Back to the on-screen lesson ·
Three questions to put to every line of a worked example or textbook paragraph, a prediction to make before the next one, and what a failed prediction tells you.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will work down a worked example or a textbook paragraph asking what changed, what rule allows it and why it was chosen, and predict the next line before you look.
In lesson 7 you asked why would that be true? of a fact and answered it. This lesson points the same habit at a different kind of page: a worked example, or a textbook paragraph that builds an idea one sentence at a time. Here the question is not why a fact is true but why each step is there — and what the next one will be.
| Term | What it means |
|---|---|
| Self-explanation | Explaining to yourself, aloud or on paper, why each line of an example or text is there and how it connects to the rest. |
| Restatement | Saying what a line shows. Useful as a start, but it adds nothing the page did not already say. |
| Reason | The rule or definition that makes a step allowed. |
| Choice | Why the writer made this move rather than another allowed one. |
| Prediction | What you expect the next line to be, said before you uncover it, so it can turn out wrong. |
A worked example shows what was done. It rarely says why that move was made rather than another that was also allowed — and that choosing is exactly what you need when you face a problem on your own.
So work down the example one line at a time. What changed from the line above? What rule allows it? Why was it chosen here? Then cover the next line and predict it. If the prediction is right, go on. If it misses, go back: somewhere above, you misread a line, and the miss tells you where to look.
The same moves work on a textbook paragraph. After each sentence, ask what it adds, how it connects to the sentences before, and what the next one is likely to say. Say it out loud or write it in the margin. Keeping it in your head makes it too easy to nod along.
Another way: picture
Think of following a friend's directions across a city. Reading them tells you the turns. Asking why turn here? at each corner tells you the shape of the city, and that is what gets you home when a street is closed.
Another way: steps
Chi and colleagues (1989) listened to college students talk through the worked examples in a physics textbook. The students who later solved problems well had explained the examples to themselves much more — saying why each step was taken and noticing when they did not understand one. The weaker solvers mostly read the lines and moved on.
That study showed a link, not a cause, so Chi, de Leeuw, Chiu and LaVancher (1994) ran an experiment. Eighth graders read a textbook passage on the human circulatory system. One group was prompted to explain each sentence to themselves; another read the passage twice. The prompted group gained more, and the students who explained the most all ended up with a correct picture of how blood flows.
Bisra and colleagues (2018) pooled 64 research reports on prompting people to self-explain and found a moderate average benefit. The benefit varied from study to study, and it is a finding about groups of learners, not a promise about any one person.
Self-explaining an example takes three or four times as long as reading it. That is a real cost, so spend it well. Two examples explained line by line usually leave you better placed than eight read through, because reading through is what produces the familiar feeling of understanding everything and being unable to start anything.
There is a natural stopping point, too. When your predictions start coming out right, the example has given you what it has. Move on to a problem of the same kind, which is the next lesson. And if you are too tired for this — it is demanding work — one line explained properly is worth more than a page skimmed.
Listen to what you say. If every remark starts with so they… or then they…, you are restating: describing lines the page already describes. A reason sounds like because… or that works since…. A choice sounds like instead of…. A prediction sounds like next they will… and is said with the next line covered. Aim for all four on every line that matters.
The heart has four chambers. Blood coming back from the body enters the right atrium, passes to the right ventricle, and is pumped to the lungs; blood from the lungs enters the left atrium, passes to the left ventricle, and is pumped out to the body. This is the kind of passage Chi and colleagues used.
Take a fictional student, Dev, reading it one sentence at a time. After blood from the body enters the right atrium, he says: that blood has given up its oxygen, so the right side handles oxygen-poor blood — a reason. Then, covering the next sentence: it must go to the lungs next, to pick up oxygen — a prediction, and it is right. Later he predicts that the left ventricle's wall is thin, and the textbook says it is the thickest. He goes back and asks why: it pumps blood to the whole body, not just the lungs next door, so it needs more force. The failed prediction taught him the one fact he would otherwise have read straight past.
"I understood every line, so I understand the example." Seeing that each move was allowed is not the same as knowing why it was chosen, and only the first is on the page.
"Restating each line is explaining it." Saying they divided by 2 repeats the page. Say which rule allows it and why it was the move to make.
"Predicting is pointless if I might be wrong." A wrong prediction is the useful case: it shows you where your understanding and the example part ways.
"Self-explanation is only for math." Chi and colleagues used a biology passage. Any text that builds an idea step by step can be explained this way.
Say what changed from line 1 to line 2.
Line 1: 7, 3, 9, 4. Line 2: 3, 4, 7, 9. Changed: the values were put in order.
The restatement comes first because the other questions rest on it.
Name the rule that allows it.
Rule: reordering a list loses no values, and the median is defined on an ordered list.
The reason says why the move is legal.
Say why it was chosen.
Goal: the middle value. Sorting first, because middle only means something once the list is in order.
This is the part the page never prints, and the part you need to start the next problem alone.
Cover line 3 and predict it.
Prediction: four values, so average the middle two → (4 + 7) ÷ 2 = 5.5. Uncovered: 5.5 ✓
A right prediction is evidence you followed the reasoning, not just the arithmetic.
Read the first line and say what changed.
A price rose from 40 dollars to 50 dollars. Change: 50 − 40 = 10 dollars.
The restatement: the line found the size of the rise.
Cover the next line and predict it.
Prediction: 10 ÷ 50 = 20 percent
A commitment made before looking, so it can be checked.
Uncover it and compare.
Line 2: 10 ÷ 40 = 0.25 = 25 percent ✗
The miss is the useful case: something above was misread.
Go back and find the misread line.
Definition, two paragraphs up: percent change = change ÷ original value. The original is 40.
The failed prediction found the rule she had read past, before a test found it for her.
Say what the sentence adds.
When the price of coffee rises, people buy more tea. Adds: a change in one price moves the demand for another good.
The restatement, in your own words.
Name the reason.
Because coffee and tea can stand in for each other — they are substitutes.
The reason links the sentence to an idea from earlier in the chapter.
Cover the next sentence and predict it.
A fictional student is studying a worked example that finds the median of 7, 3, 9 and 4. Its second line reads *3, 4, 7, 9*. Which thing she could do next is self-explanation?
A fictional student has 24 minutes for worked examples tonight. Reading one through takes him 3 minutes; self-explaining one takes four times as long. Complete the worked plan.
Find the time for one self-explained example.
3 minutes × four = a minutes
Asking three questions of every line and predicting the next one is several times slower than reading.
Find how many examples he can self-explain.
24 ÷ a = b examples
Fewer examples, worked harder: each one now gives him the reasons and choices the page leaves out.
Compare with reading them through.
24 ÷ 3 = c examples read, none explained
More examples read is the plan that leaves a student able to follow everything and start nothing.
A fictional cook scales a recipe for 4 people up to 6. The worked example multiplies every amount by 6 ÷ 4 = 1.5, so 6 eggs become 9. Four things he said while working through it are below. Name the kind of each.
| Kind of remark | |
|---|---|
| They multiplied the eggs by 1.5 | |
| The same multiplier keeps the proportions | |
| Multiplying, not adding 2 of everything, keeps the balance | |
| Next they will multiply the flour by 1.5 too |
A fictional student works through a percent-change example line by line. Put the five moves of self-explanation in the order she makes them on one line, including the move she makes only if her prediction misses.
| Move | |
|---|---|
| Move 1 | |
| Move 2 | |
| Move 3 | |
| Move 4 | |
| Move 5 |
A fictional student self-explains a worked example of 10 lines. She predicts every line after the first before uncovering it, and 4 of her predictions are right. Each line takes her about 3 minutes. How many lines does she go back from, and how many minutes does the example take?
Lines to go back from: a
Minutes for the example: b
Self-explanation works on a textbook paragraph as well as on a worked example. A fictional student reads three sentences about the Electoral College. For each, choose the self-explanation that gives a reason or a prediction.
| Self-explanation | |
|---|---|
| There are 538 electors | |
| The smallest states have 3 electors | |
| A candidate needs 270 to win |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A worked example finds a 15 percent tip on a 48 dollar bill in three lines. Self-explain each line: choose the rule that allows it and the reason the writer chose it.
| Rule that allows it | Why it was chosen | |
|---|---|---|
| Line 1: 4.80 | ||
| Line 2: 2.40 | ||
| Line 3: 7.20 |
You can explain an example to yourself rather than read it. Take one worked example from your own course, cover everything below line 2, and predict line 3 before you look. Next: pairing worked examples with problems. You can stop in the middle of any of this. Closing the page is the whole of stopping — your place and anything you had typed are already saved, and the lesson opens again where you left it.
12. Your turn: a sentence in an economics text, step 3
Prediction: with more people buying tea, the price of tea may rise too.
A prediction that the next sentence can confirm or correct.