Compare two live hypotheses before revealing the next case
Inductive inference means proposing more than one rule from limited examples, predicting new cases before seeing their memberships and revising without erasing the original prediction. This pack begins with three fictional cards. The learner generates two candidate rules, predicts all three hidden test memberships and locks confidence before opening one staged key. The goal is a better-supported rule with visible uncertainty, not certainty from a tiny pattern set.
Tutorial curriculum · current public edition · Revision 7T · Full Tutorial Edition
One source of teaching truth
Full individual tutorial · TLU-PWR-114
Inductive inference means proposing more than one rule from limited examples, predicting new cases before seeing their memberships and revising without erasing the original prediction. This pack begins with three fictional cards. The learner generates two candidate rules, predicts all three hidden test memberships and locks confidence before opening one staged key. The goal is a better-supported rule with visible uncertainty, not certainty from a tiny pattern set.
Revision 7T · Full Tutorial Edition · complete governed practice tutorial
Compare two live hypotheses before revealing the next case
Inductive inference means proposing more than one rule from limited examples, predicting new cases before seeing their memberships and revising without erasing the original prediction. This pack begins with three fictional cards. The learner generates two candidate rules, predicts all three hidden test memberships and locks confidence before opening one staged key. The goal is a better-supported rule with visible uncertainty, not certainty from a tiny pattern set.
Authority and safety
Use only the fictional colour-and-shape cards. Do not infer traits, motives, diagnosis, intelligence, or capacity from a real person.
Performance on this fixture does not establish general reasoning ability, dementia prevention, scientific expertise, or transfer to consequential decisions.
A rule that fits all supplied cards remains bounded to this fixture; another untested rule may also fit.
Exact materials
The six staged fictional card rows below
A blank sheet for two learner-generated rules
Prediction and confidence columns for both rules on D1, C1 and N1
One staged membership key, kept closed until all six test predictions are locked
Set up in this order
Read I1–I3 only. Generate at least two distinct rules that fit all three opening memberships; call them H1 and H2 and write them in full.
For D1, C1 and N1, derive the membership predicted by H1 and by H2. Lock all six predictions and a confidence rating for each rule before opening the key.
Open the staged key once. Copy the three memberships beside the locked predictions without editing any prediction.
Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it.
Update confidence with a reason tied to a revealed card. If both rules fail, generate a repaired third rule without erasing H1 or H2.
Finish by naming the better-supported current rule, an untested alternative and one new card whose membership would distinguish them.
Supplied fixture
I1–I3 are opening evidence. Generate H1 and H2, then lock all D1/C1/N1 predictions before opening the staged membership key.
Card id
Phase
Colour
Shape
Membership status
Prediction H1 before key
Prediction H2 before key
Confidence H1 0 to 100
Confidence H2 0 to 100
I1
opening evidence
blue
triangle
M
[check fit]
[check fit]
[record]
[record]
I2
opening evidence
red
circle
N
[check fit]
[check fit]
[record]
[record]
I3
opening evidence
green
square
N
[check fit]
[check fit]
[record]
[record]
D1
hidden test
blue
circle
[OPEN KEY AFTER ALL SIX PREDICTIONS]
[lock]
[lock]
[locked before key]
[locked before key]
C1
hidden test
red
triangle
[OPEN KEY AFTER ALL SIX PREDICTIONS]
[lock]
[lock]
[locked before key]
[locked before key]
N1
hidden test
yellow
triangle
[OPEN KEY AFTER ALL SIX PREDICTIONS]
[lock]
[lock]
[locked before key]
[locked before key]
Check your work only after you finish
Lock every response first. The checking page is separate so the answers are not exposed inside this exercise.
Award 2 points for two distinct learner-generated rules that fit I1–I3, 1 for each of six locked H1/H2 test predictions, 1 for each of six correctly scored predictions after the key, 2 for evidence-linked confidence updates, 1 for preserving a failed rule and 1 for a bounded alternative/new-card statement: 18 total. Any test prediction written after the key earns 0.
Worked example
Separate mini-example: opening evidence is silver circle=M and orange square=N.
H1 says circles belong to M; H2 says silver cards belong to M. Both fit the opening evidence.
For a hidden silver square, H1 predicts N and H2 predicts M. Lock both before reveal.
The mini-example reveals silver square=N, supporting H1 and contradicting H2.
Keep H2 in the record, update confidence and propose an orange circle as another discriminating card.
Correct result: The mini-example shows generation, discrimination, locked prediction and revision without exposing D1, C1 or N1 memberships.
Right and wrong
Right and wrong comparison
Moment
Right / safer
Wrong / riskier
Why
Generating rules
Write two distinct rules that fit every opening card.
Copy one supplied rule and call it two hypotheses.
Induction requires genuine alternatives before test evidence.
Testing
Lock predictions for all hidden cards before opening the key.
Open one membership, then rewrite the rule before predicting the others.
Post-reveal editing hides failed predictions.
Updating
Preserve a failed rule and lower confidence with a card citation.
Delete the rule so the final page looks error-free.
The error record is evidence about the inference.
Concluding
Name the best current rule and an untested alternative.
Call a three-card test universal proof.
Induction remains open to new cases.
Common mistakes and fixes
Common mistakes and corrections
Mistake
Fix
Both hypotheses make the same predictions on every test card.
Generate a genuinely different rule or add a card where the predictions differ.
Confidence is entered after the key.
Lock rule, prediction and confidence together before reveal.
A failed prediction is erased.
Preserve it and add a separate revision line.
A fitted rule becomes certainty.
Name an untested card or rival rule that could change the conclusion.
Evidence boundary
What the tutorial may—and may not—claim.
Supportable claim
Targeted inductive-reasoning training produced durable task gains in older adults, with limited evidence of everyday functional benefit.
Measurement boundary
Declare inference domain, item novelty, baseline cognition, sensory/language access, delay and functional tasks; trained test performance is not diagnosis or prevention.
Myth
Reverse cognitive ageing with pattern drills
Metric
Accuracy on novel inductive problems and objective chosen functions after delay
Boundary
Durable task gains do not prove dementia prevention or general intelligence.
Negative and limiting findings
Objective functional transfer in ACTIVE was not uniform.
A large independent online trial found trained-task improvement without transfer to untrained tasks.
Neither study establishes dementia prevention or general reasoning enhancement.
Sherry L. Willis; Sharon L. Tennstedt; Michael Marsiske; Karlene Ball; Jeffrey Elias; Kathy Mann Koepke; John N. Morris; George W. Rebok; Frederick W. Unverzagt; Anne M. Stoddard; Elizabeth Wright; ACTIVE Study Group · 2006 · PRIMARY_RESEARCH
Supports only the bounded empirical proposition in the declared configurations. Constrains generalisation, transfer, certainty or efficacy; it is not optional context.
Adrian M Owen; Adam Hampshire; Jessica A Grahn; Robert Stenton; Said Dajani; Alistair S Burns; Robert J Howard; Clive G Ballard · 2010 · PRIMARY_RESEARCH
Supports only the bounded empirical proposition in the declared configurations. Constrains generalisation, transfer, certainty or efficacy; it is not optional context.
Tutorial delivery controls
Learn, adapt, troubleshoot and resume
Estimated timeEstimated 18 min reading and worksheet pass
DifficultyIntroductory
EquipmentBasic stationery or digital tools
SpaceDesk / seated
Method qualityEstablished10 of 10 structural checks present. Automated method-readiness band; human editorial sign-off is separate.
Evidence contextG1; Focused research depthScientific support is evaluated separately from teaching-method structure.
Editorial reviewPending manual sign-offNo human approval is claimed until reviewer, date and content hash are recorded.
Progress is saved only in this browser on this device.
Step-by-step learner mode
Each activity includes its success check, a nearby accessible alternative and an “I’m stuck” correction path. Alternatives preserve the target where possible; when they change the task, Titan labels them as related rather than equivalent.
01
Read I1–I3 only
Read I1–I3 only. Generate at least two distinct rules that fit all three opening memberships; call them H1 and H2 and write them in full.
Why this step exists
“Read I1–I3 only” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion.
Success check
A legible entry directly completes “Read I1–I3 only” and records the requested condition, decision or boundary without adding a new claim.
I’m stuck on this step
Reset: Re-read this authored instruction — “Read I1–I3 only. Generate at least two distinct rules that fit all three opening memberships; call them H1 and H2 and write them in full.” — and its success check, then attempt only this step.
Possible snag: The result from “Read I1–I3 only. Generate at least two distinct rules that fit all three opening memberships; call them H1 and H2 and write them in full.” does not yet meet this declared check: A legible entry directly completes “Read I1–I3 only” and records the requested condition, decision or boundary without adding a new claim.
Correction: Return to the start of “Read I1–I3 only”, reduce complexity or pace, and repeat only the part needed to satisfy: “A legible entry directly completes “Read I1–I3 only” and records the requested condition, decision or boundary without adding a new claim.”
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
02
For D1, C1 and N1, derive the membership predicted by H1 and…
For D1, C1 and N1, derive the membership predicted by H1 and by H2. Lock all six predictions and a confidence rating for each rule before opening the key.
Why this step exists
“For D1, C1 and N1, derive the membership predicted by H1 and by H2” carries the authored Inductive inference method into a reviewable output without adding an unstated task, dose or claim.
Success check
Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “For D1, C1 and N1, derive the membership predicted by H1 and by H2. Lock all six predictions and a confidence rating for each rule before opening the key.”
I’m stuck on this step
Reset: Re-read this authored instruction — “For D1, C1 and N1, derive the membership predicted by H1 and by H2. Lock all six predictions and a confidence rating for each rule before opening the key.” — and its success check, then attempt only this step.
Possible snag: Confidence is entered after the key.
Correction: Lock rule, prediction and confidence together before reveal.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
03
Open the staged key once
Open the staged key once. Copy the three memberships beside the locked predictions without editing any prediction.
Why this step exists
“Open the staged key once” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion.
Success check
A legible entry directly completes “Open the staged key once” and records the requested condition, decision or boundary without adding a new claim.
I’m stuck on this step
Reset: Re-read this authored instruction — “Open the staged key once. Copy the three memberships beside the locked predictions without editing any prediction.” — and its success check, then attempt only this step.
Possible snag: A failed prediction is erased.
Correction: Preserve it and add a separate revision line.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
04
Score each rule out of three and write which evidence supported, contradicted…
Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it.
Why this step exists
“Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion.
Success check
The work shows the value requested by “Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it”, retains the supplied units or signs and leaves any unsupported value unknown.
I’m stuck on this step
Reset: Re-read this authored instruction — “Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it.” — and its success check, then attempt only this step.
Possible snag: The result from “Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it.” does not yet meet this declared check: The work shows the value requested by “Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it”, retains the supplied units or signs and leaves any unsupported value unknown.
Correction: Return to the start of “Score each rule out of three and write which evidence supported, contradicted…”, reduce complexity or pace, and repeat only the part needed to satisfy: “The work shows the value requested by “Score each rule out of three and write which evidence supported, contradicted or failed to distinguish it”, retains the supplied units or signs and leaves any unsupported value unknown.”
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
05
Update confidence with a reason tied to a revealed card
Update confidence with a reason tied to a revealed card. If both rules fail, generate a repaired third rule without erasing H1 or H2.
Why this step exists
Keep this exact Inductive inference action explicit and reviewable: “Update confidence with a reason tied to a revealed card. If both rules fail, generate a repaired third rule without erasing H1 or H2.”
Success check
Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “Update confidence with a reason tied to a revealed card. If both rules fail, generate a repaired third rule without erasing H1 or H2.”
I’m stuck on this step
Reset: Re-read this authored instruction — “Update confidence with a reason tied to a revealed card. If both rules fail, generate a repaired third rule without erasing H1 or H2.” — and its success check, then attempt only this step.
Possible snag: Both hypotheses make the same predictions on every test card.
Correction: Generate a genuinely different rule or add a card where the predictions differ.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
06
Finish by naming the better-supported current rule, an untested alternative and one…
Finish by naming the better-supported current rule, an untested alternative and one new card whose membership would distinguish them.
Why this step exists
“Finish by naming the better-supported current rule, an untested alternative and one new card whose membership would distinguish them” establishes the exact Inductive inference question or boundary that every later comparison must preserve.
Success check
Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “Finish by naming the better-supported current rule, an untested alternative and one new card whose membership would distinguish them.”
I’m stuck on this step
Reset: Re-read this authored instruction — “Finish by naming the better-supported current rule, an untested alternative and one new card whose membership would distinguish them.” — and its success check, then attempt only this step.
Possible snag: A fitted rule becomes certainty.
Correction: Name an untested card or rival rule that could change the conclusion.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
Correct versus incorrect execution
These accessible process diagrams are built from the tutorial’s own right/wrong teaching. They are not anatomical illustrations and do not add technique beyond the canonical tutorial.
Generating rules — Induction requires genuine alternatives before test evidence.
Correct / safer
Write two distinct rules that fit every opening card.
Wrong / riskier
Copy one supplied rule and call it two hypotheses.
Lock predictions for all hidden cards before opening the key.
Wrong / riskier
Open one membership, then rewrite the rule before predicting the others.
Updating — The error record is evidence about the inference.
Correct / safer
Preserve a failed rule and lower confidence with a card citation.
Wrong / riskier
Delete the rule so the final page looks error-free.
Concluding — Induction remains open to new cases.
Correct / safer
Name the best current rule and an untested alternative.
Wrong / riskier
Call a three-card test universal proof.
Method-structure checklist
10 of 10 structural checks present
✓ Ordered, Power-specific instructions — present
✓ Every activity has a success check — present
✓ Materials or supplied records are declared — present
✓ Measurement or assessment rule is present — present
✓ Tutorial-specific troubleshooting is present — present
✓ Stopping or escalation boundary is present — present
✓ Every activity has an adjacent alternative — present
✓ Correct-versus-incorrect comparison is present — present
✓ Evidence context is bound to the Power record — present
✓ Planning metadata is present — present
The method-readiness band and presence checklist assess tutorial presentation and are separate from evidence quality for the underlying Power. They are automated editorial aids, not human approval.
Manual editorial sign-off: Pending. This tutorial must not display a human-approved state until an identified editor signs the exact content hash.