Cognitive load: the same page weighs less once practice has made chunks¶

Level: 101 · for anyone who has read the same paragraph three times while someone talked nearby

One line: Working memory holds about four chunks, and what counts as a chunk is whatever practice has made automatic. So the same formula is 19 items for a beginner and 1 for an expert, a conversation in the room can be the load that tips a student over, and practice lowers the load by turning the parts that repeat into chunks.

Three kinds of load¶

Chapter 4 of Todd Zakrajsek's The New Science of Learning (third edition, 2022), "Improving the Learning Process", explains John Sweller's cognitive load theory (1988): there is a limit to how much you can process at once, and past it errors rise and study time is wasted. The book names three kinds of load:

Intrinsic load is the complexity of the task itself: a physics chapter against a novel, a language you are just learning against your first one. It falls as you gain expertise, "because those with expertise can combine elements".
Extraneous load is whatever in the room takes attention and does not help: the TV, a debate about dorm food, a phone. Study Tip 4.2: check your environment to minimize extraneous load before you start to study; put your phone away.
Germane load is the effort of building the structures that make later learning easier: automaticity, practising something until it takes no thought, like reading the word "and"; and schemas, organised knowledge you can pull up whole, like knowing where the counter is in any McDonald's.

The book's claims are about people. This page makes the one piece of it a program can check exact: why expertise lowers intrinsic load, and what practice actually builds.

Chunks¶

George Miller (1956) put the span of working memory at "seven, plus or minus two"; later work, summarised by Nelson Cowan (2001), puts it nearer four chunks. A chunk is a unit you already know: for a reader, a word rather than its letters; for a historian, 1492 rather than four digits. The program reads a string the way a learner with a given set of known chunks would, taking at each point the longest piece they know.

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

1. The same string, three readers

   2851012, to someone who knows counting: 7 chunks
     2 | 8 | 5 | 1 | 0 | 1 | 2
   1234567, to someone who knows counting: 1 chunk
     1234567

   knows digits only: 12 chunks
     1 | 4 | 9 | 2 | 1 | 7 | 7 | 6 | 1 | 9 | 4 | 5
   knows the years 1492, 1776, 1945: 3 chunks
     1492 | 1776 | 1945

   a beginner, who knows the symbols: 19 chunks
     ( | a | + | b | ) | ^ | 2 | = | a | ^ | 2 | + | 2 | a | b | + | b | ^ | 2
   a student, who knows the two sides: 3 chunks
     (a+b)^2 | = | a^2+2ab+b^2
   an expert, who knows the identity: 1 chunks
     (a+b)^2=a^2+2ab+b^2

   Nothing on the page changed. The load is in the reader.

2. A budget of 4: intrinsic load plus whatever else is in the room

   Suppose a conversation nearby takes 2 places and a phone on the desk
   takes 1: numbers for the example, not measurements.

   reader                  quiet room     phone on the desk   conversation nearby
   beginner             19 overloaded         20 overloaded         21 overloaded
   student                     3 fits                4 fits          5 overloaded
   expert                      1 fits                2 fits                3 fits

   The expert reads this formula anywhere. The student reads it in a
   quiet room or beside a phone, but not beside a conversation: that is
   the load that tips it over, and moving to another room is the fix, as
   the book says. For the beginner no room is quiet enough; only
   practice helps.

3. Practice makes chunks: merge the pair found in the most lines

   Practice sheet, five expansions of a square:
     (a+b)^2=a^2+2ab+b^2
     (x+y)^2=x^2+2xy+y^2
     (p+q)^2=p^2+2pq+q^2
     (u+v)^2=u^2+2uv+v^2
     (s+t)^2=s^2+2st+t^2
   Test line, never practised: (m+n)^2=m^2+2mn+n^2

   merge   new chunk     chunks in the test line
       0                  19
       1   ')^'           18
       2   ')^2'          17
       3   ')^2='         16
       4   '^2'           14
       5   '^2+'          13
       6   '^2+2'         12

   The test line now reads as: ( | m | + | n | )^2= | m | ^2+2 | m | n | + | n | ^2

   Practice took the line from 19 chunks to 12, and every chunk it built
   is a part that repeats across lines: '^2', ')^2=', '^2+2'. The letters
   change from line to line, so they never became chunks, and what
   practice built carries over to m and n, never practised.

   What is left is the two letters, three times each. Merging can go no
   further; the last step is to see the line as one chunk with two slots,
   (first + second)^2 = first^2 + 2 first second + second^2. That is a
   schema, in the book's word, and it is how the expert in section 1
   holds the identity as one chunk. Every merge cost effort on the
   practice sheet: that effort is germane load.

The load is in the reader¶

Section 1 reads strings with different knowledge. Zakrajsek's chapter 6, "Finding and Using Patterns", gives the first pair: 2851012 is seven digits to hold, and 1234567, also seven digits, is one chunk, "the numbers up to 7", to anyone who can count. Twelve digits are twelve chunks, or three years to someone who knows 1492, 1776 and 1945. The identity (a + b)² = a² + 2ab + b² is 19 symbols to a beginner, 3 chunks to a student who knows its two sides, and 1 to an expert who knows it as a fact. The page did not change. Chapter 6 adds an everyday case: nine grocery items are over the budget, but eggs, bacon, orange juice; toilet paper, shampoo, toothpaste; hamburger, buns, chips are three schemas, breakfast, bathroom and lunch, and each one brings its three items back as cues. That is the book's point that intrinsic load depends on expertise, made exact: intrinsic load is not a property of the material but of the material and the reader together.

One budget for everything¶

Section 2 puts everything in one budget of four places, and supposes, for the example, that a nearby conversation takes two and a phone on the desk takes one. The expert reads the identity anywhere. The student can in a quiet room or beside the phone, but a conversation pushes them to five and over. That is the book's reading-beside-a-conversation example: one of the two has to stop, and moving rooms is the fix. For the beginner, at 19, no room is quiet enough. Removing extraneous load helps only the reader who is close to the limit; the beginner needs intrinsic load to fall, and only practice does that.

Practice builds the parts that repeat¶

Section 3 models practice. The learner works through five expansions of a square, with different letters each time, and after each pass merges the pair of neighbouring pieces found in the most lines into a new chunk. This is byte-pair encoding (Philip Gage, 1994), the same algorithm large language models use to build their vocabularies.

The chunks it builds are "^2", ")^2=", "^2+2": exactly the parts that repeat. The letters differ from line to line and never become chunks, so what practice built carries over to a line with m and n that was never practised, reading it in 12 chunks instead of 19. What merging cannot do is the last step, seeing the whole line as one chunk with two slots, (first + second)² = first² + 2·first·second + second². That is a schema, and it is how the expert in section 1 holds the identity as a single chunk. Each merge cost effort on the practice sheet, and that effort is germane load: a short-term cost, in the book's words, for a long-term gain.

This is also why the book tells you to identify the foundational material of a course and make it automatic. Every foundation made automatic is a place freed in the budget for the new material.

What the program does not show¶

Four is an approximate capacity from experiments, not a constant, and the loads assigned to a conversation and a phone are invented for the example. People do not build chunks by counting pairs. What the model shows exactly is the arithmetic: a fixed budget, a load that depends on what the reader already knows, and practice that shrinks the load by chunking whatever repeats. The book's evidence on phones (Whittington, 2019: students who put phones in a sealed envelope scored better on exams, and 79% said it helped) is about people, and it is the book's to report.

Try it¶

Check the room before you start. List what is taking attention, and remove one thing.
Sort your to-do list by intrinsic load. Gathering material for flashcards is light and can go beside a show; a new organic chemistry chapter is heavy and needs the quiet room.
Name the foundation. Pick the five terms or formulas that every page of a course uses, and practise them until they are automatic.
Change the sheet. Add a line with a minus sign, (a − b)² = a² − 2ab + b², to the practice sheet and rerun: which chunks does practice build now?

Flashcards¶

The page as a deck of Anki cards: cognitive_load.txt. Import with File → Import. Tags: definition, chunk, budget, practice, trap.

Po polsku, w skrócie¶

Pamięć robocza mieści naraz około czterech porcji informacji (Cowan). Porcją jest to, co już znamy na tyle dobrze, że robimy to automatycznie: dla czytelnika słowo, a nie litery; dla historyka rok 1492, a nie cztery cyfry. Wzór (a + b)² = a² + 2ab + b² to 19 symboli dla początkującego, 3 porcje dla ucznia i 1 dla eksperta. Obciążenie nie tkwi więc w materiale, tylko w materiale razem z czytelnikiem.

Sweller wyróżnia trzy rodzaje obciążenia. Wewnętrzne to trudność samego zadania, i spada z doświadczeniem. Zewnętrzne to wszystko w otoczeniu, co zabiera uwagę: telewizor, rozmowa, telefon. Wszystko to dzieli jeden budżet, dlatego rozmowa obok może przepełnić ucznia, a ekspertowi nie przeszkadza. Trzecie, właściwe, to wysiłek budowania nowych porcji i schematów.

Program pokazuje, jak ćwiczenie buduje porcje: łączy najczęściej powtarzające się pary sąsiednich kawałków (ten sam algorytm, BPE, buduje słownik modeli językowych). Powstają porcje z tego, co się powtarza, a zmienne litery nimi nie zostają, więc zdobyta wiedza przenosi się na nowe przykłady. Ostatni krok, zobaczenie całego wzoru jako jednej porcji z dwoma miejscami, to schemat.