Curriculum·G702 Pedagogical Fundamentals·about 32 min

Worked examples and cognitive load

By the end of this lesson you can

→State what the 1985 algebra experiments found about studying worked examples against solving equivalent problems, and where the effect stopped
→Explain cognitive load as the reason a novice solving problems learns less than a novice studying solutions, and say when the reverse becomes true
→Compute the learning cost of a problem-solving search against a worked example from the experiments' own ratios, and read the transfer limit
→Write a worked example the way this Academy writes them: the incident's own figures, every step shown, the learner computing the next one

Graduate · enrolled learners

This lesson opens with The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra, 1985.

What happened: John Sweller and Graham Cooper reported five experiments in Cognition and Instruction on how students acquire algebra problem-solving skill; in Experiments 2 to 5 students learning algebraic manipulation were given either conventional problems to solve or worked examples to study. Worked examples required considerably less time to process than conventional problems, and subsequent problems similar to the initial ones were solved more rapidly and with fewer mathematical errors, with a secondary summary reporting the example group taking roughly half the time and making about a fifth as many errors. Both findings were specific to problems identical in structure to the studied ones. The authors' account was that problem-solving search by a novice consumes the working memory needed to acquire the underlying schema, so the novice solves the problem and learns little from it, while studying a solution leaves the capacity free to learn the pattern.
The decision point: The intuition, then and now, is that a learner learns by doing, so give them problems. For a novice the experiments said the opposite: the doing consumed the capacity the learning needed. The novice who solved twenty problems had spent twenty problems searching, and the novice who studied twenty solutions had spent them acquiring the pattern. The limit is as important as the effect: once the pattern is held, problems become the right tool, and examples that differ from the test do not carry. That is why every lesson in this Academy has a worked example built from the incident's own figures, every step shown, and why the labs that follow are problems rather than examples.

What you will be able to answer

→What did the 1985 algebra experiments find?
→Why does a novice learn less from solving?
→When do problems become the better tool?
→How does this Academy use the finding?

Orientation and Year One are open: anyone can read them without an account. From Year Two onward the lessons are for enrolled learners, because progress through the later years only means anything if it is tracked against a record.

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Terms used here

Liquidation

Sources and review

Confidence medium·Volatility low·Reviewed 2026-09-14·Owner unassigned

Contested

The 'half the time, a fifth of the errors' figures are from a secondary summary of the experiments (Andy Matuschak's notes), not from the paper's own tables, which we could not read; the abstract reports the direction, less time and fewer errors, without ratios. The direction and the transfer limit are the original findings relied on; the ratios are used in the worked example as an illustration of their size and are labeled as such.

The expertise reversal effect, that worked examples become less effective and can become harmful as learners gain expertise, was established in later work by Kalyuga and colleagues rather than in the 1985 paper, which reported the novice effect and its transfer limit.

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