Worked examples with subgoals
Claim: a method is taught by a solved example whose steps are named by what they achieve, then faded: the next examples leave more steps to the reader.
- Grade: measured, for novices; reversed for experts.
- Evidence: learning science (strand 3).
- Check:
shape-conformance(exact, for documents declared as reports in config): the plan and its steps are present; whether the steps name goals is judgment. - Reader styles: strengthened by novice; relaxed by expert.
What it asks
- The first problem of a kind is solved in full, every step titled by its goal ("Isolate the variable"), not by the operation it performs.
- The next leaves its last steps to the reader; a later one is a whole problem, with the answer folded.
- Varied examples of one method, rather than several of the same surface.
- Correct examples first; an erroneous one only with a prompt to find the error.
Why
Worked examples beat problem solving in mathematics, g = 0.48, about 18 percentile points (Barbieri 2023). Removing steps one by one beats jumping to whole problems (Renkl 2004). Subgoal labels transfer to new problems, more when they appear in both the text and the example (Catrambone 1998; Margulieux 2016).
Limits
For assistance in general, the benefit reverses with expertise (Tetzlaff 2025, a meta-analysis): novices gain from more (d = +0.51) and advanced learners from less (d = -0.43). For worked examples, lab studies reviewed in Kalyuga 2003 found the benefit vanished with training, and problem solving then did better. For a new procedure, examples beat testing on an immediate test; a week later testing caught up, and pulled ahead only on problems identical to those practised (Yeo 2019).