◊ K–12 Math Tutoring

Math tutoring that measures learning, not completion.

10 math strands, 20 learning pathways, 1,180 adaptive missions. The AI tutor asks questions — it never gives answers. 103 misconception detectors. 8 languages. Dyscalculia accommodations. Any browser, any device.

Try the math tutor free → Open-source model See the research
◊ 10 Math Strands

From counting to calculus.

Each strand is a structured learning progression — not a playlist. The adaptive engine selects the right mission at the right difficulty, and no skill is marked mastered until the student can transfer it.

K–3 · 72 missions
1. Number Sense & Place Value
PlaceValueLab — drag-to-regroup base-10 blocks. Progression: counting → place value → regrouping → multi-digit operations.
3–6 · 156 missions
2. Fractions & Decimals
FractionForge — visual fraction bars and area models. Progression: unit fractions → equivalence → operations → fraction-decimal conversion.
6–8 · 118 missions
3. Ratios & Proportional Reasoning
ProportionLab — triple-linked ratio table, graph, and number line. Progression: ratios → unit rates → proportions → percent applications.
3–8 · 134 missions
4. Word Problems & Modeling
WordProblemEngine — step-by-step parsing. Progression: one-step → multi-step → multi-operation → modeling with equations.
6–9 · 142 missions
5. Expressions & Equations
AlgebraLab — visual balance beam. Progression: variable expressions → one-step → multi-step → distribution → systems.
7–10 · 124 missions
6. Linear & Nonlinear Functions
GraphVerse — slider-driven coefficient manipulation. Progression: linear → quadratic → exponential → transformations.
6–10 · 108 missions
7. Geometry & Measurement
GeoPROOF — visual proof constructor. Progression: angle relationships → area/volume → similarity → coordinate geometry.
9–12 · 96 missions
8. Proof & Logical Reasoning
ProofBuilder — algebraic and visual proofs. Progression: conditional logic → two-column → algebraic proof → proof by contradiction.
9–12 · 112 missions
9. Statistics & Probability
StatsPhERE — student-run experiments. Progression: data displays → measures of center → sampling → hypothesis testing.
7–10 · 118 missions
10. Problem Solving & Transfer
EquationSolver + cross-strand challenges. Progression: strategy selection → multi-strand → real-world modeling → novel contexts.
◊ 103 Misconception Detectors

Find the bug in their thinking.

The type of wrong answer is diagnostic. 103 misconception detectors across all 10 strands trigger specific repair prompts — not generic hints.

Number Sense & Place Value

Grades K–3
Digit Swap in Regrouping
Repair: "You carried the wrong digit. Let's use the base-10 blocks — when you have 14 ones, which part stays and which moves up?"
Grades 1–3
Treats Subtraction as Commutative
Repair: "You got 3 - 7 = 4. Let's try it with cubes — start with 3 cubes. Can you take away 7?"

Fractions & Decimals

Grades 3–5
Fraction as Two Separate Numbers
Repair: "You wrote 3/4 as 3 and 4. Let's look at a fraction bar — can you shade the part that 3/4 represents?"
Grades 4–7
Decimal Place Confusion
Repair: "You said 0.12 > 0.5. Let's line them up on a number line — which one is closer to 1?"

Ratios & Proportional Reasoning

Grades 6–8
Additive Instead of Multiplicative
Repair: "You added 3 to both sides. But ratios scale — let's check with the ratio table. Does adding keep the relationship?"
Grades 6–8
Cross-Multiply Everything
Repair: "You cross-multiplied, but these aren't equal fractions. When does cross-multiplication apply? Let's check with a proportion table."

Word Problems & Modeling

Grades 2–5
More Means Add
Repair: "The problem says 'three times more.' Let's draw both quantities side by side — is it addition or multiplication?"
Grades 3–8
Keyword Trap
Repair: "You saw 'left' and subtracted. But re-read — who has what? Let's draw the situation before choosing an operation."

Expressions & Equations

Grades 6–8
Forgot to Distribute
Repair: "You wrote 2(x + 3) = 2x + 3. Let's use an area model — what are the two parts inside the parentheses?"
Grades 7–10
Negative Sign Errors
Repair: "You lost a negative sign at step 3. Let's walk through on a number line — what direction does subtracting move you?"

Functions, Geometry, Proof, Statistics, Transfer

Grades 8–12
Equality as Assignment
Repair: "You used = as 'the answer is.' But look at the balance model — both sides must weigh the same. What keeps them equal?"
Grades 7–10
Slope as Counting Boxes
Repair: "You counted grid squares instead of computing rise/run. Let's use the graph — what's the actual vertical change per horizontal change?"

103 detectors total across all 10 strands. Shown above are examples — the full detection library is part of the adaptive engine.

◊ Productive Struggle

The right amount of hard.

The AI tutor monitors three signals to keep each student in the zone where struggle builds understanding rather than frustration.

Hint Independence

Tracks scaffolding frequency. As independence grows, hints fade.

Transfer Success

Measures whether skills learned in one mode apply in another — the evidence that understanding is durable.

Affect Tracking

Response time, retry rates, and pause durations estimate affect. The tutor intervenes before frustration takes hold.

The AI tutor never gives answers. It asks the question that leads the student to discover the answer themselves.

◊ Learning Arc

Every micro-skill follows five missions.

No skill is marked "mastered" until the student can transfer it to an unfamiliar context. The 5-mission sequence ensures understanding, not just pattern matching.

1
Discover
Visual exploration with full scaffolding. The student encounters the concept through simulation.
2
Challenge
Harder problems with reduced scaffolding. Misconception detectors active.
3
Practice
Fluency building with no hints. Speed and accuracy tracked for automaticity.
4
Explain
Teach-back to the AI tutor. The student must articulate why, not just how.
5
Transfer
Apply the skill in an unfamiliar context. This is the mastery gate.
◊ Evidence Packets

Nine dimensions of evidence.

Every student generates an evidence packet per micro-skill. Teachers and districts see growth across nine measurable dimensions — not a single score.

Dimension 1
Accuracy
Dimension 2
Fluency
Dimension 3
Hint Independence
Dimension 4
Explanation Quality
Dimension 5
Transfer Success
Dimension 6
Misconception Resolution
Dimension 7
Productive Struggle
Dimension 8
Persistence
Dimension 9
Growth Trajectory

Actively seeking pilot partners. QLM launched in April 2026. These evidence dimensions are designed and implemented in the platform but have not yet been validated with large-scale student data. We welcome research partnerships to validate measurement quality.

research@quantumlearningmachines.com

◊ Every Student

Built for the students who need it most.

Designed to reach the students furthest from opportunity first.

Behind Grade Level

The engine meets students where they are — age-appropriate engagement, ability-appropriate difficulty.

English Learners

8 languages. Visual simulations mean language supports the experience but is never the gate.

Dyscalculia

Color-coded place values, graph paper overlay, enlarged numbers. The engine distinguishes symbol manipulation difficulty from quantitative reasoning difficulty.

No Barriers to Access

Any device with a browser. No app to install. No IT ticket.

◊ For Teachers

Teachers in control. AI as copilot.

The teacher decides what to teach. The system provides data, simulations, and scaffolding.

Instructional Alignment
Assign by standard, unit, or skill
Assign math modes by standard, unit, or skill. CCSS mapped to every mode.
Interaction Logs
See how students think, not just what they got right
Teachers see reasoning patterns, not just scores — what students tried, where they got stuck, which misconceptions surfaced.
Classroom Dashboard
Standards coverage heatmap in real time
Real-time standards heatmap. AI copilot suggests small groups and targeted activities.
Parent Reports
One-click plain-language summaries
Plain-language per-student reports with strengths, growth areas, and home activities. 8 languages. Printable PDF.
◊ Open Standards

Measurement that the research community can inspect.

Our measurement specifications are open and our benchmark results are published honestly, including results that do not favor us. We welcome research partnerships.

research@quantumlearningmachines.com

Interested in bringing adaptive math to your school or district? partnerships@quantumlearningmachines.com

Start a pilot → See the research K–12 overview