The 60-second card
The finding
Beginners learn math faster by studying a fully solved problem and then trying a near-twin than by solving problems cold.
Do this
Pair every new problem type: a solved example on the left, a matching problem on the right. Remove solved steps one at a time as students improve.
Best evidence
A meta-analysis of random-assignment studies, most run in classrooms, found worked examples improved math performance (g = 0.48), whether used for first learning or for practice (Barbieri et al. 2023(opens in a new tab)).
g = 0.48
gain in math from worked examples, across random-assignment studies
The 5-minute brief
Why it works
Solving a new kind of problem from scratch makes a beginner search for a method, and the search crowds out learning. A solved example shows the method directly, so working memory goes to understanding the steps. The finding goes back to Sweller and Cooper's 1985 algebra studies.
Two details from the meta-analysis matter for classrooms. Correct examples on their own worked better than incorrect examples or mixed correct-and-incorrect sets. Adding self-explanation prompts actually lowered the benefit in these studies (Barbieri et al. 2023(opens in a new tab)).
What it looks like
| Grade band | In practice |
|---|---|
| K–2 | A solved "make ten" problem with drawings, then a matching one students complete. |
| 3–5 | Split-page worksheet: solved fraction comparison on the left, twin problem on the right. |
| 6–8 | Solved two-step equation with each step labeled; next problem has the last step blank, then the last two. |
| 9–12 | Solved chemistry stoichiometry problem, then a matched problem, then a mixed set without examples. |
Common mistakes
- Showing one example on the board, then giving 20 problems with no examples. Pair them.
- Leaving examples in place for students who already know the method. Fade them, since support can get in the way once students know it.
- Starting with "spot the mistake" problems for beginners. Start with correct examples.
What a leader looks for in 5 minutes
- When a new problem type appears, is there a fully solved example in front of students?
- Do practice sets start with example-problem pairs and move toward problems alone?
What we don't know yet
Most worked example research is in math and science. Evidence for writing and history is thinner. The meta-analysis also found large variation between studies, so results depend on how well the examples are built.
Go deeper
- Researcher
- John Sweller; Christina Barbieri; Alexander Renkl (fading)
- Translator
- Craig Barton; Zach Groshell
Also called: worked example effect, solved examples