Teachers often ask:

What example should I use?

It sounds like a small question.

It is not.

The first example can determine what the learner notices.

A second example can either deepen the structure or accidentally contradict it.

A third can reveal the boundary.

A badly chosen example can create a misconception that later explanations struggle to remove.

Training example selection is the deliberate choice and ordering of examples so that each example makes the next important relationship easier to see, practise and transfer.

The example is not simply a container carrying content.

Its numbers, wording, representation, surface story, difficulty, ambiguity and relationship to neighbouring examples all affect what the learner can infer from it.

This means a strong teacher does not merely possess good examples.

A strong teacher sequences examples for a purpose.

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Quick Read: Every Example Has a Job

Before using an example, ask what job it performs.

• Entry example: make the new idea accessible.
• Clean example: show the structure with low irrelevant complexity.
• Contrast example: make one important difference visible.
• Nonexample: reveal where the rule stops.
• Variation example: change the surface while preserving the structure.
• Transfer example: test whether the learner can recognise the rule in unfamiliar form.
• Stress example: place the idea among competing demands.
• Diagnostic example: expose one suspected misconception or weak decision.

A useful sequence often looks like:

Clean Example → Aligned Variation → Contrast → Near-Miss → Mixed Case → Transfer

Not every lesson needs all six.

The sequence should stop when the training purpose has been achieved.

Why the First Example Matters

The first example becomes a candidate template.

If it contains unnecessary complexity, learners may treat irrelevant details as part of the concept.

If every first example of direct proportion involves money, a child may associate the topic with price rather than constant ratio.

If every inference example concerns emotions, Jonas may fail to recognise inference when the question concerns intention, attitude or cause.

If every Science experiment uses plants, Nadia may attach experimental reasoning to plant apparatus instead of the underlying logic of change, control and measurement.

The first example should therefore make the target structure unusually visible.

Example Selection Can Create Ambiguity

Recent research makes this point unusually clear.

A 2025 Contemporary Educational Psychology study examined how the specific problem chosen for a worked example can change the ambiguity of the solution learners see. Across several experiments, examples built from more ambiguous problems produced poorer learning, more misconceptions and greater overconfidence than less ambiguous examples.

This means teachers should not evaluate worked examples only by checking whether the final solution is correct.

Ask whether the example makes the intended relationship easy to reconstruct.

A technically correct example can still be instructionally poor.

The Clean Example

A clean example removes irrelevant difficulty so the learner can see the new relationship.

When Mira first learns the Chain Rule, a useful example is:

y = (3x + 1)⁵

The inner function is simple.

The outer structure is visible.

The derivative of the inner function produces a clear extra factor.

If the first example also contains fractions, multiple products and difficult algebraic simplification, Mira may fail for reasons unrelated to the Chain Rule.

Clean does not mean permanently easy.

It means the first representation foregrounds the intended structure.

The Second Example Should Not Merely Repeat the First

After one clean example, the next example should have a reason to exist.

It can hold the structure stable while varying the surface.

For the Chain Rule:

y = (2x − 5)⁻²

The exponent changes.

The inner expression changes.

The nested structure remains.

Ask Mira:

What changed, and what did not?

The second example now teaches invariance rather than merely adding volume.

The Third Example Can Reveal the Boundary

Once the learner has a candidate rule, give a case where the rule almost applies.

This connects to Training Nonexamples.

If Mira believes every straight line is direct proportion, show:

y = 3x + 2

It is linear.

It does not pass through the origin.

The near-miss reveals that “straight line” is not the defining condition.

One carefully selected nonexample may teach more than ten additional positive examples.

Example Selection and Structural Alignment

Examples become easier to compare when irrelevant differences are controlled.

This is why Training Contrast works best when cases are alignable enough for the critical difference to stand out.

A 2025 intervention study on example selection and Variation Theory found that contrastive example sets outperformed induction-only examples in the specific kindergarten Chinese-character task studied. The result should not be treated as a universal rule that “contrast always wins,” but it reinforces a useful design point: the relationships among examples matter, not only the quality of each example in isolation.

Example selection is therefore partly about building a set.

The first example creates a reference.

The next examples change what the learner can infer from that reference.

Mathematics: Choose Examples That Expose Structure Before Arithmetic

If method selection is the target, do not choose examples where difficult arithmetic dominates attention.

Suppose Mira is learning when factorisation is efficient.

Use:

x² − 9 = 0

Then:

x² + x − 1 = 0

The contrast is clean.

Now ask which structural feature makes immediate factorisation attractive in the first case.

Later, increase arithmetic and algebraic complexity after method choice is stable.

Mathematics: Choose Examples That Reveal Representation

A good Mathematics example can make a representation necessary rather than decorative.

If the target is graph interpretation, choose a problem where the graph reveals something difficult to see algebraically.

If the target is algebraic modelling, choose a story where the relationship is compactly expressed by an equation.

Example selection should show the learner why a representation earns its place.

English: Choose Passages That Isolate the Reading Decision

Jonas is weak at evidence-bounded inference.

The first training passage should not contain extremely difficult vocabulary, unusual syntax and an obscure context all at once.

Otherwise a wrong answer becomes difficult to interpret.

Choose a passage where the evidence is linguistically accessible but the inference still requires genuine reasoning.

Then progressively vary:

• genre;
• distance between evidence and question;
• strength of plausible distractors;
• vocabulary difficulty;
• amount of implicit information.

The example sequence grows with readiness.

English: Choose Writing Examples That Expose Function

Two polished model essays may be less useful than one carefully selected paragraph pair.

One paragraph develops an idea.

One repeats it.

Keep vocabulary and topic similar.

Now the difference in architecture becomes visible.

Ask Jonas to explain what each sentence contributes.

The example was chosen not because it is beautiful.

It was chosen because it reveals the training target.

Science: Choose Examples That Separate Content From Evidence

Nadia knows the Science concept but struggles with experimental reasoning.

A useful first example uses familiar content so the experiment structure can become the focus.

Once Nadia can identify what changes, what is measured and what is controlled, the apparatus can become more unfamiliar.

Now the training tests whether experimental logic transfers beyond familiar content.

The example sequence should progressively remove protection without changing every dimension at once.

Example Selection and Training Readiness

The same example can be excellent for one learner and poor for another.

A novice may need:

• clean structure;
• familiar vocabulary;
• few interacting elements;
• clear correspondence with the worked explanation.

A more advanced learner may need:

• surface variation;
• competing methods;
• plausible distractors;
• unfamiliar representation;
• reduced prompting.

Example quality is therefore conditional on Training Readiness.

Example Selection and Training Granularity

If the learning target is one method-selection decision, a two-page problem may be too large.

If the target is full-paper navigation, a one-line item is too small.

Choose the example at the granularity of the capability.

See Training Granularity.

Example Selection and Training Perturbation

Once a good base example exists, Training Perturbation can generate the next examples systematically.

Change one coefficient.

Change one connective.

Change one experimental control.

Change one contextual feature.

Now the example family grows by design rather than by random collection.

Example Selection and Training Generation

Eventually the learner should help choose or create examples.

Ask Mira:

Create the next example that would make this rule harder to apply without changing the rule itself.

Ask Jonas to produce a passage where the inference is less obvious but still evidence-bounded.

Ask Nadia to modify the apparatus while preserving the same experimental structure.

This connects to Training Generation.

A learner who can create a good example often understands which features matter.

Failure Mode: Interesting Example, Wrong Teaching Job

The example is memorable.

It contains a funny story or unusual numbers.

But the learner spends all available attention understanding the story instead of the relationship.

Interesting is not automatically instructive.

The example must earn its complexity.

Failure Mode: Every Example Is Too Clean

Clean examples are useful during acquisition.

If they never become messier, the learner never trains selection under realistic conditions.

Eventually add irrelevant details.

Change representation.

Include plausible alternatives.

Restore authentic timing.

The example sequence should progress with the learner.

Failure Mode: Every Example Is Different in Every Way

The learner cannot tell what is invariant.

Reduce variation.

Align cases.

Control one or two features.

Then widen later.

Failure Mode: Example Selection Follows the Textbook Rather Than the Learner

The next page contains a difficult example.

The learner is not ready for that exact difficulty.

The page order is not sacred.

Select the example that exposes the next trainable structure.

Then return to the textbook sequence once the learner can carry it.

Mira’s Example Sequence

Mira is learning direct proportion.

Example 1: y = 3x.

Clean structure.

Example 2: y = 5x.

Coefficient changes, structure remains.

Example 3: y = 3x + 2.

Near-miss; intercept breaks direct proportion.

Example 4: map scale.

Context transfer.

Example 5: mixed set containing direct, inverse and unrelated increasing relationships.

Discrimination.

Five examples.

Five different jobs.

Jonas’s Example Sequence

Jonas is training inference.

• short accessible passage with obvious evidence;
• same question type with evidence farther apart;
• contrast pair: defensible vs overclaimed inference;
• new genre with the same evidence rule;
• mixed comprehension where inference is not labelled.

The sequence moves from understanding toward independent classification.

Nadia’s Example Sequence

Nadia is training experimental reasoning.

• familiar plant setup with one obvious changed variable;
• similar setup with a different measured outcome;
• flawed setup where two variables change;
• unfamiliar heat experiment with the same logic;
• mixed Science paper where the experimental structure is embedded among other tasks.

Again, the examples form a path.

The Parent Example-Selection Audit

• Does the first example make the target structure visible?
• Does the next example teach something new rather than merely repeat?
• Are important nonexamples included?
• Does variation expand gradually?
• Are examples matched to the child’s readiness?
• Does the learner eventually meet mixed and unfamiliar cases?
• Can the child explain why one example was chosen after another?

The Tutor Example-Selection Audit

• What is this example supposed to reveal?
• What irrelevant difficulty does it contain?
• Could the worked solution be ambiguous?
• What feature should remain invariant in the next example?
• What feature should change?
• Which near-miss would expose the boundary?
• What later example will test transfer?

The Deeper Idea: Examples Are a Language for Showing Structure

A teacher can explain a rule in words.

Examples show what the rule does.

A carefully chosen sequence can show:

• what belongs;
• what almost belongs;
• what changes without changing the rule;
• what change breaks the rule;
• how the rule survives in another context.

That is more than demonstration.

It is curriculum at the scale of examples.

The right example is not simply easy, interesting or correct. It is the example that makes the next important structure visible to this learner now.

Research Foundations

Useful current sources include the 2025 Contemporary Educational Psychology study on worked-example problem selection and ambiguity, the 2025 intervention study comparing contrastive and induction-focused example selection, the 2025 systematic review of erroneous and contrasting erroneous examples, and the 2025 Instructional Science study of learner-generated and provided illustrative examples. Together they support a careful conclusion: examples should be selected for the learning relationship they make visible, with ambiguity, prior knowledge, prompts, feedback and later transfer all considered.

Continue Through How Training Works

Read this alongside Training Contrast, Training Nonexamples, Training Invariants, Training Perturbation, Training Generation and Training Readiness.

Next: How Training Works | Training Case Families — Build Examples, Near-Misses, Variations and Transfer as One System.