Verified learning impact vs. general reach
Reach is not the same as learning impact.
Physoly separates broad prep reach from verified learning impact. Public prep resources help students discover AP/F=ma reasoning traps, while diagnostic completions and cohort pre/post data are used for measured learning claims.
diagnosetrap code
interveneatlas + rung
measurepre/post delta
Do not combine casual reach with verified learning impact.
19,185
Physics Prep Users
Students who use Learn pages, challenge problems, or public prep resources.
2,102
Diagnostic Users
Students who complete the diagnostic and receive a mistake-pattern report.
9,902
Practice Engagement
Ladder and problem-bank problems opened or attempted, plus completed rungs. Diagnostic responses are tracked separately.
65
Verified Cohort
Verified cohort members, including 45 learners with matched pre/post records.
00 Evidence packet
What each number is allowed to prove.
The numbers stay visible, but the claim boundary is explicit: reach, adoption, engagement, and paired learning evidence are not interchangeable.
| Metric | Evidence level | Counts | Claim boundary | Artifact | Status |
|---|---|---|---|---|---|
| 19,185 Physics Prep Users | Broad reach | Students reached through Physoly prep resources, challenge problems, Learn pages, or public prep channels. | Supports reach. It does not prove learning gain. | Dated aggregate reach summary across Physoly learning and distribution channels. | published aggregate |
| 2,102 Diagnostic Users | Platform adoption | Learners who completed a diagnostic and received a coded report. | Supports product usage and diagnostic adoption. | De-duplicated diagnostic completion summary for the reporting period. | published aggregate |
| 9,902 Practice Attempts | Learning engagement | Ladder and problem-bank problems opened or attempted, plus completed practice actions. Diagnostic responses are tracked separately. | Supports engagement depth, not correctness by itself. | Aggregate diagnostic and ladder activity using the definitions below. | published aggregate |
| 65 Verified Cohort Members | Research sample | Students who complete baseline, assigned repair work, held-out follow-up, and feedback. | Supports cohort-scale analysis; 45 learners have matched pre/post records. | Consent records and de-identified paired summaries for the reporting period. | verified cohort aggregate |
01 Q-matrix
What the diagnostic claims to measure.
This matrix is the coverage contract. Thin rows are not failures; they are where the next content expansion should go.
| Trap family | Items | Distractors | Atlas | Rungs | Status |
|---|---|---|---|---|---|
| Constraint missed | 7 | 9 | 8 | 10 | core |
| False equilibrium assumption | 14 | 15 | 4 | 4 | core |
| Wrong conservation law | 15 | 22 | 8 | 9 | core |
| Force / acceleration confusion | 20 | 21 | 8 | 4 | core |
| Sign convention error | 8 | 9 | 5 | 4 | core |
| Vector / scalar confusion | 8 | 9 | 4 | 3 | core |
| Circular-motion direction error | 5 | 7 | 3 | 2 | core |
| Energy vs. momentum misuse | 11 | 13 | 4 | 5 | core |
| Circuit equivalence error | 4 | 6 | 6 | 0 | core |
| Rotation / torque-arm error | 4 | 5 | 5 | 3 | core |
| Path vs. state confusion | 2 | 2 | 4 | 2 | core |
| Dimensional inconsistency | 20 | 26 | 9 | 7 | core |
02 Item map
Question to trap to repair path.
This is the table a reviewer or teacher can audit. It is also the table you improve from interview and item-stat data.
| Item | Topic | Target | Distractor map | Rung | Map |
|---|---|---|---|---|---|
| Q01 AP | mechanics | NL-07 The normal force is not always mg | B:Force / acceleration confusion | C:Vector / scalar confusion | D:False equilibrium assumption | R2 Choose axes on an incline | mapped |
| Q02 AP | mechanics | NL-07 The normal force is not always mg | A:False equilibrium assumption | C:Vector / scalar confusion | D:Dimensional inconsistency | R3 Find the normal force on an incline | mapped |
| Q03 AP | mechanics | NL-04 Static friction is not always at its maximum | A:Constraint missed | B:False equilibrium assumption | D:Dimensional inconsistency | R4 Static friction threshold | mapped |
| Q04 AP | mechanics | NL-05 Centripetal acceleration points inward | A:Circular-motion direction error | B:Circular-motion direction error | C:Force / acceleration confusion | R7 Circular motion: force direction | mapped |
| Q05 F=ma | mechanics | NL-05 Centripetal acceleration points inward | B:Circular-motion direction error | C:Energy vs. momentum misuse | D:Force / acceleration confusion | R7 Circular motion: force direction | mapped |
| Q06 AP | energy | EN-01 Energy conservation fails when external work is hidden | A:Wrong conservation law | C:Wrong conservation law | D:Path vs. state confusion | R19 Frictional loss over a path | mapped |
| Q07 AP | energy | EN-02 The normal force usually does no work | A:Wrong conservation law | B:Sign convention error | D:Wrong conservation law | R1 Identify the forces on a block | mapped |
| Q08 AP | momentum | MOM-01 Momentum is conserved only when external impulse is negligible | A:Energy vs. momentum misuse | B:Wrong conservation law | C:Constraint missed | R27 Classify the collision | mapped |
| Q09 F=ma | momentum | MOM-03 Impulse is a vector — signs matter | B:Sign convention error | C:Sign convention error | D:Dimensional inconsistency | R23 Impulse from a force-time graph | mapped |
| Q10 AP | rotation | ROT-02 Torque uses the perpendicular lever arm | A:Rotation / torque-arm error | C:Vector / scalar confusion | D:Dimensional inconsistency | R32 Torque arm projection | mapped |
| Q11 AP | rotation | ROT-01 Equilibrium needs Στ = 0, not just ΣF = 0 | A:Rotation / torque-arm error | B:Constraint missed | D:False equilibrium assumption | R31 Beam torque equilibrium | mapped |
| Q12 AP | circuits | CIR-01 Series and parallel don't combine by 'adding up' | A:Circuit equivalence error | B:Circuit equivalence error | C:Circuit equivalence error | - No ladder rung yet | mapped |
| Q13 AP | mechanics | NL-10 Axes are bookkeeping, not physics | B:Vector / scalar confusion | C:False equilibrium assumption | D:Force / acceleration confusion | R2 Choose axes on an incline | mapped |
| Q14 AP C | mechanics | NL-13 Constraint equations need signed directions | A:Sign convention error | C:Constraint missed | D:Constraint missed | R12 Signed string constraints | mapped |
| Q15 AP | mechanics | NL-14 Apparent weight is the normal force | A:False equilibrium assumption | B:Sign convention error | D:Force / acceleration confusion | R11 Apparent weight in an elevator | mapped |
| Q16 F=ma | mechanics | NL-12 Kinetic friction opposes relative slipping | A:Force / acceleration confusion | B:Dimensional inconsistency | C:False equilibrium assumption | R13 Friction from relative motion | mapped |
| Q17 F=ma | mechanics | NL-18 Banked-curve friction direction depends on speed | B:Circular-motion direction error | C:Force / acceleration confusion | D:Circular-motion direction error | R14 Banked curve speed regimes | mapped |
| Q18 AP | mechanics | NL-19 Projectile components are independent only after forces are split | A:Force / acceleration confusion | C:Vector / scalar confusion | D:Force / acceleration confusion | R15 Projectile components | mapped |
| Q19 AP | energy | EN-06 Spring energy uses displacement squared | A:Dimensional inconsistency | B:Wrong conservation law | D:Dimensional inconsistency | R18 Spring turning point | mapped |
| Q20 AP | energy | EN-07 Friction work depends on path length | A:Path vs. state confusion | B:Wrong conservation law | C:Sign convention error | R19 Frictional loss over a path | mapped |
| Q21 AP C | energy | EN-09 Work-energy uses net work | B:Wrong conservation law | C:Wrong conservation law | D:Sign convention error | R16 Net work changes kinetic energy | mapped |
| Q22 F=ma | momentum | MOM-09 A ballistic pendulum needs two separate models | A:Energy vs. momentum misuse | C:Energy vs. momentum misuse | D:Wrong conservation law | R24 Ballistic pendulum sequence | mapped |
| Q23 AP | momentum | MOM-06 Explosions conserve momentum while kinetic energy can increase | A:Energy vs. momentum misuse | B:Constraint missed | D:Energy vs. momentum misuse | R21 Explosion momentum | mapped |
| Q24 F=ma | momentum | MOM-07 Momentum components conserve separately | A:Vector / scalar confusion | B:Wrong conservation law | C:Constraint missed | R22 Two-dimensional momentum | mapped |
| Q25 AP | momentum | MOM-08 Impulse is area under force-time, not peak force | B:Dimensional inconsistency | C:Dimensional inconsistency | D:Dimensional inconsistency | R23 Impulse from a force-time graph | mapped |
| Q26 F=ma | rotation | ROT-05 Angular momentum needs a no-external-torque axis | A:Force / acceleration confusion | C:Wrong conservation law | D:Dimensional inconsistency | R36 Angular momentum axis check | mapped |
| Q27 AP C | rotation | ROT-06 Static friction can cause rolling without doing work | A:Wrong conservation law | B:False equilibrium assumption | D:Force / acceleration confusion | R35 Static friction in rolling | mapped |
| Q28 AP | rotation | ROT-07 Torque sign follows your rotation convention | A:Sign convention error | B:Dimensional inconsistency | C:Rotation / torque-arm error | R40 Torque sign convention | mapped |
| Q29 AP | rotation | ROT-08 Angular acceleration follows net torque, not angular velocity | B:Force / acceleration confusion | C:Dimensional inconsistency | D:Circular-motion direction error | R41 Torque causes angular acceleration | mapped |
| Q30 AP C | rotation | ROT-10 The parallel-axis theorem adds Md² | A:Rotation / torque-arm error | C:Rotation / torque-arm error | D:Dimensional inconsistency | R33 Shift the axis | mapped |
| Q31 AP | circuits | CIR-06 Series shares current; parallel shares voltage | A:Circuit equivalence error | B:Dimensional inconsistency | D:Energy vs. momentum misuse | - No ladder rung yet | mapped |
| Q32 AP | circuits | CIR-05 Current is not used up | A:Circuit equivalence error | B:Dimensional inconsistency | C:False equilibrium assumption | - No ladder rung yet | mapped |
| Q33 AP C | circuits | CIR-07 A charged capacitor blocks steady DC | B:Circuit equivalence error | C:Dimensional inconsistency | D:Force / acceleration confusion | - No ladder rung yet | mapped |
| Q34 AP | waves | SHM-02 Wave speed is set by the medium, not the source | A:Dimensional inconsistency | C:Dimensional inconsistency | D:Force / acceleration confusion | - No ladder rung yet | mapped |
| Q35 AP | waves | SHM-04 Mass-spring period does not depend on amplitude | A:Force / acceleration confusion | B:Dimensional inconsistency | D:Energy vs. momentum misuse | - No ladder rung yet | mapped |
| Q36 AP | thermo | TH-03 Adiabatic means no heat transfer, not constant temperature | A:Sign convention error | B:Wrong conservation law | C:Wrong conservation law | - No ladder rung yet | mapped |
| Q37 AP | mechanics | NL-06 Internal tension needs the right system choice | B:Constraint missed | C:Constraint missed | D:Force / acceleration confusion | R5 Pulley constraint | mapped |
| Q38 AP | mechanics | NL-06 Internal tension needs the right system choice | A:Force / acceleration confusion | C:False equilibrium assumption | D:Dimensional inconsistency | R6 Two-block system: choosing the system | mapped |
| Q39 AP | energy | EN-01 Energy conservation fails when external work is hidden | A:Energy vs. momentum misuse | B:Wrong conservation law | D:Wrong conservation law | R19 Frictional loss over a path | mapped |
| Q40 AP | energy | MOM-01 Momentum is conserved only when external impulse is negligible | A:Energy vs. momentum misuse | B:Wrong conservation law | C:Wrong conservation law | R27 Classify the collision | mapped |
| Q41 AP | mechanics | NL-05 Centripetal acceleration points inward | B:Vector / scalar confusion | C:Force / acceleration confusion | D:Vector / scalar confusion | R14 Banked curve speed regimes | mapped |
| Q42 AP | mechanics | NL-05 Centripetal acceleration points inward | A:False equilibrium assumption | C:Circular-motion direction error | D:Force / acceleration confusion | R7 Circular motion: force direction | mapped |
| Q43 AP | rotation | ROT-06 Static friction can cause rolling without doing work | A:Energy vs. momentum misuse | B:Wrong conservation law | D:Dimensional inconsistency | R50 The rolling race | mapped |
| Q44 AP | rotation | ROT-05 Angular momentum needs a no-external-torque axis | A:Wrong conservation law | B:Energy vs. momentum misuse | C:Wrong conservation law | R36 Angular momentum axis check | mapped |
| Q45 AP | circuits | CIR-08 Changing equivalent resistance changes the source current | B:False equilibrium assumption | C:Energy vs. momentum misuse | D:Dimensional inconsistency | - No ladder rung yet | mapped |
| Q46 AP | circuits | CIR-07 A charged capacitor blocks steady DC | A:False equilibrium assumption | C:Force / acceleration confusion | D:False equilibrium assumption | - No ladder rung yet | mapped |
| Q47 AP | mechanics | SHM-03 In SHM, velocity and acceleration peak a quarter-cycle apart | A:False equilibrium assumption | B:Vector / scalar confusion | D:Force / acceleration confusion | - No ladder rung yet | mapped |
| Q48 AP | mechanics | SHM-01 SHM needs a linear restoring force | A:Dimensional inconsistency | B:Dimensional inconsistency | C:Dimensional inconsistency | - No ladder rung yet | mapped |
03 Validation protocol
How the map becomes evidence.
Each wrong option has one intended trap code and one linked remediation path.
This build ships the mapping table and deterministic report logic.
At least 5-10 learners explain why they chose each high-frequency distractor.
Confirms whether the intended trap is the actual reasoning trap.
Track item difficulty, top distractors, and high-confidence wrong responses.
Identifies items that are too easy, ambiguous, or not discriminating.
Use a parallel form with the same misconception coverage and different surface problems.
Lets pre/post gains measure transfer instead of memorized answers.
Only paired, consented, stage-tagged records can support learning-impact numbers.
Exports recreate the exact numbers in the writeup.
04 Cohort protocol
The cohort is the evidence surface.
- 1
Week 0
Baseline
Students take the diagnostic in normal mode or research mode; the report assigns top traps and first rungs.
- 2
Week 1
Interview + repair
Review high-confidence wrong answers with 5-10 students and fix ambiguous distractors.
- 3
Weeks 2-3
Targeted ladder work
Students complete assigned rungs; completion and recurring trap data feed the admin console.
- 4
Week 4
Held-out follow-up
A parallel form tests the same misconception matrix with fresh contexts.
- 5
After
Public findings
Publish anonymized trap distributions, item caveats, and paired gains with sample sizes.
05 Flagship repairs
Deep solutions only where they earn their space.
Not every problem needs a full essay. These selected rungs carry the deeper model setup, common wrong path, and transfer check.
Circular motion: force direction
Any time the path curves, draw the inward acceleration before writing forces. Then ask which real interaction can point inward.
Open rung ->Banked curve speed regimes
For every static-friction problem, first identify the motion that would happen without friction. The friction direction is opposite that relative slipping.
Open rung ->Ballistic pendulum sequence
When a problem has a collision plus a later motion, place a boundary line immediately after the collision and choose laws separately on each side.
Open rung ->Orbit energy bridge
For orbit problems, use force first to get the circular speed, then energy second to evaluate the state.
Open rung ->Static friction in rolling
Before labeling friction as dissipative, ask whether the contact point is slipping. No slip means static friction can do zero work.
Open rung ->Massive pulley Atwood acceleration
Whenever a pulley has rotational inertia, keep the pulley as its own equation instead of hiding it inside the string constraint.
Open rung ->next Build the evidence
The strongest next milestone is not more visual polish. It is student cohorts, item statistics, learner interviews, and one honest findings report.