--- title: "Show a worked example first | DuckyHelper" url: "https://duckyhelper.com/research/principles/worked-examples/" description: "The worked example effect: why studying solved problems helps beginners more than solving alone, when it stops helping, and how DuckyHelper shows steps." updated: "2026-10-09" --- Worked examples # Show a worked example first For beginners, studying a worked example, a problem solved step by step, teaches more than struggling through the same problem alone. Sweller and Cooper (1985) found worked examples took less time and led to faster, more accurate solving of similar problems. The benefit fades as skill grows. DuckyHelper shows short worked steps, one move each, and works similar examples when you are stuck. > “worked examples, as expected, require considerably less time to process than conventional problems” [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.](https://doi.org/10.1207/s1532690xci0201_3) From Sweller and Cooper (1985), Cognition and Instruction. Reproduced for commentary. Source: [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.](https://doi.org/10.1207/s1532690xci0201_3). In DuckyHelper ## Worked steps, one move each In the film, Sweller and Cooper's line is followed by the real Steps card. A worked example in DuckyHelper is short and comes when it helps: - Worked steps, one move each (Mac and web) - A similar example, not your homework (Mac and web) - Worked out on the blackboard (Mac and web) - The worked step is a rung, not the start (Mac app) ## What the research found John Sweller and Graham Cooper had algebra students either solve problems or study worked examples of the same problems. The examples took considerably less time to work through, and the students who studied them then solved similar problems faster and with fewer mistakes: > subsequent problems similar to the initial ones also were solved more rapidly (Sweller & Cooper, 1985) Sweller's cognitive load theory explains why: searching for a solution uses up the working memory a beginner needs to learn the pattern behind it. > conventional problem‐solving activity is not effective in schema acquisition (Sweller, 1988) ### How to use examples well Reviews of the research give practical rules. Examples work best right next to practice problems of the same kind: > examples should be presented in close proximity to matched practice problems (Atkinson et al., 2000) > Learning from examples is a very effective means of initial cognitive skill acquisition (Renkl, 2014) The same U.S. Department of Education guide that recommends spacing also recommends alternating worked examples with problems to solve (Pashler et al., 2007). The key word in Renkl's sentence is *initial*. As learners get better, full examples stop helping and can even get in the way (the expertise reversal effect, Kalyuga et al., 2003), so the steps should fade into practice. ## Feature by feature Ask "solve this step by step": 3 to 6 steps, each a single move, explained in a sentence (what changes and why) with the math beside it. In the Mac app, **Keep** turns them into a note you can drag anywhere. In Eddy, they open as a Worked out window. *Mac and web.* ### A similar example, not your homework On homework, the steps show only how far you got plus a hint for the next one. When you are stuck, the tutor works a similar problem with you, then hands yours back. *Mac and web.* ### Worked out on the blackboard On Eddy's blackboard, math is written one step per beat, the part that changes circled and the rule noted beside it, then a question for you. *Mac and web.* ### The worked step is a rung, not the start In the Mac app's hint ladder, the worked step comes after a nudge and a bigger hint, so the example arrives when you need it. *Mac app.* Ducky answers out loud and the real Steps card streams in, one move per step. What this page does not claim These studies tested other people, other schools and other tools. DuckyHelper has not been tested in a study like these, so none of these results are DuckyHelper's results. They are the reasons behind how it teaches. ## The papers on this page ### The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra Sweller & Cooper, 1985. Cognition and Instruction. Studying worked examples beat problem solving for novices: faster, with fewer errors. ### Cognitive Load During Problem Solving: Effects on Learning Sweller, 1988. Cognitive Science. Conventional problem solving eats working memory needed to learn the underlying schemas. ### Learning from Examples: Instructional Principles from the Worked Examples Research Atkinson, Derry, Renkl & Wortham, 2000. Review of Educational Research. Good worked examples are integrated and placed right next to matched practice. ### Toward an Instructionally Oriented Theory of Example-Based Learning Renkl, 2014. Cognitive Science. Examples are a very effective way to start learning a new skill. ### The Expertise Reversal Effect Kalyuga, Ayres, Chandler & Sweller, 2003. Educational Psychologist. Techniques that help novices can backfire with more experienced learners. ### Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching Kirschner, Sweller & Clark, 2006. Educational Psychologist. For novices, minimal guidance is less effective than strong, explicit guidance. ### Organizing Instruction and Study to Improve Student Learning Pashler et al., 2007. IES Practice Guide (NCER 2007-2004), U.S. Department of Education. Seven research-based recommendations, including spacing, worked examples and quizzing. ### Analogical problem solving Gick & Holyoak, 1980. Cognitive Psychology. A solved story helps crack an analogous problem, mostly when learners are hinted. ### Learning and transfer: A general role for analogical encoding Gentner, Loewenstein & Thompson, 2003. Journal of Educational Psychology. Comparing two cases side by side helped learners pull out the shared idea and use it later. ## Frequently asked questions ### What is the worked example effect? Beginners learn more from studying problems that are already solved, step by step, than from solving the same problems on their own. Sweller and Cooper (1985) showed it with algebra; many later studies found the same. ### Do worked examples always help? No. They help most at the start. As a learner gets better, full examples can stop helping (the expertise reversal effect), so good teaching fades them into practice. ### Will DuckyHelper do my homework step by step? It will show you how with a similar example, and show your steps so far with a hint for what comes next. It is built not to hand over the full solution to graded work. ## Sources 1. [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.](https://doi.org/10.1207/s1532690xci0201_3) (accessed 2026-10-09) 2. [Sweller, J. (1988). Cognitive Load During Problem Solving: Effects on Learning. Cognitive Science, 12(2), 257-285.](https://doi.org/10.1207/s15516709cog1202_4) (accessed 2026-10-09) 3. [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.](https://doi.org/10.3102/00346543070002181) (accessed 2026-10-09) 4. [Renkl, A. (2014). Toward an Instructionally Oriented Theory of Example-Based Learning. Cognitive Science, 38(1), 1-37.](https://doi.org/10.1111/cogs.12086) (accessed 2026-10-09) 5. [Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The Expertise Reversal Effect. Educational Psychologist, 38(1), 23-31.](https://doi.org/10.1207/S15326985EP3801_4) (accessed 2026-10-09) 6. [Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75-86.](https://doi.org/10.1207/s15326985ep4102_1) (accessed 2026-10-09) 7. [Pashler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing Instruction and Study to Improve Student Learning. IES Practice Guide (NCER 2007-2004), U.S. Department of Education.](https://ies.ed.gov/ncee/wwc/PracticeGuide/1) (accessed 2026-10-09) 8. [Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12(3), 306-355.](https://doi.org/10.1016/0010-0285(80)90013-4) (accessed 2026-10-09) 9. [Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95(2), 393-408.](https://doi.org/10.1037/0022-0663.95.2.393) (accessed 2026-10-09) ## Related principles ### Draw it as you explain: pictures and words Multimedia learning in plain words: why words with pictures beat words alone, why watching a drawing appear helps, and how DuckyHelper draws as it talks. ### Quiz, don't re-read: retrieval practice The testing effect: why pulling an idea out of memory beats re-reading it, with the real numbers from Roediger and Karpicke, and how DuckyHelper quizzes you. ### Space it out: spaced practice and forgetting The spacing effect and the forgetting curve: why reviewing after a gap beats cramming, what 317 experiments found, and how DuckyHelper schedules review. ## Keep reading ### Scaffolding: just enough help, one step at a time What scaffolding means in learning science (Wood, Bruner and Ross; Vygotsky), why help should fade, and how DuckyHelper's hints and tutorials do it. ### The learning-science library: 100+ papers 100+ real learning-science papers behind DuckyHelper, sorted by principle, each with a citation, a link to the publisher and a one-line summary. ### Worked steps, one move each, that you can keep, and graphs you can hover, zoom and slide Ask DuckyHelper to work it out and get worked steps, one move each, plus graphs you can hover, zoom and change with sliders. Keep the steps as a note. ### Learn an app inside the app: Ducky shows each step, waits for you, and moves on when you did it On a Mac, DuckyHelper teaches you an app inside the app itself: it shows where to click, waits for you to do each step, and moves on when you did. ## Ready to learn DuckyHelper is ready on your Mac. Learn with Eddy on its blackboard, or with Ducky right on your screen. [Download for Mac](https://duckyhelper.com/download/) [See what it does](https://duckyhelper.com/features/) The Mac app needs Apple silicon and macOS 14 Sonoma or later. There is no Chromebook, Windows or web version right now.