# PWR-091 — Path integration: learner worksheet Release: Revision 7T · Full Tutorial Edition Estimated time: Estimated 28 min reading and worksheet pass Difficulty: Intermediate Equipment: Common household or practice equipment — Six printed coordinate traces, each with a start, two to five straight segments and quarter turns.; Blank coordinate sheets, pencil, ruler, protractor or accessible angle tool and correction overlays.; Optional raised-line traces or screen-reader-compatible turn-and-length lists. Space: Desk / seated Automated structural checklist: 10 of 10 structural checks present Evidence quality/context: G1; Focused research depth Automated method-quality band: Comprehensive Method-rating basis: Structure coverage, instruction/check specificity, alternative distinctness, source troubleshooting, comparison depth and whether purpose/check fields are authored rather than derived. Editorial review: Pending manual editorial sign off ## Before you begin - [ ] I read the tutorial authority and stop conditions. - [ ] I have the required equipment/space or a declared accessible alternative. ## Canonical source context Path integration updates an internal estimate of the starting point as successive translations and turns occur. Drift normally accumulates. This safe fixture uses coordinate traces on paper or screen, never eyes-closed locomotion. The learner follows a sequence once, conceals it, marks a straight homeward bearing and magnitude, then quantifies angular and length error and tests the effect of one fixed external reference cue. Target outcome: The learner calculates homeward-bearing and magnitude error on six novel coordinate traces and reports how an external reference changes those two errors. ### Authority and setup conditions - Work seated with no physical motion challenge. - Learn how up, right, down and left on the sheet represent four fixed headings. - Set the scoring rule: bearing error in degrees and magnitude error in grid units. ### Required or supplied materials - Six printed coordinate traces, each with a start, two to five straight segments and quarter turns. - Blank coordinate sheets, pencil, ruler, protractor or accessible angle tool and correction overlays. - Optional raised-line traces or screen-reader-compatible turn-and-length lists. ## 1. Read the start frame Mark the origin, the initial facing arrow and the fixed upward axis. Why: A homeward vector is meaningless without an origin and heading frame. Success check: Origin, facing arrow and upward axis are visible before tracing. Accessible alternative: Complete “Mark the origin, the initial facing arrow and the fixed upward axis.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “Origin, facing arrow and upward axis are visible before tracing.” Provide turn-and-length text with an accessible vector-response format. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 2. Trace each segment Follow the sequence once, counting units and naming every clockwise or counter-clockwise quarter turn. Do not calculate the final vector yet. Why: Segment-by-segment updating supplies the self-motion analogue in a consequence-free fixture. Success check: The learner reaches the endpoint with the prescribed segment count. Accessible alternative: Complete the same research action — “Follow the sequence once, counting units and naming every clockwise or counter-clockwise quarter turn. Do not calculate the final vector yet.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The learner reaches the endpoint with the prescribed segment count.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 3. Maintain a heading ledger At each turn, draw a small arrow showing the new facing direction and state the estimated east–west and north–south change so far. Cover the ledger before the final return estimate. Why: A heading ledger teaches how successive rotations and translations update position while still preserving an unaided final test. Success check: Every turn has one correct facing arrow, and the final answer is committed without reopening the ledger. Accessible alternative: Complete “At each turn, draw a small arrow showing the new facing direction and state the estimated east–west and north–south change so far. Cover the ledger before the final return estimate.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “Every turn has one correct facing arrow, and the final answer is committed without reopening the ledger.” Use raised-line coordinate sheets and tactile heading arrows. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 4. Hide and estimate the bearing Cover the sequence and draw one arrow from the endpoint straight toward the remembered origin. Why: The arrow captures the accumulated heading-and-position estimate. Success check: One homeward arrow is committed before feedback. Accessible alternative: Replace small or visual-only information with enlarged text, high-contrast display, spoken description or tactile/verbal cueing while preserving the same decision and success check. Provide turn-and-length text with an accessible vector-response format. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 5. Estimate vector magnitude Write how many grid units the direct homeward line should span without reversing the outbound sequence. Why: Displacement magnitude differs from total travel length. Success check: One magnitude estimate is written beside the arrow. Accessible alternative: Complete the same research action — “Write how many grid units the direct homeward line should span without reversing the outbound sequence.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “One magnitude estimate is written beside the arrow.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 6. Reveal and quantify error Place the correction overlay on top. Measure the smaller angular gap between arrows and the absolute difference between estimated and exact magnitudes. Why: Bearing and magnitude reveal two different forms of drift. Success check: Both numerical errors are retained for every trace. Accessible alternative: Complete “Place the correction overlay on top. Measure the smaller angular gap between arrows and the absolute difference between estimated and exact magnitudes.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “Both numerical errors are retained for every trace.” Use raised-line coordinate sheets and tactile heading arrows. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 7. Resolve the displacement components Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow. Why: Component arithmetic provides a transparent correction key while keeping the earlier perceptual estimate uncoached. Success check: The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error. Accessible alternative: A supported, seated, reduced-range or slower version of “Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow.” is equivalent only when it keeps the same trained or measured target, declared configuration and success check: “The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error.” If any of those change, record it as a related alternative rather than an equivalent repetition. Alternative relationship: Conditional equivalence requires target and configuration check Learner notes: ________________________________________________________________________________ Completed: [ ] ## 8. Relate drift to sequence complexity After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions. Why: Accumulated drift may respond differently to rotations and translations. Success check: The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern. Accessible alternative: Complete the same research action — “After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 9. Compare an external-reference condition Repeat matched traces with the origin marker left visible, then try a fresh sequence after 48 hours. Keep unaided and reference-cue scores separate. Why: A stable external reference can correct accumulated drift; a delayed unfamiliar sequence checks method use. Success check: The report compares both cue conditions and includes a delayed trace. Accessible alternative: Replace spoken or audio cues with visible text, captions or haptic timing while keeping the same sequence and success check. Use raised-line coordinate sheets and tactile heading arrows. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## Reflection What changed? ________________________________________________________________________________ What remains difficult? ________________________________________________________________________________ What will I repeat, adapt, ask for help with, or stop? ________________________________________________________________________________ --- Completion of this worksheet demonstrates tutorial participation only. It does not establish capability, qualification, safety clearance, diagnosis, treatment or independent validation.