The Feynman technique, step by step, with a worked example from Grade 12 maths

The Feynman technique is studying by explaining: pick one idea, write an explanation of it on a blank page in plain words as if to a younger student, mark every place you had to hedge or skip, go back to the textbook for exactly those places, then rewrite the explanation shorter. The gaps you find are what you do not yet understand. Ten minutes per idea before class is enough. A full example from Grade 12 maths follows, with the first draft's hedges left in so you can see what a gap looks like on the page.

What the Feynman technique is (and where the name comes from)

Four steps, as it is usually taught: choose an idea; explain it in plain words as if to someone younger; find the places where the explanation breaks down; go back to the source, then simplify. It is named after Richard Feynman, the physicist, whose lectures and whose refusal to hide behind jargon made him the model of explaining plainly.

An honest note belongs here. There is no primary source in which Feynman describes "the Feynman technique". The four steps are a modern packaging of how he worked, put together by later writers. That does not make the method weak. It makes it a name for two things that have been tested on their own: explaining to yourself, and preparing to teach. Both are below.

Why explaining works

Chi and colleagues (1994) had Grade 8 students read a passage on the circulatory system. Half were prompted to explain each line to themselves as they read. The self-explainers understood more, and the students who explained the most gained the most, including on questions the text never answered directly (Chi et al. 1994). Fiorella and Mayer (2013) found that students who prepared a lesson expecting to teach it learned more than students who prepared for a test, and that students who actually taught it kept the gain a week later (Fiorella and Mayer 2013). Nestojko and colleagues (2014) found the expectation alone was enough on an immediate test: students told they would teach a passage recalled more of it, and recalled it in better order, than students told they would be tested, even though nobody ended up teaching anything (Nestojko et al. 2014). In the review that rated ten study methods, self-explanation received a moderate rating, and the authors noted that it works best when you already have some knowledge to connect the new idea to (Dunlosky et al. 2013). The hub explains where self-explanation sits in the ranking and why "moderate" is still worth your ten minutes.

Put together, the technique is active recall with the gaps made visible. Writing the explanation from memory is retrieval. The hedges you circle afterwards are where retrieval failed, written down so you can act on them.

The four steps, with times

Ten minutes for one idea. Use a pen. The times matter, because the method dies when step 1 becomes a half-hour of writing.

1. Explain it from memory (4 minutes). Write the idea's name at the top of a blank page. Below it, explain the idea in plain words to a student two years younger than you, with one example. Notes closed. Do not stop to look anything up. If you do not know, write "I'm not sure why" and keep going.
2. Circle the gaps (1 minute). Read it back. Circle every hedge ("basically", "sort of", "it just works"), every step you skipped, and every term you used without saying what it means. Those circles are the output of the whole exercise.
3. Go to the source for the circles only (3 minutes). Open the textbook or your notes and read the part that answers each circle. Not the whole chapter. Write the answer beside the circle.
4. Rewrite it shorter (2 minutes). Write the explanation again, from the top. The second draft must be shorter than the first. If an analogy is true, use it. If you have to say "it's sort of like", it is not true enough.

Chapter 5 of the free playbook carries these steps on one page.

Worked example: the remainder theorem

MHF4U, the idea called dividing polynomials and the remainder theorem. The theorem says: when you divide a polynomial P(x) by (x − a), the remainder is P(a).

Draft 1, four minutes, as a student might write it, hedges and all:

When you divide a polynomial by (x − a) the remainder is P(a). This works because basically plugging in a makes the (x − a) part zero so only the remainder is left. Example: divide something by (x − 2), plug in 2, that's the remainder. I think it works for (2x − 1) too but I'm not sure what you plug in.

Step 2, the circles: "basically" (a hedge in front of the one thing that needs explaining); "makes the (x − a) part zero so only the remainder is left" (why does that get rid of the quotient?); "something" (no example was done); "not sure what you plug in" for (2x − 1).

Step 3, the source, read for those circles only. Division writes any polynomial as P(x) = (x − a)Q(x) + R, where Q(x) is the quotient and R is a number. Put x = a: the first term is (a − a)Q(a) = 0 × Q(a) = 0, so P(a) = R. The quotient disappears not because of a trick but because it is multiplied by zero. For a divisor like (2x − 1), the same argument works with whichever x makes the divisor zero: 2x − 1 = 0 at x = 1/2, so the remainder is P(1/2).

Draft 2, two minutes, shorter, with a worked check:

Any polynomial can be written P(x) = (x − a)Q(x) + R, with R a number. Put x = a: the first term is zero, so P(a) = R. Example: divide x^3 − 2x^2 + 3x − 5 by (x − 2). P(2) = 8 − 8 + 6 − 5 = 1, so the remainder is 1. For (2x − 1), use x = 1/2.

Draft 2 is shorter than draft 1, and it contains a computed number, so it can be checked. Check it by synthetic division with 2 and the coefficients 1, −2, 3, −5: bring down the 1; 1 × 2 = 2 and −2 + 2 = 0; 0 × 2 = 0 and 3 + 0 = 3; 3 × 2 = 6 and −5 + 6 = 1. The bottom row reads 1, 0, 3 | 1: quotient x^2 + 0x + 3, remainder 1. Multiply back to be sure: (x − 2)(x^2 + 3) = x^3 − 2x^2 + 3x − 6, and adding the remainder 1 gives x^3 − 2x^2 + 3x − 5, the polynomial we started with. Both routes agree. P(2) = 1 is the remainder.

The thing draft 1 could not do — say why the quotient vanishes — draft 2 does in one line, and that line is what you learned. If you are working through the MHF4U course map, this is the third idea on it, and the two after it (the factor theorem, and factoring polynomials) rest on exactly this line.

What the gaps tell you

A circle is a diagnosis. "Basically" in front of a step means you have memorized the result and not the reason, and the reason is what an exam question will change. Treat the circled words as a "cannot" pile. Each one goes onto tomorrow's recall list as a question ("Why does P(a) equal the remainder?"), because the circled words go into tomorrow's list is the whole point of finding them tonight. A gap the textbook does not close — the book states it and you still do not see it — is a question for your teacher, a tutor, or an AI tutor that coaches instead of handing over an answer. The guide on what an AI tutor should do when you bring it a gap says what to ask for and what to refuse.

Ten minutes before class

The most useful version of the technique is the smallest. The night before, or in the ten minutes before a lesson, take one index card and explain yesterday's idea on it from memory. Circle the gaps. Do not even go to the source. Then walk into class. The lesson now fills gaps you have already found, and you listen for the answers to your own questions instead of listening to everything equally. This beats reading ahead, because reading ahead produces familiarity with the next idea, and familiarity feels like understanding until the question comes. An index card of your own gaps produces attention, which is rarer.

Where the technique fails

It fails on ideas you have not met yet, because there is nothing to explain. Read the idea once first, then explain it. It fails on procedures: you can explain why synthetic division works and still make an arithmetic slip in the third column. For a procedure, pair the explanation with worked examples and a redo from a blank page, because procedures need worked examples more than they need words. And it fails quietly when the explanation is memorized words rather than a rebuilt argument. The test is to change the example. If you can explain the remainder theorem for (x − 2) and not for (x + 3), you have the words and not the idea. (For (x + 3), the zero is x = −3, and the remainder is P(−3).)

Summary box

• Four steps, ten minutes: explain from memory (4), circle the gaps (1), read the source for the circles only (3), rewrite shorter (2).
• The second draft must be shorter than the first.
• The circled words are your real study list; each becomes a recall question for tomorrow.
• The technique has no primary source in Feynman's own writing. Self-explanation and expecting to teach do have evidence, and the technique is both.
• Use it on ideas and theorems. For procedures, add worked examples and a redo from blank.
• Before class, one index card on yesterday's idea, gaps circled.