay.learnItems.0
- →docs.misconceptions.lunaWay.learnItems.1
- →docs.misconceptions.lunaWay.learnItems.2
- →docs.misconceptions.lunaWay.learnItems.3
The Misconception Library
Every common error has a name and a fix.
Luna maintains a living taxonomy of misconceptions — currently 1,200+ named patterns across K–12. When a student's freewrite matches one, the teacher sees the diagnosis and the targeted re-teach in one click.
M-117Math
Equates "squared" with "doubled"
High frequency, grades 5–7
M-204Math
Treats negative signs as subtraction-only
Persists through Algebra I
R-031ELA
Confuses author claim with evidence
SAT reading marker
S-088Science
Conflates mass with weight
NGSS PS2 cluster
M-312Math
Distributes exponents over sums
Algebra II flag
R-074ELA
Reads tone as topic
Affects inference items
For the Teacher
The dashboard a working classroom needs when student thinking is the signal.
Luna doesn't replace what you do. It gives you the instrumentation you've always wished a textbook came with.
Misconception alerts, live.
A small panel on the dashboard pings when three or more students hit the same misconception in the same lesson. The teacher can re-teach mid-period instead of waiting for the quiz.
Student-thought timeline.
Click any student to replay every chain they ran this week — every atom, every captured thought, every link they made into their zettelkasten. The conference becomes specific.
Re-teach in one click.
Every named misconception is paired with a 90-second mini-lesson, a worked example, and a fresh practice set. Push it to one student, a small group, or the whole class.
Standards-based gradebook.
Proficiency rolls up by standard automatically. Parent conferences shift from "she has a B-" to "she is proficient in 14 of 16 algebra standards, and here is what to work on."
Author your own prompts.
The teacher can write one-step prompts and drop them into any chain. Luna captures the student thoughts the same way and threads the new notes into the zettelkasten.
Weekly insight digest.
Every Friday Luna produces a one-page summary: who advanced, who stalled, what misconceptions are spreading, and three specific moves to make next week.
Special Education
Designed for intervention. Built for IEPs.
For a student with an IEP, vague progress notes are not enough. Luna records atom-level evidence: what was attempted, what support was needed, and what misconception appeared.
The Psychologist Dashboard
The school psychologist has a unified view, pulling direct fluency and misconception data from daily play to streamline IEP writing and progress monitoring.
Inclusion (ICT) vs. District 75
Integrated Co-Teaching classrooms benefit from seamless differentiation without stigmatizing alternate interfaces. For District 75 and intensive intervention settings, Luna provides explicit scaffolded pathways, larger hit-targets, and text-to-speech scaffolding.
IDEA & MTSS Compliant
Granular, timestamped performance tracking directly supports MTSS (Multi-Tiered Systems of Support) reporting requirements and delivers the objective data required under IDEA to demonstrate Free Appropriate Public Education (FAPE).
Compliance Citations & Frameworks
- ●IDEA & FAPE (20 U.S.C. § 1400)Luna's granular progression mapping provides the objective tracking required to demonstrate that a student is receiving a Free Appropriate Public Education in the Least Restrictive Environment.
- ●MTSS / RTI IntegrationAutomated capture of Tier 2 and Tier 3 interventions, fulfilling evidence requirements before evaluating for specific learning disabilities.
- ●FERPA & COPPA CompliantIEP goals and progress data are fully encrypted and siloed, ensuring strict compliance with federal student privacy laws.
- ●District 75 / Specialized AlignmentAlternative navigation modalities ensure accessibility for cognitive delays and multiple disabilities per NYSED continuum of services.
Deployment
Six weeks to A. The rest of the semester is yours.
Luna compresses the time required to reach grade-level proficiency on the traditional course, freeing the rest of the term for deeper, more generative teaching.
Semester · 18 weeksProficiency gate at the boundary
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Phase 1 · Proficiency
Phase 2 · Deep Instruction
Weeks 1–6
Computers in class. Differentiated. A-band by week six.
The Gate
Pencil-and-paper unit exam confirms transfer.
Weeks 7–18
Laptops at home. Teacher in front of the room.
Phase 1 · Intensive Blended Proficiency
Weeks 1–6
Luna takes the wheel. Every student reaches A.
Class time is at the laptop. The platform differentiates atom-by-atom — a student who already knows slope skips it; a student who doesn't gets unlimited targeted practice in six different formats. The teacher spends the period on the four or five students the dashboard flags as stuck. Spaced repetition runs in the background, so no Friday is spent on review.
- ~85% proficiency on standards-tagged atoms across the section
- Daily atom-granular dashboard with a "stuck" list by name
- Curveball warm-ups, live, projected to the room
- Homework is spaced repetition only — 10–15 min nightly
Phase 2 · Teacher-Led Deep Instruction
Weeks 7–18
You take the wheel. Build the course you came here to teach.
With the class already at grade level, laptops retreat to the edges of the room. Class becomes pencil-and-paper, board work, discussion, projects, live games. Luna runs at home for retention. Your authoring canvas is open — you fork canonical modules into your voice and write the units the textbook never had.
- Teacher-authored modules become the recurring class material
- Live formats (Curveball, Crucible Isle) re-pointed at your skills
- Assessment is yours: portfolios, projects, oral defenses, exams
- Standards proficiency keeps reporting itself in the background
The Promise
Luna doesn't replace the teacher. It gives the teacher the year back.
In Phase 2, school leadership sees the teacher doing the most visible craft of their career: building original units, running project work, leading discussion. The platform is in the room, but it is no longer the room.
FAQ
What the teacher and principal ask first.
Atoms aren't "graded" the way essays are. Each atom describes a single thinking step, and the student's response is read for whether the step occurred — did the move land, was a key term named, did the chain advance. The reading is anchored to exemplars the teacher can review. Spelling, grammar, and "writing quality" are never the signal unless an atom explicitly asks for them.
Luna supports voice transcription, dictation by a teacher, drawing tablets, and a structured "show your work" canvas for early grades. The underlying signal — what the student did, and in what order — is what matters, not the modality.
No. Student writing is never used as training data for foundation models, ours or anyone else's. Freewrites are encrypted at rest, scoped to the classroom, and deleted on schedule per the school retention policy. FERPA + COPPA aligned by default.
A generic LLM tutor reads each student in isolation and re-derives them every time. Luna acts as an extended mind in the Clark & Chalmers sense: every thought from every chain is written into the student's own zettelkasten and linked to prior notes. The diagnosis isn't a conversation — it's a growing personal cortex that follows the student across subjects and years.
Yes. CSV exports are available per student, per class, and per standard. SIS integrations can be scoped during the school deployment.
About 40 minutes for the core loop: roster, assign, read the dashboard, and push a re-teach. In the private-school pilot, the freewrite-reading view is designed to replace the exit-ticket workflow.
See it in a class of yours.
Thirty minutes, a real prompt, a real class section. We'll show what live thought-capture looks like on a roster, with school standards.