How teachers and learners can use worked examples to understand decisions instead of merely copying steps
By Arbab Naseebullah Kasi, Chief Executive Officer - CEO, Feel Worldwide Foundation Inc.
Comparing a completed model with work in progress makes room to discuss the decisions behind a task. Original conceptual painting.
Watching someone complete a task can feel reassuring. Every step seems to follow naturally. The calculation balances, the explanation makes sense, and the finished object looks exactly as it should. Then the learner faces a slightly different task and discovers that recognising a solution is easier than choosing how to begin.
One reason is that a demonstration can show the actions while leaving the decisions hidden. The experienced person knows what to notice, which information matters and why one step comes before another. A beginner sees the sequence but may not yet see the reasoning that holds it together.
A good worked example brings some of that reasoning into view. It shows a task, a route through it and the result. Used thoughtfully, it gives learners something to examine before they have to make every decision independently.
This can be useful in a mathematics lesson, an adult learning session or a practical explanation between colleagues. The aim is to help someone understand enough to adapt the approach when the next task is different.
Show the choice behind the step
Consider an illustrative lesson about scaling a simple craft pattern. An instructor doubles every measurement, draws the new outline and shows the finished shape. The learner can copy those actions. But what happens if the next pattern needs to be one and a half times its original size?
The important idea is the relationship between the original and the new measurements. If that relationship stays invisible, the learner may remember “double the numbers” rather than understand how scaling works.
An instructor could pause at the first measurement and explain why the same scale factor must apply to each length. The learner could then predict another measurement before the instructor continues. Now the example offers a decision to understand, not only a sequence to repeat.
This is a proposed teaching approach, not a report of a particular classroom experiment. It illustrates a practical question worth asking of any demonstration: what does the experienced person know that the learner cannot see?
Sometimes the missing information is small. Why use this tool? Why check that condition first? Why ignore one detail but pay attention to another? A short explanation at the decision point can be more useful than a long introduction that the learner cannot yet connect to the task.
Use an example as part of learning rather than the whole lesson
The Institute of Education Sciences published its practice guide Organizing Instruction and Study to Improve Student Learning in September 2007. It recommended alternating worked solutions with problems learners attempt themselves and rated the evidence for that recommendation as moderate. The guide also advised reducing the proportion of examples as learners develop expertise. This is research-based instructional guidance, particularly relevant to mathematics, science and technology, rather than a guarantee for every learning situation. IES practice guide
The practical value is in the connection between seeing and trying. An example can give a beginner a way into the task. An attempt can then reveal which parts of the reasoning are understood and which still need explanation.
Reading several completed solutions without using them can leave important gaps unnoticed. At the other extreme, assigning a difficult problem before a learner has any workable approach can produce a great deal of activity without much clarity.
A manageable lesson can move between the two. Examine a relevant example, attempt a related task, and return to the example with a more specific question. This need not become a rigid formula. The balance should respond to what the learner can actually do.
Keep the first example small enough to follow
A demonstration can become confusing when it tries to teach several unfamiliar things at once. A learner may be asked to understand a new concept, navigate a new tool and interpret unfamiliar vocabulary while the instructor moves steadily ahead.
Choose a first example with a clear purpose. If the lesson concerns scaling, keep decorative details out of the way until the relationship between measurements is understood. If it concerns writing a clear explanation, choose a short passage rather than an entire report.
State the starting conditions and what a successful result should accomplish. Keep the information needed for a step close to that step. Where possible, let learners see the original and the changed version together so they do not have to reconstruct the comparison from memory.
These are practical design suggestions. They should be adjusted to the learners, the materials and any accessibility needs. A well-designed handout is not helpful if someone cannot read it, and a spoken explanation may need a written version that can be revisited at a comfortable pace.
The first example should make the central idea easier to inspect. Additional complexity can come later, when there is a reason to introduce it.
Invite explanation without turning it into a performance
Asking learners to explain a step can reveal more than asking whether everything is clear. The question should help them think, rather than make them defend themselves in front of a group.
Try asking what the step accomplishes, what information it uses or what would change if one condition were different. A learner can answer in a short note, talk with a partner or point to the relevant part of a diagram. Speaking confidently is not the only way to show understanding.
MIT's Teaching + Learning Lab describes worked examples that invite students to explain the reasoning. It also documents a real teaching approach in a conversational social science research course: learners examined a well-constructed and a poorly constructed interview protocol, made annotations, and compared them with the instructor's explanations. This is an institutional example of teaching practice, not evidence that the same activity will produce a particular outcome elsewhere. MIT worked examples resource
The useful feature is that the learner has something specific to examine. “What makes this question useful?” is easier to work with than a broad invitation to “think critically.” The example provides a shared object of attention, and the explanation makes room for differences in reasoning.
If an answer is incomplete, use it to locate the next explanation. A learner who can describe what happened but not why may need the principle clarified. Someone who understands the principle but misreads the task may need help noticing the relevant information.
Let an error teach something precise
A carefully chosen error can make an important distinction visible. It can also confuse people if they are not told that the example contains a mistake or if the correction remains unclear.
In a November 2016 conference paper, Julie Booth, Kreshnik Begolli and Nicholas McCann reported a study involving 75 Algebra 1 students. Some textbook practice problems were replaced with correct, incorrect or incomplete worked examples and prompts for explanation. The authors reported improvements in procedural knowledge and the ability to anticipate errors. The study concerned an equation-solving unit; it does not establish that showing mistakes improves every subject or every learner's performance. Original research paper
For an everyday lesson, choose an error connected to the idea being taught. In the illustrative scaling activity, a deliberately incorrect version might enlarge the width while leaving the height unchanged. Ask what relationship has been lost, then show the corrected version and explain why it works.
Keep the mistake separate from any real learner's identity. There is no need to use someone's recent work as a public example without their agreement. An invented, clearly labelled example can make the same teaching point without embarrassment.
Finish with a clear account of the correct reasoning. Leaving a wrong example on the page without resolution may preserve the confusion rather than address it.
Change the next task in a meaningful way
After an example, a related task gives the learner a chance to make some decisions. The change should be large enough to require thought and small enough that the earlier explanation remains useful.
In the craft-pattern illustration, changing the scale factor would test whether the learner understands the relationship. Changing the material, the measuring tool and the shape all at once would make it harder to tell which part caused a difficulty.
Later, broader variations can be valuable. A learner might explain when scaling every dimension is appropriate and when it is not. A person learning to write an explanation might adapt it for a different audience rather than simply replace a few words.
Ask what stayed the same between the example and the new task. Then ask what had to change. Those questions can help distinguish a reusable idea from a detail that belonged only to the original situation.
Do not treat a single successful attempt as proof that the skill is secure everywhere. It is evidence about that attempt. More varied work, feedback and time may be needed before someone can use the approach comfortably in unfamiliar circumstances.
Remove support when it is no longer needed
Helpful guidance should leave room for growing independence. Once a learner can make a decision reliably, the next task may not need that decision explained in full again.
An instructor might leave one part of an example unfinished, ask the learner to choose the next step, or offer a complete problem with the example available only if needed. These are possible adjustments, not a fixed ladder everyone must climb at the same speed.
Watch for different kinds of readiness. One person may need more help with vocabulary but understand the underlying idea. Another may use the right terms while still relying on the original sequence. Give support where the difficulty actually lies.
Learners can make similar choices when studying alone. Find a trustworthy completed example, identify a decision you do not understand, and look for an explanation of that decision. Then try a related problem and compare the reasoning, not just the final answer. Where errors would have serious consequences, use qualified instruction and appropriate supervision rather than relying on a sample alone.
Make expertise easier to learn from
The most impressive demonstration is not always the most helpful one. Speed and fluency can hide the small judgements that a beginner needs to understand.
A thoughtful example slows down at the right places. It shows what matters, explains a choice and gives the learner a manageable opportunity to use the idea. It can include an error, a comparison or an unfinished step when those features serve a clear purpose.
For teachers, the challenge is to remember which decisions have become automatic. For learners, it is to look beyond the finished result and ask how the person knew what to do next.
The next time you explain a task, which decision could you make visible so that someone else can eventually make it without you?
