Count the vowels: the task decides what you remember¶

Level: 101 · for anyone who has read a chapter and remembered none of it

One line: Memory keeps what you did with something, not what passed in front of your eyes: count the vowels in fifteen phrases and you remember about three of them; know that the goal is to remember, find the principle that orders them, and you remember twelve. Nobody got smarter in between.

Do the exercise first¶

This is Saundra McGuire's exercise from chapter 3 of Teach Yourself How to Learn (Figure 3.3), and it only works if you do it before reading on. Set a timer for 45 seconds and count all the vowels in these phrases:


Dollar bill	Cat lives
Dice	Bowling pins
Tricycle	Football team
Four-leaf clover	Dozen eggs
Hand	Unlucky Friday
Six-pack	Valentine's Day
Seven-Up	Quarter hour
Octopus

Now scroll the table out of sight, and write down as many of the phrases as you can remember. Score yourself: the number you got, divided by 15, times 100.

In McGuire's workshops the average is 3 of 15, or 20%. "Let's call it F minus."

Then she asks the group to look at the list again, reading each column from top to bottom, and find the principle that organises it. Try for fifteen seconds before you look at the program's output. Then give yourself another 45 seconds, this time to memorise the list, hide it, and write it down again. The workshop average for the second round is 12 of 15, or 80%, and many people get all fifteen.

What made the difference?¶

McGuire's question: "between our first and second attempts to recall the list, we had not become any smarter. So what made the difference?" Two things.

The goal. The first time, the task was to count vowels. Counting vowels needs the letters and never the meaning, so the letters are all your mind worked on, and what you did not work on, you did not keep. The second time you knew the goal was to remember. McGuire's warning is that students often do the first kind of task without knowing it: "read chapter 1" gets done as skimming chapter 1 between messages, and a problem set gets done to hand in correct answers, when the professor wanted the concepts that solve problems not on the sheet. A practice test gets memorised question by question, when it was a sample of what the concepts must be able to answer.

The principle. The list counts from 1 to 15: one dollar, two dice, three wheels, and on to a quarter of an hour. Once you see it, you no longer hold fifteen unrelated phrases. You hold one rule, and you walk through the numbers you already know, asking at each "what comes in n?". Section 4 of the program makes that concrete.

The second difference is also the fourth ability of metacognition at work: with the principle, a gap shows up by itself. If you reach 11 and find nothing, you know you forgot something and what to look for. Without it, fifteen phrases and twelve phrases feel much the same from the inside.

What the program prints¶

It does the first task, counting the vowels, which is the answer key for the exercise. Then it does the second: it states the principle, checks that the list really runs 1 to 15, and works out how unlikely that order would be by accident, which is how you know there was a principle to find. Spoiler below.

Verified output of count_the_vowels.py — regenerated by tools/run_examples.py, never hand-typed.

1. THE TASK YOU WERE GIVEN: COUNT THE VOWELS (a, e, i, o, u; y not counted)
   Dollar bill         3   running total   3
   Dice                2   running total   5
   Tricycle            2   running total   7
   Four-leaf clover    6   running total  13
   Hand                1   running total  14
   Six-pack            2   running total  16
   Seven-Up            3   running total  19
   Octopus             3   running total  22
   Cat lives           3   running total  25
   Bowling pins        3   running total  28
   Football team       5   running total  33
   Dozen eggs          3   running total  36
   Unlucky Friday      4   running total  40
   Valentine's Day     5   running total  45
   Quarter hour        5   running total  50
   Total: 50 vowels (54 if y counts, as in 'Tricycle' and 'Friday').
   The task never needed the meaning of a single phrase. Letters are all it
   asked the eyes for, so letters are all the memory was given to keep. In
   McGuire's workshops the average recall afterwards is 3 phrases of 15: 20%.

2. THE ORGANISING PRINCIPLE (spoiler)
    1  Dollar bill        one dollar
    2  Dice               a pair of dice
    3  Tricycle           three wheels
    4  Four-leaf clover   four leaves
    5  Hand               five fingers
    6  Six-pack           six cans
    7  Seven-Up           seven, in the name
    8  Octopus            eight arms
    9  Cat lives          nine lives
   10  Bowling pins       ten pins
   11  Football team      eleven players on the field
   12  Dozen eggs         twelve eggs
   13  Unlucky Friday     Friday the 13th
   14  Valentine's Day    February 14th
   15  Quarter hour       fifteen minutes
   Read down the columns and the numbers go 1, 2, 3, ..., 15:
   in order, with nothing missing: True.

3. COULD THAT ORDER BE AN ACCIDENT?
   15 phrases can be listed in 15! = 1,307,674,368,000 orders.
   Only one of them counts 1 to 15, so a list shuffled at random would do it
   with probability 1/15! = 7.6e-13. The order is a principle, and
   finding it is the point of looking again.

4. HOW MUCH THERE IS TO REMEMBER, BEFORE AND AFTER
   Without the principle, recall has to find 15 unrelated phrases, and nothing
   says which one comes next or whether one is missing. With it, recall is a
   walk through 1, 2, 3, ..., 15, asking at each step 'what comes in n?':
     what comes in  1?  ->  Dollar bill
     what comes in  7?  ->  Seven-Up
     what comes in 12?  ->  Dozen eggs
     what comes in 15?  ->  Quarter hour
   The counting numbers are already in memory, so they cost nothing to store,
   and each one is a cue for exactly one phrase. A gap shows up at once: if
   you reach 11 and find nothing, you know that you forgot, and what to search
   for. That is metacognition inside the recall itself: you can check your
   own answer, because the principle tells you what a complete answer is.

5. THE WORKSHOP'S ARITHMETIC (McGuire's averages)
   first try, counting vowels           3 / 15 x 100 =  20%
   second try, knowing goal and rule   12 / 15 x 100 =  80%
   Same people, same list, same 45 seconds, and nobody became smarter in
   between. Two things changed: they knew the goal was to remember, not to
   count, and they had a principle that organised what they saw.

Why this is a mathematics lesson¶

Section 3 is the reason mathematics is learnable at all. A random list has no shortcut, so it has to be stored item by item. A list with a principle can be regenerated from the principle, and the chance of fifteen items falling into order by accident, 1 in 15!, is about 1 in 1.3 trillion. Mathematics is almost nothing but principles of this kind. The addition and multiplication rules for significant figures ↗ are two rules to memorise until you see that one rule, about absolute and relative error, produces both. The area and volume formulas ↗ are eleven formulas until one check on their dimension tells them apart. Memorising the outputs of a principle is counting its vowels.

Questions¶

1. How many vowels are in the fifteen phrases?

Answer

50, counting a, e, i, o and u. 54 if y counts too (Tricycle, Unlucky, Friday, Day).

2. What is the organising principle of the list?

Answer

Numbers from 1 to 15, read down the columns: one dollar, a pair of dice, a tricycle's three wheels, four leaves, five fingers, and so on to fifteen minutes in a quarter hour.

3. What were the two differences between the first and the second attempt?

Answer

Knowing the goal (remember, not count vowels), and having a principle that organised the list.

4. Why does counting the vowels leave so little in memory?

Answer

The task needs only the letters, not the meaning, so that is all your mind works on. Memory keeps what you did with something, not what your eyes passed over.

5. A professor assigns "Read chapter 1". What goal does McGuire suggest the assignment really has?

Answer

To understand the concepts of the chapter well enough to use them, not to have passed your eyes over every page. Reading while scrolling a phone is counting the vowels.

6. Why is memorising the answers to a practice test a mistake?

Answer

The practice test is a sample of what the concepts must be able to do. The real test asks different questions, and only the concepts transfer to them.

7. How does the principle let you check your own recall?

Answer

It says what a complete answer looks like: fifteen items, one for each number. A number with nothing next to it is a gap you can see and go looking for.

How to practise¶

Before you read or study, say the goal out loud. Not "read chapter 1" but "be able to explain why the converse needs its own proof".
Look for the principle before memorising the items. When a page gives a list of rules, ask what produces all of them.
Treat a practice test as a sample. For each question, ask which concept it tests and make up a different question on the same concept.
Try the exercise on someone else, without telling them the goal the first time. It is the fastest way to believe the result.
Take a picture walk first. Oakley and Sejnowski's Learning How to Learn (2018) asks for a minute or two spent on a chapter's headings, pictures and summary before reading it, like a map before a journey. Their picture is a closet: the walk puts up the hangers, and without them the clothes fall on the floor in a jumble. It is this page's second difference, the principle, made cheap: the headings are the rule that organises the paragraphs, so each paragraph read afterwards has a place to go, and a paragraph that fits no heading is a gap you notice. On this site the headings are the page's table of contents, and a chapter's table of lessons is the walk for the whole chapter.

Flashcards¶

The page as a deck of Anki cards: count_the_vowels.txt. Import with File → Import. Tags: exercise, principle, goal, trap.

Po polsku, w skrócie¶

To ćwiczenie Saundry McGuire. Masz 45 sekund na policzenie samogłosek w piętnastu hasłach: banknot dolarowy, kostki do gry, trójkołowy rowerek, czterolistna koniczyna i tak dalej. Potem, bez uprzedzenia, masz wypisać z pamięci jak najwięcej haseł. Średnio ludzie pamiętają trzy z piętnastu, czyli 20%.

Za drugim razem wiedzą, że celem jest zapamiętanie, i szukają zasady porządkującej listę: hasła odpowiadają liczbom od 1 do 15 (jeden dolar, dwie kostki, trzy kółka, cztery listki, pięć palców… kwadrans to 15 minut). Średnio pamiętają dwanaście z piętnastu, czyli 80%. Nikt w tym czasie nie zmądrzał. Zmieniły się dwie rzeczy: znajomość celu i zasada, która porządkuje materiał.

Pamięć zatrzymuje to, co robiliśmy z materiałem, a nie to, co przesunęło się przed oczami. Liczenie samogłosek potrzebuje tylko liter, więc tylko litery zostają. W matematyce jest tak samo: zamiast uczyć się na pamięć wyników, trzeba znaleźć zasadę, z której wynikają, bo z niej da się je odtworzyć i sprawdzić, czy czegoś nie brakuje. Stąd rada Barbary Oakley: zanim przeczytasz rozdział, przejrzyj przez minutę jego nagłówki i rysunki. To jak wieszaki w szafie: dopiero na nich można porządnie powiesić to, co przeczytasz.

Count the vowels: the task decides what you remember¶

Do the exercise first¶

What made the difference?¶

What the program prints¶

Why this is a mathematics lesson¶

Questions¶

How to practise¶

Flashcards¶

Po polsku, w skrócie¶

See also¶