Worked Examples First¶

Strategy · All strategies
Evidence · 9 claims (7 for, 1 mixed, 1 against) · 15 studies (7 causal, 4 quant-synthesis, 2 review, 1 associational, 1 theoretical), q2–q4 · 3 of 15 report an effect size · 3 claims rest on one study

Description¶

Worked Examples First is a sequencing strategy: before learners attempt problems on their own, they study one or more fully solved, step-annotated examples of the same problem type. The example substitutes for early problem solving, showing both the procedure and the reasoning behind each step, and is typically followed by a similar problem the learner solves independently.

Design Implications¶

For novices, unguided problem solving forces working memory to be spent on search — trying solution paths, backtracking, and holding partial results — rather than on building a schema for the problem type Worked examples reduce unnecessary search for novices. [+M]. Studying a worked example externalizes those intermediate states, letting learners attend to why each step follows from the last. The strategy works best when learners actively self-explain the steps rather than passively read them Self-explanation prompts improve learning from worked examples. [+S], and when each example is immediately paired with a problem to solve Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+S].

Context¶

Requirements¶

• Examples that are isomorphic or near-isomorphic to the target problems, so the studied schema transfers directly
• Step-level annotation or explanation of reasoning, not just the final solution (Think-Aloud narration or written rationale)
• An immediate follow-on problem for the learner to solve (Practice)
• A plan for fading: alternating example–problem pairs, then completion problems, then full problems (Fading)
• Well-structured tasks with a correct, generalizable solution method
• A fading plan: full examples → completion problems (partially worked) → unsolved problems
• Problems with a well-structured, convergent solution path
• A worked example that is clear, correctly solved, and annotated with reasoning — not just the steps
• Optional: self-explanation prompts ("Why did we do this step?") before moving to independent practice

Constraints¶

• Examples alone, without paired practice, produce strong illusions of competence and poor transfer Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [-S]
• For learners with substantial prior knowledge, worked examples are redundant and can impair learning relative to problem solving Worked-example guidance becomes less effective as learner expertise increases. [~S] — the expertise reversal effect
• Splitting an example across a diagram and separate text forces split attention and degrades learning Split-attention from separated sources degrades worked-example learning. [+M] — integrate steps with the diagram
• A single example can anchor learners to one solution method; multiple contrasting examples reduce this Comparing contrasting cases improves learning. [+M]
• For learners with substantial prior knowledge, worked examples impose redundancy and slow learning relative to problem solving Worked-example guidance becomes less effective as learner expertise increases. [-S] — the expertise reversal effect
• Ill-structured or open-ended tasks (design, argumentation) lack a single canonical solution, limiting the strategy's applicability [~M]
• Splitting attention between a problem statement, diagram, and solution steps degrades the benefit; integrate text and visuals physically (Cognitive Load Management)
• Example study alone, without paired practice, produces overconfidence and poor transfer Pairing worked examples with practice or fading supports transfer better than examples alone. [-M]
• Ill-suited to ill-structured domains (open design, negotiation) where no single canonical solution exists
• Learners often skim examples superficially; without self-explanation prompts or completion tasks, study time collapses and learning gains vanish [~M]
• Less effective for open-ended or design tasks where there is no single correct approach

Implementation Variability¶

• Alternating pairs: example, then isomorphic problem, repeated across a sequence — the classic Sweller–Cooper format
• Completion problems: give the setup and partial solution; learners fill in missing steps as a bridge between studying and solving
• Multiple contrasting examples: two examples differing on one feature, studied side by side to highlight the condition that matters
• Erroneous examples: learners find and fix a flawed worked solution, sharpening discrimination (Non-Examples)
• Example–problem pairs: alternate one worked example with one isomorphic practice problem — the most robustly supported format [+S]
• Completion problems: present a partially worked solution the learner must finish, bridging observation and independent performance
• Faded worked examples: a sequence of examples with progressively more steps omitted
• Erroneous examples: present a flawed solution for learners to diagnose, sharpening discrimination of common misconceptions
• Example–problem pairs: alternate one worked example with one isomorphic problem — the most robustly supported format Renkl, A. (2014) [+S]
• Completion problems: present a partially worked solution the learner finishes, bridging example and independent solving Fading
• Erroneous examples: present a flawed solution for learners to find and fix, which builds conceptual understanding and error discrimination Erroneous examples help learners identify and correct misconceptions. [+M]
• Faded worked examples: progressively remove later steps across a sequence as competence grows Fading support promotes transfer of responsibility. [+M]
• Faded examples: Progressively remove steps from successive examples, requiring learners to complete the missing parts — bridges toward fully independent problem solving
• Incorrect examples: Present a worked example with a deliberate error and ask learners to find and fix it — effective for building error-detection and deepening procedural understanding
• Comparison: Present two worked examples solving the same problem by different methods and ask which is more efficient or generalizable

Target Learners¶

• Novices encountering a new problem type, who otherwise waste capacity on means-ends search Worked examples reduce unnecessary search for novices. [+M]
• Learners with low prior knowledge in the domain; benefit shrinks and can reverse as expertise grows Worked-example guidance becomes less effective as learner expertise increases. [~S]
• Less suitable for advanced learners, who learn more from solving problems directly
• Learners prone to math or code anxiety, for whom a safe model to study lowers the cost of early failure
• Learners with low prior knowledge in mathematics, science, programming, and other structured problem domains
• Novices in any domain where problem-solving involves learnable steps: mathematics, programming, science, writing, clinical reasoning

Target Learning Goals¶

• Procedural fluency: acquiring standard solution procedures efficiently
• Schema construction: recognizing problem types and mapping them to solution methods
• Conditional knowledge: knowing when a method applies (best served by contrasting examples)
• Procedural fluency: algorithms, transformations, syntax, and multi-step methods
• Schema construction: recognizing which solution method applies to which problem structure
• Conditional knowledge: via annotated examples, learning when and why to apply a procedure
• Schema construction: recognizing which solution method applies to which problem type
• Conceptual discrimination: via erroneous examples and Non-Examples
• Early procedural fluency: understanding the steps of a solution process
• Schema acquisition: recognizing the structure shared by a class of problems
• Metacognitive awareness: monitoring one's own understanding of each step

Instructions¶

1. Select or write a fully solved example isomorphic to the target problem type, with each step annotated with its rationale.
2. Present the example first, integrated with any diagram, and prompt learners to self-explain key steps Self-explanation prompts improve learning from worked examples. [+S].
3. Immediately follow with an isomorphic problem the learner solves alone Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+S].
4. Fade support across the sequence: full example → completion problem → full problem (Fading).
5. As expertise grows, drop examples and shift to unsupported problem solving Worked-example guidance becomes less effective as learner expertise increases. [~S].

Related Strategies¶

• Completion Problems First — the intermediate rung between studying full examples and solving alone
• Self-Explanation Prompting — the mechanism that converts example study into schema construction
• Contrasting Cases — multiple examples that highlight when a method applies
• Think-Aloud Modeling — narration method that makes worked steps pedagogically meaningful
• I Do, We Do, You Do — a live, interactive variant of the same gradual-release logic
• Erroneous Examples — flawed worked examples that build error-detection skill
• Worked Example Routine — a structured classroom routine that formalizes this cycle
• Comparing Multiple Solution Methods — an extension that pairs two worked examples for comparison
• Consider alternatives to self-explanation — instructional explanations, sequenced problem solving, retrieval practice — given its time demands

Examples¶

• Sweller & Cooper's algebra sequence (1985) — alternating worked-example/problem pairs replaced conventional problem solving in algebra instruction, halving time-to-criterion while improving test accuracy.
• Khan Academy — narrated step-by-step solution videos precede practice sets; on-demand hints function as partial worked examples during problem solving.
• Codecademy — annotated working code shown before each exercise; learners modify a demonstrated solution before writing their own.
• Sweller & Cooper's algebra studies — learners studying worked example–problem pairs outperformed those solving the same problems unaided, with far less time on task (doi:10.1207/s1532690xci0201_3).
• Khan Academy — narrated worked examples precede practice sets; on-demand hints function as progressive fading within each exercise.
• Codecademy — annotated reference code is shown before each coding exercise, enacting the example–problem pair.
• Brilliant.org — sequences solved examples with step-by-step explanations before escalating to independent problems.
• Sweller & Cooper's algebra studies (1985) — students studying worked examples solved subsequent algebra problems faster and with fewer errors than students practicing equivalent problems throughout Sweller, J., & Cooper, G. A. (1985).
• Khan Academy — narrated step-by-step solution videos paired with practice exercises and on-demand hints, which function as progressive sub-fading.
• Codecademy — annotated code examples shown inline before learners write their own version in the same exercise.

Key Sources¶

• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. doi:10.1207/s1532690xci0201_3
• Renkl, A. (2002). Learning from worked-out examples: Instructional explanations supplement self-explanations. Journal of Educational Psychology, 94(2), 392–400. doi:10.1016/s0959-4752(01)00030-5
• van Gog, T., & Rummel, N. (2010). Example-based learning: Integrating cognitive and social-cognitive research perspectives. Educational Psychology Review, 22(2), 155–174. doi:10.1007/s10648-010-9134-7
• Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23–31. doi:10.1207/S15326985EP3801_4
• Renkl, A. (2014). Toward an instructionally oriented theory of example-based learning. Cognitive Science, 38(1), 1–37. doi:10.1111/cogs.12086
• Clark, R. C., & Mayer, R. E. (2016). E-Learning and the Science of Instruction (4th ed.). Wiley. doi:10.1002/9781119239086
• van Gog, T., Kester, L., & Paas, F. (2011). Effects of worked examples, example–problem, and problem–example pairs on novices' learning. Contemporary Educational Psychology, 36(3), 212–218. doi:10.1016/j.cedpsych.2010.10.004
• Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214. doi:10.3102/00346543070002181