How to learn this
Every other module on this site has the same parts: key ideas, a worked example, practices and questions with answers. This one says how to use them, and why. The short version is that the feeling of understanding comes cheaply from reading, and the evidence of it comes only from producing the thing yourself, later, without the page.
12 sources · fact-checked and reviewed
Key ideas
Worked examples first
While a topic is new, studying a fully worked solution teaches more than attempting the same problem unaided, at least for problems of the same kind; the finding goes back to Sweller and Cooper's 1985 study of algebra. It helps most when you explain each step to yourself as you go, rather than reading it through.[1][2][3]
Predict before you look
Trying to answer a question before studying improves later recall of what that question asked about, even when the attempt fails. In Richland and colleagues' experiments with a text on vision, a test taken first, mostly answered wrongly, beat spending the same time studying; material the pretest had not asked about did no better than with extra study. Predicting a number before you compute it is the same move applied to engineering, an extension of the finding rather than something it tested.[5]
Test yourself instead of rereading
In Roediger and Karpicke's experiments, students either reread a passage or recalled it. Five minutes later, rereading had done better; two days and a week later, recalling had, substantially. Rereading also left students more confident. A review of ten techniques rated practice testing among the most useful, and rereading and highlighting among the least.[6][7]
Fluency is not learning
Students who watched a short video of a fluent, confident lecturer predicted they would score higher than those who watched a halting one, and then scored the same. In Derek Muller's research, a clear physics video left misconceptions largely where they were, while a video that voiced the misconceptions and then corrected them roughly doubled scores, and took more effort to watch.[8][9][10]
Spread it out
Distributed practice, the same study spread over several sessions instead of massed into one, is the other technique the review rated most useful. Coming back to a module after a few days, and finding what has gone, is part of the method rather than a sign it has failed.[7]
Worked example: one module, start to finish
Module 04, on tests and sanitizers, as the specimen. No answer on the pages is hidden, so the covering is up to you: a sheet of paper, or scrolling no further than the step you are on. The same five moves work on any module here, and on any lecture of the Modern Robotics course.
Predict
Before opening module 04's worked example, write down which of its two tests catches the planted bug, and what exit code a program with signed overflow returns under UBSan's default settings. Commit to an answer; being wrong is fine.[5]
Come back in a few days
Cover the answers to the module's questions and answer them yourself, then read them. Whatever you missed is where the next session starts.[7]
Why each step is there
Each move maps onto one of the findings above.[1][2][3][4][5][6][7]
The five moves and the evidence behind them Move Finding Source Predict A failed attempt before study improves recall of what it asked Richland, Kornell and Kao (2009) Study and explain Worked examples beat unaided problems for novices, especially when self-explained Sweller and Cooper (1985); MIT Open Learning Less help The benefit of examples fades with expertise Renkl and Atkinson (2003); MIT Open Learning Recall Testing beats rereading after a delay Roediger and Karpicke (2006) Come back Spread practice is among the most useful techniques Dunlosky and colleagues (2013)
Reading a page well produces the feeling of knowing it. Only writing it from memory, a few days later, shows whether you do.
Best practice
Write down a prediction before running anything.
A number committed to in advance turns every result into feedback. Pretests that were mostly failed still improved later recall of what they asked.[5]
Explain each step of a worked example to yourself.
Worked examples help most when you work out why each step is there, rather than reading the steps in order.[1]
Drop the scaffolding as soon as you can.
Once a method is familiar, studying more worked examples of it adds little. Move to problems with less of the solution given.[1][2][4]
Test yourself; do not reread.
Recall beat rereading on tests two days and a week later; rereading won only at five minutes, and it raised confidence more.[6][7]
Distrust the glow after a good video.
A fluent explanation raises how much you think you learned more than how much you did. Close the video and reproduce the argument before deciding you have it.[8][9]
Spread sessions over days.
Distributed practice is one of the two techniques rated most useful in a review of ten.[7]
Questions
- Isn't struggling with a problem first better than being shown the answer?
- The two findings answer different questions. A short attempt before studying, even a failed one, improves later recall of what it asked about. The study itself, while the topic is new, goes better from a worked example than from long unaided problem solving. Together they suggest: guess, then study the example, then solve with less help. The question is not closed: a 2018 meta-analysis that could pool only twelve experimental studies on learning from failure, drawn from research on productive failure and failure-driven memory, reported a moderately positive effect.[1][5][11]
- Are lecture videos a waste of time, then?
- No, but watching one is not the same as being able to do what it shows. Treat a lecture as a worked example: stop it before each result and predict, and afterwards reproduce the derivation without it.[8][9]
- How do I know when to stop using worked examples?
- When you can do the next problem without looking back, not merely when the example feels familiar; familiarity is the fluency the page warns about. That is the expertise reversal: the same support that helped a beginner gets in the way.[1][2]
- Does rereading help at all?
- In Roediger and Karpicke's experiments it won only on a test five minutes later. After two days and after a week, recall won. The review of ten techniques rated rereading low.[6][7]
- How does this site use these ideas?
- It does not enforce them: every answer is printed. Each module has a worked example, most have results you can predict before reading on, and all have questions with answers you can cover. The faded part is yours to supply: a problem like the example, with the solution left out.
Watch
- listed
Khan Academy and the Effectiveness of Science Videos (opens in a new tab)[12]
Derek Muller · Veritasium (YouTube), 17 March 2011
Derek Muller on why a clear explanation can leave a misconception untouched.
Read
- read
Worked and Faded Examples (opens in a new tab)[1]
MIT Open Learning, research-based learning findings
Worked and faded examples in one page, with the references.
- read
Improving students' learning with effective learning techniques: Promising directions from cognitive and educational psychology (opens in a new tab)[7]
John Dunlosky, Katherine A. Rawson, Elizabeth J. Marsh, Mitchell J. Nathan, Daniel T. Willingham · Psychological Science in the Public Interest 14(1), 2013; summarised in an APS press release
The review's headline ratings, as summarised by the Association for Psychological Science.
- read
Test-enhanced learning: Taking memory tests improves long-term retention (opens in a new tab)[6]
Henry L. Roediger III, Jeffrey D. Karpicke · Psychological Science 17(3), 249–255 (2006). doi:10.1111/j.1467-9280.2006.01693.x
The testing effect, in the paper's own abstract.
- read
Helll-ooo! Watching Videos Does Not Necessarily Lead to Learning (opens in a new tab)[9]
Cathie Norris, Elliot Soloway · THE Journal (21st Century Learning), 6 May 2015
What happened when physics videos stated misconceptions instead of skipping them.
Sources
Numbered in order of first use on this page. read: checked against the claim. listed: exists and covers the topic, wording not checked. derived: worked out here and checked numerically.
- [1]read
Worked and Faded Examples (opens in a new tab)
MIT Open Learning, research-based learning findings
Novices learn more from studying step-by-step solutions than from solving problems, provided they self-explain them; experts benefit more from solving; support should be faded as expertise grows.
- [2]read
Worked-example effect (opens in a new tab)
Wikipedia
The worked-example effect, first described from a cognitive-load perspective by Sweller and Cooper (1985); worked examples lose effectiveness as expertise grows (expertise reversal), which fading addresses.
- [3]read
John Sweller, Graham A. Cooper · Cognition and Instruction 2(1), 59–89 (1985). doi:10.1207/s1532690xci0201_3
Five experiments in algebra. Experiment 1 compared levels of expertise; in Experiments 2–5, worked examples took less time to process than conventional problems, and later problems of the same structure were solved faster and with fewer errors. Abstract read from a reproduction of the paper’s record (synapsesocial.com); DOI 10.1207/s1532690xci0201_3.
- [4]listed
Alexander Renkl, Robert K. Atkinson · Educational Psychologist 38(1), 15–22 (2003)
Proposes fading, in which problem-solving elements are successively integrated into example study until learners solve problems on their own. The link is the research record of a 2016 reprint; its abstract was read, the 2003 article itself was not.
- [5]read
The pretesting effect: Do unsuccessful retrieval attempts enhance learning? (opens in a new tab)
Lindsey E. Richland, Nate Kornell, Liche Sean Kao · Journal of Experimental Psychology: Applied 15(3), 243–257 (2009). doi:10.1037/a0016496
Taking a test before studying, even one mostly failed (5–22 % correct), improved later recall of the pretested information more than spending the same time studying; untested information did not differ from the extended-study condition. The material was a factual text on vision.
- [6]read
Test-enhanced learning: Taking memory tests improves long-term retention (opens in a new tab)
Henry L. Roediger III, Jeffrey D. Karpicke · Psychological Science 17(3), 249–255 (2006). doi:10.1111/j.1467-9280.2006.01693.x
After 5 minutes, repeated studying beat repeated testing; after 2 days or 1 week, prior testing produced substantially better retention than studying, although studying raised confidence more.
- [7]read
John Dunlosky, Katherine A. Rawson, Elizabeth J. Marsh, Mitchell J. Nathan, Daniel T. Willingham · Psychological Science in the Public Interest 14(1), 2013; summarised in an APS press release
Of ten techniques reviewed, practice testing and distributed practice were rated high utility; summarisation, highlighting and rereading were among those rated low. (Read from the APS release.)
- [8]read
Shana K. Carpenter, Miko M. Wilford, Nate Kornell, Kellie M. Mullaney · Psychonomic Bulletin & Review (2013), doi:10.3758/s13423-013-0442-z; summarised by the BPS Research Digest
After a one-minute video, students who watched a fluent lecturer predicted they would do better on a test than those who watched a disfluent one; both did equally well. (Read from the BPS summary.)
- [9]read
Helll-ooo! Watching Videos Does Not Necessarily Lead to Learning (opens in a new tab)
Cathie Norris, Elliot Soloway · THE Journal (21st Century Learning), 6 May 2015
Reports Derek Muller’s PhD research. Students scored about 6 of 26 before instruction and “did abysmally, again” after a clear expository physics video, though they rated it clear and felt confident in their answers. After a video in which a student voiced misconceptions and a teacher corrected them, scores roughly doubled to almost 12 of 26, and students reported more mental effort.
- [10]listed
Derek A. Muller, J. Bewes, Manjula D. Sharma, Peter Reimann · Journal of Computer Assisted Learning 24(2), 144–155 (2008)
A peer-reviewed study from the same research programme on misconception videos. Citation from Muller’s publications page and the journal record; not read for this page.
- [11]read
Learning from failure: a meta-analysis of the empirical studies (opens in a new tab)
A. Darabi, T. L. Arrington, E. Sayilir · Educational Technology Research and Development 66, 1101–1118 (2018)
Of 187 publications, 62 were relevant, and only 12 used experimental designs and reported statistics suitable for meta-analysis, all from productive-failure and failure-driven-memory research; together they showed a moderately positive effect of learning from failure. (Abstract read.)
- [12]listed
Khan Academy and the Effectiveness of Science Videos (opens in a new tab)
Derek Muller · Veritasium (YouTube), 17 March 2011
Muller on why a clear science video can leave viewers’ misconceptions in place. Listed from the NUS Physics Society’s video archive, not watched for this page; Muller’s research on the same question is reported in THE Journal, 6 May 2015.