Teachers have examples everywhere.

Textbooks contain examples.

Worksheets contain examples.

Past-year papers contain examples.

The internet contains more examples than any learner could finish in a lifetime.

So the educational problem is no longer scarcity.

It is selection.

Training example selection is the deliberate choice of an example because of what it will make the learner notice, practise, compare, predict, explain or transfer next.

A good example is therefore not simply one that is correct.

It has a job.

It might reveal a structure.

Expose a misconception.

Reduce cognitive load.

Create a contrast.

Bridge from familiar to unfamiliar.

Prepare the learner for a new representation.

Or test whether an earlier repair survives transfer.

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Quick Read: Every Example Should Earn Its Place

Before using an example, ask:

• What should the learner notice?
• What prior knowledge does the example assume?
• Which features are essential?
• Which features are distracting?
• Is the example meant to teach, diagnose, compare or transfer?
• What should come immediately after it?
• What would make this example too easy or too hard for this learner?

One useful planning chain is:

Training Goal → Learner State → Example Job → Example Choice → Learner Response → Next Example

The example is not the centre of the lesson.

The learner’s changing state is.

Example Selection Begins With the Training Target

If Mira’s weakness is sign control, choose an example where sign handling is visible.

If Jonas’s weakness is evidence-bounded inference, choose a passage where the tempting overclaim is plausible enough to reveal the boundary.

If Nadia’s weakness is experimental reasoning, choose a design where the changed variable, control and evidence relationship can be inspected clearly.

The wrong example can bury the target under unrelated difficulty.

A long, linguistically dense Mathematics problem may be a poor first example for a learner whose immediate target is algebraic equivalence.

A Science investigation containing unfamiliar apparatus, technical vocabulary and graph interpretation may be a poor first example if the tutor wants to isolate one variable-control decision.

Good selection makes the intended mechanism visible.

The First Example Should Often Be Cleaner Than the Final Task

When learners first meet a new structure, they may benefit from a relatively clean example.

Clean does not mean childish.

It means the target relationship is not hidden under too much incidental complexity.

Suppose Mira is first learning the Chain Rule.

A useful early example is:

y = (3x + 1)⁵

The outer and inner functions are visible.

The derivative of the inner function is simple.

The example makes the nested structure easier to inspect.

Later examples can add trigonometric, exponential or composite complexity.

The learner first sees the structure, then carries it into harder forms.

Example Selection and Training Readiness

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

This is why Training Readiness matters.

A novice may need an example with:

• fewer interacting elements;
• familiar notation;
• clear structure;
• limited irrelevant variation;
• supporting explanation.

A more advanced learner may need:

• mixed cues;
• less obvious structure;
• near-neighbour categories;
• representation changes;
• greater transfer distance.

The example should move with the learner.

Example Selection and Worked Examples

Worked examples are especially sensitive to selection.

A worked solution can reduce unnecessary search for novices and make the route visible.

But a worked example should not simply be the hardest problem in the textbook with all answers filled in.

Choose one where the organisation of the method can be seen.

Then ask the learner to explain a critical step.

Then remove part of the support.

Then use a fresh problem.

The existing eduKateSengkang Worked Example State remains the deeper owner of worked-example progression. Here the training question is narrower: which example best reveals the route we need the learner to see now?

Example Selection for Contrast

Sometimes one example is not enough.

The educational job is to reveal a difference.

This is the territory of Training Contrast.

Choose two examples that are similar enough to align but different in the feature controlling the decision.

For Mathematics:

y = 3x

versus:

y = 3x + 2

The gradient remains similar.

The intercept changes the direct-proportion classification.

For English, choose two inference answers where one remains within evidence and one overclaims by one adjective.

For Science, compare two experimental designs differing in one control condition.

The pair is selected because the boundary becomes visible.

Example Selection for Nonexamples

A good nonexample should be close enough to tempt.

This is why Training Nonexamples emphasises near-misses rather than absurd errors.

If students commonly think every straight-line graph represents direct proportion, choose a line with a non-zero intercept.

If they commonly treat any plausible interpretation as inference, choose an answer that is believable but unsupported.

If they commonly confuse observation with explanation, choose a sentence that merely restates the observed change while sounding scientific.

The nonexample should be selected from the learner’s real misconception space.

Example Selection for Invariants

To reveal an invariant, select examples whose surfaces vary while one important relationship stays stable.

Recipe.

Map scale.

Currency conversion.

Similar figures.

The stories differ.

A multiplicative relationship can remain.

The example family teaches the learner to look through the surface.

See Training Invariants.

Example Selection for Perturbation

To train controlled variation, start from one example and change one feature deliberately.

This is Training Perturbation.

Example selection becomes experimental design.

Which feature should change?

Which should remain?

Should the correct response stay the same or change?

The examples are chosen to test the learner’s model.

Example Selection for Analogy

An analogy is also an example-selection problem.

Which familiar system preserves the relationship we want to teach?

A balance can help with equivalent operations.

A map can help with scientific models.

But a familiar example with poor structural alignment can mislead.

The 2026 Canadian Journal of Science, Mathematics and Technology Education article on mathematics analogies makes this point clearly: the quality of an analogy depends on the relational structure it supports, not merely familiarity.

The Example Should Often Come in a Sequence

One good example is useful.

A well-designed sequence is more powerful.

For a new mathematical structure:

Clean Example → Similar Example → Contrast Example → Near-Miss → Varied Example → Mixed Example → Transfer Example

Each example changes the training demand.

The first makes the rule visible.

The second stabilises it.

The contrast sharpens the boundary.

The near-miss prevents overgeneralisation.

The varied example reveals the invariant.

The mixed example restores choice.

The transfer example tests whether the learner can carry the structure farther.

The next article in this batch, Training Case Families, develops this sequence into a complete design system.

Do Not Select Only Beautiful Examples

Textbooks naturally favour elegant examples.

Integers factorise neatly.

Paragraphs have obvious topic sentences.

Experiments produce clean trends.

These are excellent for acquisition.

But learners also need examples where the structure is less polite.

A quadratic that does not factorise neatly.

An inference supported by several weak clues rather than one obvious sentence.

Science data with small variation instead of a perfect staircase.

The clean example teaches the idea.

The imperfect example teaches robustness.

Do Not Select Only Difficult Examples

World-class training is not a contest to find the hardest question.

A difficult example is useful only if the difficulty serves the target.

If the learner is practising inference, obscure vocabulary may add irrelevant load.

If the learner is practising algebraic structure, dense real-world wording may distract from the mechanism.

If the learner is practising experimental reasoning, unfamiliar technical apparatus may be premature.

Difficult is not a design objective.

Useful is.

Do Not Select Examples Only Because They Are Available

Convenience quietly controls many lessons.

The worksheet is already printed.

The question bank has twenty questions.

The next textbook page is there.

But training should ask whether the available example matches the current learner state.

If it does, use it.

If not, modify, skip, shorten or replace it.

The learner should not be forced to fit the worksheet simply because the worksheet exists.

Mira’s Example Sequence

Mira is learning to choose among quadratic methods.

The tutor chooses six examples deliberately.

• one clean factorisable quadratic;
• one nearly identical quadratic that does not factorise neatly;
• one where completing the square reveals the vertex efficiently;
• one where the quadratic formula is robust;
• one mixed problem where the method is not named;
• one unfamiliar context where Mira must recognise the quadratic structure herself.

Six examples.

Six different jobs.

That is training design.

Jonas’s Example Sequence

Jonas is learning evidence-bounded inference.

The tutor selects:

• one passage with obvious evidence;
• one with two weaker clues;
• one correct inference and one overclaim;
• one passage from a different genre;
• one inference where the strongest tempting answer is actually unsupported;
• one independent timed item.

The sequence moves from visibility to discrimination to transfer.

Nadia’s Example Sequence

Nadia is learning experimental reasoning.

The tutor chooses:

• a clean controlled experiment;
• a similar experiment with one control removed;
• a different apparatus preserving the same variable logic;
• a dataset whose result reverses expectation;
• a conclusion that overclaims;
• a new investigation Nadia must analyse independently.

Again, the examples form a training journey rather than a pile.

Example Selection and the Three-Student Room

Mira, Jonas and Nadia can work on the same broad idea while receiving different examples.

Mira may need a transfer example.

Jonas may need a clean contrast pair.

Nadia may need one near-miss exposing a misconception.

This is one advantage of the 3-pax small-group model: the tutor can select examples according to learner state while maintaining a shared lesson architecture.

The Parent Example Audit

• Why was this example chosen?
• Does it match the child’s current weak link?
• Is irrelevant difficulty hiding the target?
• Does the child see what feature matters?
• Are all examples too similar?
• Are all examples too difficult?
• Does the sequence eventually include variation and transfer?
• Is the learner doing pages because they are useful or because they are there?

The Tutor Example Audit

• What is the job of this example?
• What should it make visible?
• What prior knowledge does it require?
• What irrelevant complexity can I remove?
• What should the next example change?
• What misconception would a nonexample expose?
• Which invariant should survive later examples?
• What final example will test transfer?

The Deeper Idea: Examples Are Not Content; They Are Instruments

A telescope is valuable because of what it lets us see.

A good training example is similar.

It is chosen because it makes a relationship visible at the right moment.

Another example may expose a boundary.

Another may test robustness.

Another may deliberately remove support.

Another may reveal that the learner is ready to move on.

Once examples are treated as instruments rather than pages to finish, training becomes much more precise.

The best example is not the one that shows everything. It is the one that makes the next important thing learnable.

Research Foundations

This article draws on research into worked examples, structural alignment, comparison, variation and transfer. Useful current anchors include the 2025 Cognitive Science study on structural alignment and contrast, the 2026 article on structure-mapped analogies in mathematics, the 2026 Educational Psychology Review study on variability and transfer, and the eduKateSengkang Worked Example State, which owns the progression from clear model to independent transfer. Together they support a simple design principle: examples should be selected according to the cognitive job they perform, not simply because they are available.

Continue Through How Training Works

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