The Tutor Handbook Vol No.0202 | The Worked-Example-to-Problem Alternation Gate — How a Tutor Decides When the Learner Should Study a Worked Solution, Complete the Next Step, or Solve Independently Without Turning Examples Into Copying or Removing Guidance Too Quickly

The Tutor Handbook · Volume 0202 · Series ID THB-0202 The Tutor Handbook: Complete Series Index ## The learner can understand the example and still be unable to solve the next problem A tutor demonstrates a difficult Mathematics problem carefully. Every step is correct. The explanation is clear. The learner follows. They can even answer “why” questions about two of the steps. Then the tutor gives a new problem. The learner freezes. The easy diagnosis is that the example did not work. Another easy diagnosis is that the learner was not paying attention. Both may be wrong. Studying a complete worked solution and independently solving a problem are different learning activities. The first can reduce the amount of simultaneous search the learner must perform so attention can go to structure, relationships and procedure. The second requires the learner to select and execute the route without the completed solution carrying those decisions. A learner can benefit from both and still need a bridge between them. The Worked-Example-to-Problem Alternation Gate asks how a tutor decides when a learner should study a worked solution, complete part of one, solve a paired problem, compare two methods or work independently. Its purpose is to prevent two opposite errors: throwing novices into unguided problem solving before they have enough structure, and letting worked examples become a permanent copying environment that never asks the learner to generate the route. The gate is not “examples are good”. It is a sequencing decision about when the solution should be visible and when responsibility should move back to the learner. ## Quick answer Use worked examples when the learner needs a clear model of a procedure, representation or reasoning route and independent search would consume attention without producing much useful learning. Do not stop at viewing the example. Pair the example with a learner action. Ask the learner to explain a decision, complete a missing step, predict the next step, compare a minimally changed problem or solve a paired problem while the example remains available. Then reduce the amount of solution information as evidence shows the learner can carry more of the process. Move towards independent problems when the learner can identify the relevant structure, explain or reconstruct the key steps, and execute a near transfer without the example doing the decision-making for them. If independent performance collapses, diagnose why. The learner may need the example again, but not necessarily the entire example. Restore the smallest useful support: one decision cue, one earlier step, a partially worked solution or a comparison case. The alternation should respond to evidence. There is no universal rule such as “one example, then three problems”. Expertise, task complexity, prerequisite knowledge and the kind of decision being learned all matter. The goal is not to remove examples as quickly as possible. The goal is to make them increasingly unnecessary for the target performance. ## The ownership boundary Several Tutor Handbook owners sit nearby. The Dose asks how much help to give before support replaces learner thinking. The Fade owns the broader removal of prompts, models, routines and tutor control. The Interleaving Readiness Gate asks when to mix problem types so learners must choose a method rather than follow a topic label. The Example-Variation Gate asks what should change and what should remain invariant across examples to build abstraction and transfer. The present article owns a more specific transition: how solution information and learner problem solving alternate while a procedure or reasoning route is being learned. The question is not only how much help exists. It is whether the learner is currently studying a solution, generating a solution or working inside a deliberately incomplete solution—and what evidence justifies the next shift. ## Research and current guidance support worked examples, with an important sequencing boundary The What Works Clearinghouse practice guide Organizing Instruction and Study to Improve Student Learning, released in September 2007, gives a Moderate Evidence rating to the recommendation to interleave worked-example solutions with problem-solving exercises. The guide explicitly recommends alternating between reading worked solutions and trying to solve problems independently. The guide is older and broad. It does not establish one universal example-to-problem ratio for every age, subject or tutoring condition. Its useful contribution is the alternation principle: learners should not have to discover every route through unguided search, and example study should connect to independent problem solving. AERO’s Scaffold practice guide, published 29 November 2024 and updated 14 May 2026, describes worked examples as a scaffold and recommends gradually removing or fading support as proficiency grows. AERO’s Explicit instruction practice guide, last updated 8 September 2026, similarly describes using worked examples to demonstrate what students need to learn and replacing worked examples with more independent problem solving as expertise develops. EEF’s worked-example resources discuss examples, fading and alternation as ways of reducing unnecessary cognitive load and moving towards independent problem solving. These are practice resources rather than a licence to copy a single classroom sequence into every tutoring context. ## Worked examples are not answer sheets An answer sheet tells the learner what the answer is. A worked example makes the solution process available for study. The difference matters. A useful worked example makes visible the decisions, transformations or relationships that the learner needs to understand. It should not merely display a dense finished product. For an algebra equation, the example may show why the same operation is applied to both sides, not just the sequence of symbols. For a Science explanation, it may show how evidence is selected and linked causally rather than provide a paragraph to imitate. For English writing, it may annotate how an opening establishes situation, tension and direction instead of presenting “the perfect composition” as a mysterious finished object. The example should make the target structure easier to see. If the learner can only copy the surface, the example may create fluent imitation without route ownership. ## Decide what the learner is supposed to notice Before showing an example, answer one question. “What should become clearer because the solution is visible?” The answer might be a sequence. A decision rule. A representation. A relationship between two quantities. The purpose of a paragraph. The difference between evidence and explanation. The point at which one method becomes more efficient than another. If the tutor cannot state what the learner should notice, the example may simply reduce difficulty without creating transferable knowledge. This is especially important in one-to-three tuition. A polished example can hold everyone’s attention while revealing almost nothing about what each learner is learning from it. After the example, the tutor needs an individual receipt. ## The first learner action can happen before the example is complete A worked example does not have to be a monologue. The tutor can pause before a consequential step. “What must remain equal here?” “What would you do next?” “Which quantity belongs in the denominator?” “What evidence has the writer not yet connected?” The learner’s prediction turns passive viewing into a small generation task. The tutor must be careful not to make the prediction demand so hard that the example loses its scaffolding function. If the learner does not yet possess the necessary knowledge, repeated guessing adds noise. Use prediction where the learner has enough foundation to make a meaningful attempt. Then reveal the next step and compare. This creates a rhythm: observe, predict, inspect, continue. ## Example-problem pairs create a direct bridge One powerful tutoring structure is a worked example beside a minimally different problem. The example carries enough of the route that the learner can use it as a guide. The paired problem changes surface details while preserving the target structure. For instance, the tutor works through solving 2x + 5 = 17, explaining why the inverse operation preserves equality. The learner then solves 3x + 4 = 19 while the example remains visible. The purpose is not for the learner to replace 2 with 3 and 5 with 4 mechanically. The tutor can ask which parts are the same in role and which are different in value. The learner should identify the structure before executing. If they succeed only by mapping surface positions, the pair is too similar to prove much transfer. A later item should vary the form enough to require the learner to recognise the underlying relation. Example-problem pairs are bridges, not final receipts. ## Composite case: the learner who copies perfectly and cannot start alone The following case is fictional and constructed for teaching. Alicia is learning simultaneous equations by elimination. Her tutor provides four fully worked examples. Alicia follows each one accurately and can explain that one variable must be eliminated. She then completes two near-identical problems with the examples beside her. The tutor concludes that the method is secure. On a fresh problem the following week, Alicia writes nothing. A closer reconstruction shows that she learned a positional pattern: “multiply the second equation, then subtract”. She had not learned the decision rule for choosing what to multiply or whether subtraction was even the correct operation. The repair does not require another page of complete examples. The tutor places two short systems side by side and asks Alicia which variable is easiest to eliminate and why. No full calculation is required. Then one worked example is shown with the multiplication choice annotated. A second example is partially worked, stopping before the decision. Alicia completes the choice. Finally, she solves a fresh system with no example visible. The example sequence now targets the missing decision rather than replaying the visible procedure. The failure was not “too few examples”. It was an example that carried the very decision the learner needed to learn. ## Worked examples should expose choices, not hide them Many textbook examples look inevitable after the fact. The finished solution shows a clean route. It rarely shows the alternatives that were considered and rejected. Tutoring can make the choice visible. Why factor rather than expand? Why quote this evidence rather than another line? Why draw the force diagram before writing the equation? Why begin the summary with this idea? Why use a table rather than a graph here? A tutor can annotate the decision point without overwhelming the learner. “Two routes are possible. I am choosing this one because…” That sentence helps the learner build method selection rather than procedure imitation. Later, remove the explanation and ask the learner to make the choice. This is how a worked example can support Class 4 Route Designer functions rather than remain a Class 1 Explainer artefact. ## Partial examples change who owns the next step A fully worked example gives the learner the route. A partial example gives some of the route and leaves a defined part to the learner. The missing part can be chosen deliberately. Remove the final step if the learner needs to practise completion. Remove an intermediate decision if that is the bottleneck. Provide the setup but not the execution. Provide the calculation but not the interpretation. Provide the paragraph structure but not the evidence sentence. The tutor should know why the blank exists. Randomly deleting steps turns fading into a puzzle. Deliberately removing the step the learner is ready to carry turns it into a transfer of responsibility. AERO’s scaffold guidance describes gradual removal of support as proficiency grows. In tutoring, the smallest useful question is: which step can the learner now own without making the entire performance collapse? ## Backward fading can protect the start while transferring the finish For some procedures, it is useful to keep the early steps visible and remove later steps first. The learner sees the setup and carries the completion. On a later example, more of the route is removed. This can reduce the risk that the learner gets stuck at the first step and never practises the later reasoning. But backward fading is not a universal command. If the learner’s main problem is choosing the first move, preserving that move for too long can hide the bottleneck. In that case, the tutor may deliberately remove the beginning while keeping later execution support available. Fading direction should follow the target decision. The point is not to obey a pattern. It is to transfer the part of performance the learner is ready and needs to own. ## Do not alternate by a fixed ratio One example followed by one problem is a useful structure. It is not a law. A novice confronting a complex procedure may need several carefully varied examples before independent solving becomes productive. A learner with strong prerequisites may need only one model. A learner returning to a familiar method after a gap may need a thirty-second reminder and a fresh problem. A learner who can execute but cannot select methods may need almost no procedural examples and more mixed unlabeled problems. Use evidence to set the ratio. After the example, can the learner explain the critical relation? Can they predict a consequential step? Can they complete a paired problem with the example visible? Can they solve a minimally changed problem without it? Can they discriminate the method when another method is plausible? Each success transfers more responsibility. Each failure tells the tutor where support should return. ## The example can remain visible while independence grows Independence is not a binary condition in which the example must disappear immediately. A learner can solve a paired problem while the example remains visible and still do meaningful cognitive work, provided the example does not carry the target decision completely. For a new procedure, visibility can reduce memory load so attention can go to structure. The tutor can ask the learner to cover selected parts, explain differences or reconstruct a missing step. Then the example can move physically farther away, be turned face down, be available only after an initial attempt, or be replaced by a short principle card. The support condition should be recorded when it matters for interpretation. “Correct with full example visible” is not the same evidence as “correct after private first attempt with example available for checking”. Both can be useful stages. ## Compare correct examples when method selection matters Worked examples are often presented one at a time. Comparison can reveal structure more powerfully. Two correct solutions to the same problem may use different methods. Ask what each method makes easy, what knowledge it assumes and when one route becomes inefficient. Two examples from different task families may look similar on the surface. Ask which structural feature determines the method. Two examples using the same method may differ in representation. Ask what remained invariant. The Contrast-Case Gate owns the design of side-by-side comparisons. The present gate uses comparison specifically to strengthen the transition from studying solutions to selecting and producing solutions. The learner should eventually face a third case without the comparison doing the classification for them. ## Erroneous examples belong later or under controlled conditions A worked example can contain a deliberate error so the learner has to detect and repair it. This can be powerful when the learner already has enough correct knowledge to discriminate the error. It can also seed confusion when the misconception is not stable enough to reject. The Erroneous-Example Gate owns that decision. Inside an alternation sequence, a deliberate-error example can be used after correct modelling and some independent success to shift the learner from following a route to monitoring a route. For example, the learner studies two correct ratio solutions, solves one fresh problem, then examines a worked solution using the wrong base quantity. Their job is to identify the first consequential error and explain why it changes the result. This creates a new form of independence: the learner is not only generating steps but judging them. ## Self-explanation should be targeted, not ritualised “Explain every step” can become exhausting and artificial. Worked examples create good opportunities for explanation because the procedural burden is partly reduced. The tutor can ask why a particular step is legitimate, what relation is preserved, or why one representation was chosen. But explanation requires knowledge. The Self-Explanation Readiness Gate protects against asking “why?” before the learner has enough understanding to generate a useful explanation. Choose the step with the highest structural value. “Why did we multiply both sides?” “Why does this evidence support the claim?” “Why is this denominator the original quantity?” One good explanation can reveal more than commentary on every line. Then ask the learner to use the principle in a fresh problem. ## Composite case: the English model essay that becomes a copying trap This case is fictional. Beatrice is learning situational writing. Her tutor gives her a polished model email. It includes an effective subject focus, clear paragraphing, precise response to the prompt and appropriate tone. Beatrice highlights useful phrases. Her next email sounds remarkably similar to the model. The tutor is pleased until a new prompt changes the relationship and purpose. Beatrice still uses the old tone and paragraph structure. The model taught surface imitation more strongly than decision structure. The tutor redesigns the example sequence. First, they annotate the original model by function: opening establishes purpose and relationship; middle paragraphs answer required content points; closing gives the next action. Then they compare a second model written to a different audience. Beatrice identifies which features changed and which remained. Next, she receives a partial outline for a fresh task and writes only the opening and first content paragraph. Finally, she completes a new email independently. The worked example remains useful. Its role changes from language bank to decision model. This is why worked examples should reveal the architecture of performance, not merely present high-quality finished products. ## Science explanations need examples of causal structure, not memorisable wording A Science worked example can become dangerous when learners memorise phrasing without understanding the mechanism. Suppose a model answer explains condensation. If the learner copies “water vapour loses heat and condenses” into every question, they may reproduce correct language while failing to identify the source of the vapour, the condition causing cooling or the location where condensation occurs. Annotate the mechanism. Object or substance. Condition change. Relevant process. Outcome. Evidence from the question. Then vary the context. Ask the learner to reconstruct the causal chain before writing full prose. The worked example teaches a scientific relationship, not an examiner incantation. A later independent question should change the surface enough that copied wording is insufficient. ## Mathematics examples should not hide method choice behind chapter labels A worked example titled “Solving Quadratic Equations by Factorisation” has already selected the method. That can be appropriate while the learner is first learning the procedure. It becomes weak evidence of independent competence later. The alternation sequence should eventually remove the method label and mix plausible alternatives. Study the worked factorisation example. Solve a paired factorisation problem. Complete a partial example where the factor pair must be chosen. Solve an unlabeled quadratic where factorisation is suitable. Compare with a case where factorisation is awkward and another method is preferable. Now the learner moves from execution to selection. The Mixed Set owns the final discrimination problem. The worked-example gate owns the route that gets the learner there without forcing them to rediscover the procedure from scratch. ## Three-learner groups need individual accountability around examples A worked example is easy to teach to a small group because everyone can look at the same solution. That shared attention can hide unequal learning. One learner explains. One nods. One copies. Use short private actions inside the group sequence. Before the tutor reveals the next step, each learner writes a prediction. After the example, each completes one paired item independently. If one learner needs the example to remain visible, allow that support while the others attempt without it. Then bring the group back together for a comparison. The goal is not identical support at every moment. The goal is to keep each learner’s evidence visible enough that the tutor knows who can carry which part of the route. The Individual Accountability Gate remains the owner for group evidence. Worked examples should not create a group-shaped illusion of understanding. ## The example should change when the learner’s error changes Tutors often respond to failure by showing the same solution again, more slowly. That can help if the learner missed information. It can fail if the learner’s problem is different. If they cannot remember the sequence, a concise worked example may help. If they understand the sequence but choose the wrong method, compare examples across methods. If they execute correctly but cannot explain the relationship, annotate the underlying principle. If they make one recurring step error, use a partial example focused on that step. If they can follow examples but cannot start fresh problems, remove the opening step rather than replaying it. If they can solve near copies but fail changed representations, vary the example surface. The example is a tool. Its design should respond to the diagnosed bottleneck. ## Do not mistake fluent following for low cognitive load used well A learner may look calm and successful during example study because the difficult decisions have been removed. That is sometimes exactly why the example is useful. The danger is interpreting smoothness as mastery. The receipt comes after responsibility increases. Can the learner generate a step? Can they explain a structural reason? Can they solve the pair? Can they continue after a missing step? Can they start without the example? Can they choose the method in a mixed case? The transition should progressively test the cognition the example had been carrying. This is what turns reduced load into learning rather than dependency. ## Decide when to hide the example A simple protocol can help. First attempt with the example visible if the procedure is genuinely new. Second attempt with one or more steps hidden if the learner can explain the structure. Third attempt with the example available only after an initial independent start. Later fresh attempt with the example unavailable unless the learner reaches a defined help point. This is not a mandatory four-stage ladder. It illustrates a principle: visibility can become contingent rather than binary. The tutor should be able to say what evidence justified each reduction. If the learner asks to see the example immediately, the tutor can return part of the question: “Show me the first step you think belongs here. Then we’ll decide what support you need.” Help seeking remains legitimate. The learner is not punished for uncertainty. The support simply stops doing more work than necessary. ## Use delayed return to test whether the example created durable access Immediate success can be heavily supported by memory of the example. A delayed return changes the condition. Bring back one fresh problem after other material has intervened. Do not announce the exact method if method selection is part of the target. If the learner reconstructs the route, confidence in independent learning rises. If they remember fragments but not the organising decision, the tutor has useful evidence about what the example failed to establish. The delayed task does not need to be a high-stakes test. It can be one carefully chosen item. The purpose is to check whether the worked example produced knowledge the learner can retrieve and use rather than a short-lived trace of the demonstrated solution. ## Worked examples can be learner-generated later As expertise grows, ask the learner to create or annotate an example for someone else. This is not suitable at the beginning of every topic. It becomes useful when the learner can solve reliably enough that construction does not reinforce errors. The learner can write a clean solution, annotate the decision points, identify a tempting wrong route and create a paired problem. This requires them to model the structure explicitly. Then verify with a fresh independent item. A beautiful learner-generated example is still an artefact; it should not replace performance evidence. The activity can reveal whether the learner understands why the steps work or merely remembers what sequence usually appears. ## Parents: why “more examples” is not always the answer Parents sometimes ask for more model solutions when a learner is struggling. Sometimes that is exactly right. A learner cannot solve because the procedure was never clearly demonstrated. Another example with better annotation may remove unnecessary search and expose the structure. But more examples can also deepen dependency if the learner already understands the model and needs to practise generating the next move. The useful question is not “How many examples has my child seen?” It is “What part of the solution can my child now produce without the example carrying it?” A good tutor should be able to explain where the learner is on that transition. They may still need the model for one complex step. They may be ready for partial examples. They may be ready for mixed independent problems. They may need comparison because method selection is the real bottleneck. Examples are supports with a job, not proof of teaching volume. ## Failure modes The answer-sheet failure. A completed solution is shown without making the target structure or decision visible. The copy-success failure. Near-identical paired problems create fluent substitution that is mistaken for independent problem solving. The example-forever failure. The learner always has full solutions available, so the target decision is never transferred. The unguided-jump failure. The tutor removes all example support before the learner has enough structure to solve productively. The fixed-ratio superstition. One example–one problem or another ratio is applied regardless of expertise and task complexity. The hidden-choice failure. Worked examples show what to do but conceal why that method was selected. The random-fading failure. Steps are deleted arbitrarily rather than transferring a specific learner responsibility. The explanation-overload failure. The learner is required to explain every line even when only one structural decision matters. The model-essay imitation trap. High-quality writing examples become phrase banks that override purpose, audience and independent construction. The group-nod failure. One learner’s explanation stands in for the other learners’ understanding of the example. The immediate-only receipt. The learner solves directly after the model and the tutor never checks after a delay or changed condition. The more-of-the-same repair. Failure on an independent problem leads to replaying the identical complete example even though the bottleneck is method choice, representation or one specific step. ## Evidence boundaries The WWC Organizing Instruction and Study to Improve Student Learning, released September 2007, rates the recommendation to interleave worked-example solutions with problem-solving exercises as Moderate Evidence and explicitly recommends alternating reading worked solutions with trying problems independently. It is an older general practice guide, not evidence for a universal tutor sequence or fixed example-to-problem ratio. AERO’s Scaffold practice, published 29 November 2024 and updated 14 May 2026, describes worked examples, planned and contingent scaffolding, and gradual fading as proficiency grows. AERO’s Explicit instruction practice guide, last updated 8 September 2026, includes worked examples, modelling and movement towards independent problem solving. These are research-informed teaching guides, not private-tutoring trials. EEF resources on worked examples, fading and alternation provide classroom illustrations and connect examples with managing cognitive load, reasoning and independent problem solving. They are useful practice translations and should not be treated as proof that one exact sequence will be optimal for every learner. The decision architecture in this article therefore remains evidence-informed professional judgement. The tutor should use the smallest amount of solution information that makes productive learning possible, transfer responsibility as the learner becomes ready, and verify the target performance on fresh work. ## The end state A worked example has done its job when the learner no longer needs it to carry the target decision. That does not mean the learner never looks at examples again. Experts use examples too. They compare approaches, inspect elegant solutions and learn new techniques from models. The developmental question is different. Can the learner move from seeing the route to generating it? Can they explain the important structure rather than copy the visible sequence? Can they complete a missing step, solve a paired problem, begin without the model, choose the method when labels disappear and return after a delay with the knowledge still available? The tutor controls that transition by alternating example study and problem solving rather than choosing one permanently. Show enough to reveal the structure. Ask the learner to carry one more piece. Restore support when the failure is informative. Fade the part they can now own. Change the problem so imitation stops working. Return later and check again. That is the Worked-Example-to-Problem Alternation Gate. The solution should become a teacher for the learner, not a crutch that solves forever.