THE MACHINE · IN THE OPEN · FROM THE WITNESSED RUN OF 2026-10-09
tutor.py, every command showing its working.
A small Python program, standard library only. Your AI runs it; you can too. Every block below is pasted from the card’s own WITNESS.md, as printed.
plan | a study plan: spaced, interleaved sessions with review slots |
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review | the daily review load, projected |
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mastery | right|wrong [--rung N] [--date DATE] log one try |
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ladder | the hint ladder the card climbs, rung by rung |
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explain | the explain-back form the learner fills which key points an explanation covers, and whether it reads copied |
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evidence | what the research says works, and where it stops |
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calendar | the plan or the review dates as an .ics calendar file (RFC 5545) |
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selftest | 33 checks that prove the machine; it must print 33/33 |
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plan · A STUDY PLAN: SPACED, INTERLEAVED SESSIONS WITH REVIEW SLOTS
$ tutor.py plan --topics topics.txt --exam 2026-11-20 --hours-per-week 6 --from 2026-10-09 --out plan.csv
THE PLAN · 8 topic(s) · 2026-10-09 to the exam on 2026-11-20 (42 days)
budget: 6 h a week -> 7 session(s) of 50 min a week (350 min), each split into 2 block(s) of 25 min, one topic per block
sessions: 42 · learn 9 · review 37 · mixed retrieval 30 · final mixed review 8 · free 0
learn every topic by 2026-11-04 (60% of the way, a choice) · reviews 1, 3, 7, 14, 28 days after learning (a choice) · final mixed review from 2026-11-16
date day nº blocks
2026-10-09 Fri 1 LEARN limits · LEARN derivatives
2026-10-10 Sat 2 REVIEW limits · REVIEW derivatives
2026-10-11 Sun 3 LEARN chain rule · MIXED limits
2026-10-12 Mon 4 REVIEW limits · REVIEW derivatives
2026-10-13 Tue 5 REVIEW chain rule · LEARN implicit differentiation
2026-10-14 Wed 6 REVIEW implicit differentiation · LEARN related rates
2026-10-15 Thu 7 REVIEW chain rule · REVIEW related rates
2026-10-16 Fri 8 REVIEW limits · REVIEW derivatives
2026-10-17 Sat 9 REVIEW implicit differentiation · REVIEW related rates
2026-10-18 Sun 10 LEARN optimization (part 1 of 2) · MIXED chain rule
2026-10-19 Mon 11 REVIEW chain rule · LEARN optimization (part 2 of 2)
2026-10-20 Tue 12 REVIEW optimization · LEARN integrals
2026-10-21 Wed 13 REVIEW implicit differentiation · REVIEW related rates
2026-10-22 Thu 14 REVIEW integrals · REVIEW optimization
2026-10-23 Fri 15 REVIEW limits · REVIEW derivatives
2026-10-24 Sat 16 REVIEW integrals · LEARN substitution
2026-10-25 Sun 17 REVIEW substitution · MIXED chain rule
2026-10-26 Mon 18 REVIEW chain rule · REVIEW optimization
2026-10-27 Tue 19 REVIEW substitution · MIXED implicit differentiation
2026-10-28 Wed 20 REVIEW implicit differentiation · REVIEW related rates
2026-10-29 Thu 21 REVIEW integrals · MIXED limits
2026-10-30 Fri 22 MIXED derivatives · MIXED chain rule
2026-10-31 Sat 23 REVIEW substitution · MIXED optimization
2026-11-01 Sun 24 MIXED implicit differentiation · MIXED related rates
2026-11-02 Mon 25 REVIEW optimization · MIXED limits
2026-11-03 Tue 26 MIXED integrals · MIXED derivatives
2026-11-04 Wed 27 MIXED chain rule · MIXED substitution
2026-11-05 Thu 28 REVIEW integrals · MIXED implicit differentiation
2026-11-06 Fri 29 REVIEW limits · REVIEW derivatives
2026-11-07 Sat 30 REVIEW substitution · MIXED related rates
2026-11-08 Sun 31 MIXED optimization · MIXED chain rule
2026-11-09 Mon 32 REVIEW chain rule · MIXED implicit differentiation
2026-11-10 Tue 33 MIXED integrals · MIXED limits
2026-11-11 Wed 34 REVIEW implicit differentiation · REVIEW related rates
2026-11-12 Thu 35 MIXED derivatives · MIXED substitution
2026-11-13 Fri 36 MIXED optimization · MIXED chain rule
2026-11-14 Sat 37 MIXED limits · MIXED integrals
2026-11-15 Sun 38 MIXED implicit differentiation · MIXED related rates
2026-11-16 Mon 39 FINAL derivatives · FINAL substitution
2026-11-17 Tue 40 FINAL chain rule · FINAL optimization
2026-11-18 Wed 41 FINAL limits · FINAL integrals
2026-11-19 Thu 42 FINAL implicit differentiation · FINAL related rates
per topic:
- limits: learn 10-09 · reviews 10-10, 10-12, 10-16, 10-23, 11-06 · mixed 5 · final 11-18
- derivatives: learn 10-09 · reviews 10-10, 10-12, 10-16, 10-23, 11-06 · mixed 3 · final 11-16
- chain rule: learn 10-11 · reviews 10-13, 10-15, 10-19, 10-26, 11-09 · mixed 6 · final 11-17
- implicit differentiation: learn 10-13 · reviews 10-14, 10-17, 10-21, 10-28, 11-11 · mixed 5 · final 11-19
- related rates: learn 10-14 · reviews 10-15, 10-17, 10-21, 10-28, 11-11 · mixed 3 · final 11-19
- optimization: learn 10-18, 10-19 · reviews 10-20, 10-22, 10-26, 11-02 · mixed 3 · final 11-17
- integrals: learn 10-20 · reviews 10-22, 10-24, 10-29, 11-05 · mixed 3 · final 11-18
- substitution: learn 10-24 · reviews 10-25, 10-27, 10-31, 11-07 · mixed 2 · final 11-16
wrote plan.csv (84 rows); `tutor.py calendar --plan plan.csv --out study.ics` puts it in a calendar
rule: sessions a week = floor(hours x 60 / session minutes), spread evenly over the study days; each session is split into blocks of different topics (interleaving, never one topic twice in a session); every topic is learned by the learn-by date, then reviewed at the gaps after learning (a late review pushes the next ones back by the same days); every topic gets one final mixed review in the last days; spare blocks go to mixed retrieval of the topic seen least recently. Every review is retrieval: answer from memory first, then check.
source: Cepeda, Pashler, Vul, Wixted & Rohrer 2006, Psychological Bulletin 132(3):354-380 (spacing); Cepeda, Vul, Rohrer, Wixted & Pashler 2008, Psychological Science 19:1095-1102 (best gap against test delay) (for one review, the best gap was about 20-40% of a one-week delay and 5-10% of a one-year delay); Rohrer & Taylor 2007, Instructional Science 35:481-498 (shuffled maths practice); Roediger & Karpicke 2006, Psychological Science 17(3):249-255 (the testing effect); Dunlosky, Rawson, Marsh, Nathan & Willingham 2013, Psychological Science in the Public Interest 14(1):4-58
limit: the gaps, the learn-by share, the block size and the final window are planning choices, not research findings. The studies used mostly students and simple material, and whether gaps should expand or stay equal is not settled. Effects vary by subject and learner. A plan is a target; move it when life moves.
calendar · THE PLAN OR THE REVIEW DATES AS AN .ICS CALENDAR FILE (RFC 5545)
$ tutor.py calendar --plan plan.csv --exam 2026-11-20 --time 18:30 --alarm 10 --out study.ics --stamp 20261009T120000Z
wrote study.ics: 43 event(s) · 42 study session(s) from plan.csv · the exam on 2026-11-20 · timed from 18:30, floating local time
checked: CRLF line ends, lines folded at 75 octets, every BEGIN closed, every event has UID, DTSTAMP and DTSTART
rule: one event per study session (or per review day); all-day unless --time is given, then sessions back to back with 10-minute breaks; text escaped and long lines folded as the standard says.
source: RFC 5545 (2009), Internet Calendaring and Scheduling Core Object Specification (iCalendar)
limit: times are floating (no time zone): a calendar shows them at the same clock time wherever you are. Only the next due date of each card is known; later review dates depend on the grades, so re-export after each session or use --assume-grade for a projection.
review · THE DAILY REVIEW LOAD, PROJECTED
$ tutor.py review --new spanish-200.txt --out deck.csv --start 2026-10-09 --per-day 20
wrote deck.csv: 200 cards, ease 2.5, due from 2026-10-09, 20 new a day -> introduced over 10 day(s) (last new card on 2026-10-18)
blank backs: 0
projected load for 30 days if every card is graded 4 (an assumption): peak 60 reviews on 2026-10-16, average 25.3 a day
rule: SM-2: a new card has ease 2.5. Grade each recall 0-5. Grade 3 or more: the next interval is 1 day, then 6 days, then the last interval x ease, rounded; grade below 3: start the card again at 1 day. After each grade, ease += 0.1 - (5-q) x (0.08 + (5-q) x 0.02), never below 1.3. Any card graded below 4 is repeated again the same day until it scores 4 or 5. New cards are staggered: card i is first due on start + floor(i / per day).
source: Wozniak 1990, SuperMemo algorithm SM-2 (first used 1987; as published by SuperMemo); Roediger & Karpicke 2006, Psychological Science 17(3):249-255 (the testing effect); Cepeda, Pashler, Vul, Wixted & Rohrer 2006, Psychological Bulletin 132(3):354-380 (spacing)
limit: SM-2 is a 1987 rule of thumb, not a model fitted to your memory; newer schedulers fit memory data better. Grades are self-reported. Wozniak's text can be read as leaving the ease unchanged on a failed card (--keep-ef-on-fail); this machine lowers it by default, as most published versions do. Dates are targets: a late review still counts.
review · THE DAILY REVIEW LOAD, PROJECTED
$ tutor.py review deck.csv --today 2026-10-09
DUE 2026-10-09 · 20 of 200 cards (overdue first, then in deck order)
- uno (due 2026-10-09, new)
- dos (due 2026-10-09, new)
- tres (due 2026-10-09, new)
- cuatro (due 2026-10-09, new)
- cinco (due 2026-10-09, new)
- seis (due 2026-10-09, new)
- siete (due 2026-10-09, new)
- ocho (due 2026-10-09, new)
- nueve (due 2026-10-09, new)
- diez (due 2026-10-09, new)
- once (due 2026-10-09, new)
- doce (due 2026-10-09, new)
- trece (due 2026-10-09, new)
- catorce (due 2026-10-09, new)
- quince (due 2026-10-09, new)
- dieciséis (due 2026-10-09, new)
- diecisiete (due 2026-10-09, new)
- dieciocho (due 2026-10-09, new)
- diecinueve (due 2026-10-09, new)
- veinte (due 2026-10-09, new)
next 14 days: 10-10 20, 10-11 20, 10-12 20, 10-13 20, 10-14 20, 10-15 20, 10-16 20, 10-17 20, 10-18 20
how: show the front, the learner answers from memory first, then the back is shown and the learner grades 0-5:
0 complete blackout, no recall
1 wrong, but it was familiar once shown
2 wrong, but it seemed easy once shown
3 right, with serious difficulty
4 right, after some hesitation
5 right, with perfect recall
rule: SM-2: a new card has ease 2.5. Grade each recall 0-5. Grade 3 or more: the next interval is 1 day, then 6 days, then the last interval x ease, rounded; grade below 3: start the card again at 1 day. After each grade, ease += 0.1 - (5-q) x (0.08 + (5-q) x 0.02), never below 1.3. Any card graded below 4 is repeated again the same day until it scores 4 or 5.
source: Wozniak 1990, SuperMemo algorithm SM-2 (first used 1987; as published by SuperMemo); Roediger & Karpicke 2006, Psychological Science 17(3):249-255 (the testing effect)
limit: SM-2 is a 1987 rule of thumb, not a model fitted to your memory; newer schedulers fit memory data better. Grades are self-reported. Wozniak's text can be read as leaving the ease unchanged on a failed card (--keep-ef-on-fail); this machine lowers it by default, as most published versions do. Dates are targets: a late review still counts.
review · THE DAILY REVIEW LOAD, PROJECTED
$ tutor.py review deck.csv --today 2026-10-09 --grade uno=5 --grade dos=4 … (20 grades)
SESSION 2026-10-09 · 20 grade(s)
- uno: grade 5 (right, with perfect recall) · ease 2.50 -> 2.60 · reps 1 · next in 1 day(s), due 2026-10-10
- dos: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- tres: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- cuatro: grade 3 (right, with serious difficulty) · ease 2.50 -> 2.36 · reps 1 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
- cinco: grade 5 (right, with perfect recall) · ease 2.50 -> 2.60 · reps 1 · next in 1 day(s), due 2026-10-10
- seis: grade 2 (wrong, but it seemed easy once shown) · ease 2.50 -> 2.18 · reps 0 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
- siete: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- ocho: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- nueve: grade 5 (right, with perfect recall) · ease 2.50 -> 2.60 · reps 1 · next in 1 day(s), due 2026-10-10
- diez: grade 1 (wrong, but it was familiar once shown) · ease 2.50 -> 1.96 · reps 0 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
- once: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- doce: grade 3 (right, with serious difficulty) · ease 2.50 -> 2.36 · reps 1 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
- trece: grade 5 (right, with perfect recall) · ease 2.50 -> 2.60 · reps 1 · next in 1 day(s), due 2026-10-10
- catorce: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- quince: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- dieciséis: grade 2 (wrong, but it seemed easy once shown) · ease 2.50 -> 2.18 · reps 0 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
- diecisiete: grade 5 (right, with perfect recall) · ease 2.50 -> 2.60 · reps 1 · next in 1 day(s), due 2026-10-10
- dieciocho: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- diecinueve: grade 4 (right, after some hesitation) · ease 2.50 -> 2.50 · reps 1 · next in 1 day(s), due 2026-10-10
- veinte: grade 3 (right, with serious difficulty) · ease 2.50 -> 2.36 · reps 1 · next in 1 day(s), due 2026-10-10 · AGAIN TODAY
again today, until each scores 4 or 5: cuatro, seis, diez, doce, dieciséis, veinte
wrote deck.csv
rule: SM-2: a new card has ease 2.5. Grade each recall 0-5. Grade 3 or more: the next interval is 1 day, then 6 days, then the last interval x ease, rounded; grade below 3: start the card again at 1 day. After each grade, ease += 0.1 - (5-q) x (0.08 + (5-q) x 0.02), never below 1.3. Any card graded below 4 is repeated again the same day until it scores 4 or 5.
source: Wozniak 1990, SuperMemo algorithm SM-2 (first used 1987; as published by SuperMemo)
limit: SM-2 is a 1987 rule of thumb, not a model fitted to your memory; newer schedulers fit memory data better. Grades are self-reported. Wozniak's text can be read as leaving the ease unchanged on a failed card (--keep-ef-on-fail); this machine lowers it by default, as most published versions do. Dates are targets: a late review still counts.
review · THE DAILY REVIEW LOAD, PROJECTED
$ tutor.py review deck.csv --forecast 30 --today 2026-10-09
FORECAST · 200 cards · 30 days from 2026-10-09 · if every card is graded 4 (an assumption)
2026-10-10 Sat 40 ########################################
2026-10-11 Sun 43 ###########################################
2026-10-12 Mon 40 ########################################
2026-10-13 Tue 40 ########################################
2026-10-14 Wed 40 ########################################
2026-10-15 Thu 40 ########################################
2026-10-16 Fri 57 #########################################################
2026-10-17 Sat 63 ############################################################
2026-10-18 Sun 60 ############################################################
2026-10-19 Mon 40 ########################################
2026-10-20 Tue 20 ####################
2026-10-21 Wed 20 ####################
2026-10-22 Thu 20 ####################
2026-10-23 Fri 20 ####################
2026-10-24 Sat 20 ####################
2026-10-25 Sun 20 ####################
2026-10-29 Thu 1 #
2026-10-30 Fri 5 #####
2026-10-31 Sat 9 #########
2026-11-01 Sun 25 #########################
2026-11-02 Mon 20 ####################
2026-11-03 Tue 20 ####################
2026-11-04 Wed 20 ####################
2026-11-05 Thu 20 ####################
2026-11-06 Fri 20 ####################
2026-11-07 Sat 20 ####################
total 743 reviews · peak 63 · average 24.8 a day
rule: SM-2: a new card has ease 2.5. Grade each recall 0-5. Grade 3 or more: the next interval is 1 day, then 6 days, then the last interval x ease, rounded; grade below 3: start the card again at 1 day. After each grade, ease += 0.1 - (5-q) x (0.08 + (5-q) x 0.02), never below 1.3. Any card graded below 4 is repeated again the same day until it scores 4 or 5. The forecast replays that rule forward with one assumed grade.
source: Wozniak 1990, SuperMemo algorithm SM-2 (first used 1987; as published by SuperMemo)
limit: SM-2 is a 1987 rule of thumb, not a model fitted to your memory; newer schedulers fit memory data better. Grades are self-reported. Wozniak's text can be read as leaving the ease unchanged on a failed card (--keep-ef-on-fail); this machine lowers it by default, as most published versions do. Dates are targets: a late review still counts. Real grades vary; the forecast is a sketch of the load, not a promise.
calendar · THE PLAN OR THE REVIEW DATES AS AN .ICS CALENDAR FILE (RFC 5545)
$ tutor.py calendar --deck deck.csv --assume-grade 4 --days 30 --out reviews.ics --stamp 20261009T120000Z
wrote reviews.ics: 27 event(s) · 27 review day(s) from deck.csv (projected, if every card is graded 4) · all-day events
checked: CRLF line ends, lines folded at 75 octets, every BEGIN closed, every event has UID, DTSTAMP and DTSTART
rule: one event per study session (or per review day); all-day unless --time is given, then sessions back to back with 10-minute breaks; text escaped and long lines folded as the standard says.
source: RFC 5545 (2009), Internet Calendaring and Scheduling Core Object Specification (iCalendar)
limit: times are floating (no time zone): a calendar shows them at the same clock time wherever you are. Only the next due date of each card is known; later review dates depend on the grades, so re-export after each session or use --assume-grade for a projection.
ladder · THE HINT LADDER THE CARD CLIMBS, RUNG BY RUNG
$ tutor.py ladder --example fractions
THE HINT LADDER · the least help that works, one rung at a time
0 TRY — The learner tries first, alone. Ask for their attempt or their first step, even a guess: "What have you tried? Show me where you got to."
1 A QUESTION — Ask one question that points at the key idea without naming the step: "What do you notice about ...?"
2 A NUDGE — Point to where to look, still without the step: "Look at the bottom numbers. What would have to be true before you could add?"
3 A WORKED STEP OF A SIMILAR PROBLEM — Work one step of a different, similar problem out loud, then hand the learner's own problem back.
4 THE METHOD — Name the method in general steps, without doing the learner's numbers or words for them.
5 THE ANSWER — Show the answer, with the reasoning, only after an honest try at the rungs above, or when the learner, having tried, asks to see it.
THEN, ALWAYS: the learner explains it back in their own words (`tutor.py explain`).
THEN: a fresh similar problem, with no hints, to show the step is theirs. Log the try with the rung reached (`tutor.py mastery --add`).
how to climb:
- Climb one rung at a time, and only after the learner has tried at the rung they are on.
- Wait. Silence after a question is thinking time; do not fill it with the next rung.
- Go back down when the learner gets going again: the aim is the least help that works.
- Praise the effort and the method used, not being clever.
- Never jump to the answer because it is faster; go to it only when the learner has made an honest try and asks to see it.
example: 1/3 + 1/4
TRY: "Have a go. What do you think 1/3 + 1/4 is?" (A common first try is 2/7: adding tops and bottoms.)
A QUESTION: "Are thirds and quarters the same size of piece?"
A NUDGE: "We can only add pieces of the same size. What size of piece could both thirds and quarters be cut into?"
A WORKED STEP OF A SIMILAR PROBLEM: "Here is 1/2 + 1/5. Halves and fifths both cut into tenths: 1/2 = 5/10 and 1/5 = 2/10, so 5/10 + 2/10 = 7/10. Now try yours."
THE METHOD: "Find a number both bottoms divide into, rename each fraction with that bottom, then add the tops."
THE ANSWER (after an honest try): "Both 3 and 4 go into 12: 1/3 = 4/12, 1/4 = 3/12, so 4/12 + 3/12 = 7/12."
checked with exact fractions: 1/3 + 1/4 = 7/12; 1/2 + 1/5 = 7/10
rule: never the final answer before an honest try; one rung at a time: try, a question, a nudge, a worked step of a similar problem, the method, the answer; then explain back and a fresh problem without help.
source: Wood, Bruner & Ross 1976, Journal of Child Psychology and Psychiatry 17:89-100 (tutoring and scaffolding); Kornell, Hays & Bjork 2009, Journal of Experimental Psychology: Learning, Memory, and Cognition 35(4):989-998 (a failed try before the answer); Sweller & Cooper 1985, Cognition and Instruction 2(1):59-89 (worked examples); Bjork 1994, Memory and metamemory considerations in the training of human beings, in Metcalfe & Shimamura (eds), Metacognition, MIT Press, 185-205 (desirable difficulties)
limit: the ladder is this card's method built on those findings, not a protocol tested as a whole. The studies were in labs and classrooms; a learner who is upset or out of time needs a shorter ladder, and some will need the worked example sooner.
mastery · RIGHT|WRONG [--RUNG N] [--DATE DATE] LOG ONE TRY
$ tutor.py mastery homework-log.csv
MASTERY · 4 skill(s) · 20 tries · mastered = at least 80% right over the last 5 tries (a choice); a try counts as right only when it was reached by rung 2 or lower (a choice)
skill attempts right last N share last seen status
equivalent fractions 5 4 4/5 80% 2026-10-08 MASTERED
adding fractions, same bottom 5 5 5/5 100% 2026-10-08 MASTERED
adding fractions, different bottoms 5 1 1/5 20% 2026-10-07 REVISIT (2 right with heavy hints)
times tables, 7s 5 3 3/5 60% 2026-10-09 REVISIT
revisit first: adding fractions, different bottoms (1/5); times tables, 7s (3/5)
mastered, still worth one spaced check later: equivalent fractions; adding fractions, same bottom
rule: per skill, share = right tries in the last N / N. REVISIT when the share is under the threshold; MASTERED when it is at or over it with at least N tries; NOT YET otherwise. A right answer reached only after the method or the answer was shown is not counted as right.
source: Bloom 1968, Learning for Mastery, Evaluation Comment 1(2) (a mastery criterion before moving on); Cepeda, Pashler, Vul, Wixted & Rohrer 2006, Psychological Bulletin 132(3):354-380 (spacing), for why mastered skills still need review.
limit: the threshold and the window (80% over the last 5 by default) are choices, not research findings. A share over 5 tries is a small sample; one lucky or unlucky try moves it by 20 points. Mastery fades without review.
explain · THE EXPLAIN-BACK FORM THE LEARNER FILLS WHICH KEY POINTS AN EXPLANATION COVERS, AND WHET
$ tutor.py explain --topic photosynthesis
# EXPLAIN IT BACK · photosynthesis
Fill each part from memory first. Then check your notes and mark what you missed.
## 1. IN MY OWN WORDS
Explain it as if to a friend who missed the lesson. No copying from the book or the notes.
...
## 2. AN EXAMPLE OF MY OWN
One example that is not the one in the book.
...
## 3. WHY IT WORKS
The "because": why is it true, or why does the method work?
...
## 4. WHERE IT GOES WRONG
A common mistake, or a case where it does not apply.
...
## 5. THE GAPS
Any word I used but could not define, or a step I could not explain.
...
## 6. HOW SURE I AM
1 (guessing) to 5 (could teach it). Then check against the source, and say it again where it was wrong.
...
## For the tutor
- Which key points are there? Which are missing? (`tutor.py explain --check`)
- Is it in the learner's own words, or the book's?
- Ask about each gap with a question, not the answer. Then the learner explains it again.
rule: the learner explains from memory, in their own words, with an example, the why and a common mistake; gaps are named and asked about.
source: Chi, de Leeuw, Chiu & LaVancher 1994, Cognitive Science 18:439-477 (self-explanation); Dunlosky, Rawson, Marsh, Nathan & Willingham 2013, Psychological Science in the Public Interest 14(1):4-58; Roediger & Karpicke 2006, Psychological Science 17(3):249-255 (the testing effect). "Explain it simply" is often called the Feynman technique: a popular name, not a study.
limit: self-explanation helped in the studies, rated moderate utility overall; it takes time, and works best with someone to check it against the source.
explain · THE EXPLAIN-BACK FORM THE LEARNER FILLS WHICH KEY POINTS AN EXPLANATION COVERS, AND WHET
$ tutor.py explain --check explanation.txt --points points.txt --source source.txt
EXPLAIN-BACK CHECK · 1 of 5 key points covered · 50 words
- MISSING light energy is captured by chlorophyll (25% of its words) · not found: energy, captur, chlorophyll
- COVERED carbon dioxide and water are the raw materials (60% of its words)
- MISSING glucose (a sugar) is made (33% of its words) · not found: glucose, made
- MISSING oxygen is released (50% of its words) · not found: releas
- MISSING it happens in the chloroplasts (50% of its words) · not found: chloroplast
longest run copied word for word from the source: 2 words
next: ask about each MISSING point with a question (rung 1), not the answer; then the learner explains it again.
rule: a key point counts as covered when at least 60% of its content words (stemmed, common words dropped) appear in the explanation, alone or inside a longer word (a choice); 12 or more words in a row from the source reads as copied (a choice).
source: Chi, de Leeuw, Chiu & LaVancher 1994, Cognitive Science 18:439-477 (self-explanation); Dunlosky, Rawson, Marsh, Nathan & Willingham 2013, Psychological Science in the Public Interest 14(1):4-58 (self-explanation: moderate utility)
limit: a word match is not understanding: a learner can name every point and still not get it, or say it rightly in other words. Read the explanation; this only says where to look.
evidence · WHAT THE RESEARCH SAYS WORKS, AND WHERE IT STOPS
$ tutor.py evidence
WHAT THE RESEARCH SAYS WORKS · utility as rated by Dunlosky et al. 2013 where they rated it
- practice testing (retrieval) [HIGH]: Quizzing yourself beat restudying on tests two days and a week later, though restudying looked better after five minutes and felt surer (Roediger & Karpicke 2006).
- distributed practice (spacing) [HIGH]: Spreading the same study over days beats cramming; the best gap grows with how long you need to remember it (Cepeda et al. 2006, 2008).
- interleaved practice (mixing) [MODERATE]: Mixed maths problems scored 63% a week later against 20% for blocked practice, while scores during practice were the reverse, 60% against 89% (Rohrer & Taylor 2007, experiment 2).
- self-explanation [MODERATE]: Explaining each step to yourself helped understanding (Chi et al. 1994).
- elaborative interrogation [MODERATE]: Asking "why is this true?" helped learning of facts in the studies reviewed.
- trying before being told [-]: A wrong guess before the answer improved later recall over just studying the answer (Kornell, Hays & Bjork 2009).
- rereading, highlighting, summarising [LOW]: Feel productive, did little on their own in the studies reviewed.
the common thread: desirable difficulties. What feels harder while practising (recalling, spacing, mixing) often sticks better; what feels easy (rereading) often fades (Bjork 1994).
in practice: close the book and recall, then check; review the same thing again after a day, then after a week; mix problem types; explain it back; keep a record of what you get right.
rule: techniques ranked by the evidence reviewed; each study named.
source: Dunlosky, Rawson, Marsh, Nathan & Willingham 2013, Psychological Science in the Public Interest 14(1):4-58; Roediger & Karpicke 2006, Psychological Science 17(3):249-255 (the testing effect); Cepeda, Pashler, Vul, Wixted & Rohrer 2006, Psychological Bulletin 132(3):354-380 (spacing); Cepeda, Vul, Rohrer, Wixted & Pashler 2008, Psychological Science 19:1095-1102 (best gap against test delay); Rohrer & Taylor 2007, Instructional Science 35:481-498 (shuffled maths practice); Chi, de Leeuw, Chiu & LaVancher 1994, Cognitive Science 18:439-477 (self-explanation); Kornell, Hays & Bjork 2009, Journal of Experimental Psychology: Learning, Memory, and Cognition 35(4):989-998 (a failed try before the answer); Bjork 1994, Memory and metamemory considerations in the training of human beings, in Metcalfe & Shimamura (eds), Metacognition, MIT Press, 185-205 (desirable difficulties)
limit: effects vary by subject, age, material and test; most studies used college students and short lab tasks, and the mixing evidence comes mostly from maths and learning categories. None of this guarantees a grade.
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