Direct Answer: Concrete examples work when a learner uses a specific, inspectable case to make an abstract relationship easier to understand—and then connects that case explicitly back to the underlying concept. The example should reveal the structure, not become the structure. One example can make an idea memorable while accidentally teaching the learner that the idea belongs only to that situation. Strong learning therefore uses multiple examples with different surface features, asks what remains the same across them, contrasts examples with near-misses, and gradually reduces dependence on the original concrete supports. The goal is not to make everything concrete forever. It is to use the concrete case as an entry point into a concept that can later travel.
HOW LEARNING WORKS · CONCRETE EXAMPLES
The example opens the door. The concept has to walk out of it.
A good example makes an idea easier to enter without trapping the learner inside one story, one picture or one familiar set of numbers.
The simplest definition
A concrete example is a specific case used to make an abstract concept, rule or relationship easier to inspect.
“Proportionality” is abstract. A recipe that doubles ingredients is concrete. “Opportunity cost” is abstract. Choosing between two uses of the same hour is concrete. “Reliable evidence” is abstract. Comparing two claims about the same event with different source quality is concrete.
The example becomes educational when the learner can explain why it is an example of the larger concept.
The concrete-example mechanism
ABSTRACT IDEA → SPECIFIC CASE → RELATIONSHIP MADE VISIBLE → EXPLICIT LINK TO CONCEPT → SECOND DIFFERENT CASE → COMPARE → IDENTIFY INVARIANT → ADD NON-EXAMPLE → FADE SURFACE SUPPORT → FRESH APPLICATION
The important transition is from “I remember the example” to “I understand the relationship the example instantiates.”
1. Abstract ideas can be hard to enter because they remove the very details novices use to think
An expert sees “ratio” and activates a network of relationships. A novice sees a word.
Concrete examples supply objects, quantities, actions and outcomes that can be inspected. The learner has something to point to. “Two cups of flour for one cup of milk” makes the relation visible in a way that the symbol 2:1 may not initially do.
This is why concrete examples can provide an efficient entry point into unfamiliar ideas.
2. The example must carry the target relationship
A vivid example is not necessarily a useful one.
If the learner remembers the story but cannot identify the concept, the example has dominated the learning target. This can happen when the surface is unusually funny, dramatic, colourful or personally memorable.
Before choosing an example, finish the sentence: “This example is useful because it makes this relationship inspectable.”
3. One example is rarely enough
One case cannot tell the learner which features are essential and which are incidental.
If every percentage example involves shopping discounts, the learner may quietly attach the concept to prices. If every metaphor example is poetic, the learner may miss metaphor in ordinary prose. If every force diagram has the same orientation, rotated versions can feel like a new topic.
The Learning Scientists explicitly recommend multiple concrete examples with varied surface features so learners can connect them to the same underlying idea. Their Concrete Examples resource is a useful public introduction.
4. Variation teaches what can change
Use two examples that share the same deep relation but look different.
For proportionality, compare a recipe, a map scale and a machine production rate. For inference, compare a narrative passage and a factual report. For conservation, compare mass in a physical transformation and quantity in an algebraic balance.
Ask: What changed? What did not? Which relation survived?
5. Concrete examples should be linked explicitly to the abstraction
Teachers often believe the link is obvious because they already know the concept.
It may not be obvious to the learner. The candy used in a reinforcement example, the blocks used in place value, or the water analogy used for a circuit can become the memorable object while the intended relation remains weak.
Say the mapping directly: “This quantity corresponds to the whole. This change corresponds to the ratio. This feature is irrelevant. This is why the example belongs.”
6. Concrete and abstract representations should be connected, not treated as competing camps
The U.S. Institute of Education Sciences recommends connecting and integrating abstract and concrete representations of the same concept. Its practice guide rates this recommendation as supported by moderate evidence and explicitly warns that knowledge learned only in one form can remain inflexible. Organizing Instruction and Study to Improve Student Learning.
The practical sequence is not “concrete is for weak students, abstract is for strong students.” It is “use each representation to expose something the other can hide, then connect them.”
7. A concrete example can carry irrelevant structure
Physical objects have colour, size, texture and history. Stories have characters, motives and settings. Real-life contexts contain more detail than the concept requires.
Novices can focus on these features because they are visible and meaningful. The teacher must therefore help separate the concept-bearing features from the background.
Ask: “If I changed the colour, name, setting or orientation, would the principle change?” If not, the feature should not control classification.
8. Too much realism can make the target harder to see
A realistic bus timetable may contain dozens of routes, times and exceptions. If the learning target is simply reading elapsed time, realism can add unnecessary search.
A simplified example can preserve the important relationship while removing unrelated demands. Concrete does not have to mean maximally realistic.
Use the smallest world that still contains the idea.
9. Near-misses make the example diagnostic
After showing a clear example, show something that looks similar but does not belong.
If a student understands proportion only through “both numbers got bigger,” a near-miss with unequal scaling reveals the weakness. If a student identifies any comparison phrase as a simile, a sentence without a figurative comparison reveals the boundary.
Examples show inclusion. Near-misses show the edge.
10. Concreteness fading is a bridge, not a ritual
One useful approach is to move gradually from a highly concrete representation towards a more symbolic one while preserving the same relation.
Blocks may become drawings. Drawings may become bar models. Bar models may become equations. The learner should be able to explain what each transition preserves.
Do not fade because a fixed number of lessons has passed. Fade when the learner can use the underlying relationship with less support.
11. The abstract form should become useful, not merely visible
A learner can copy x, y and a formula without seeing why the symbols are more general.
Ask the learner to map each symbol back to two different concrete examples. Then ask what the formula captures that both examples share.
The abstraction becomes useful when it compresses several cases into one relationship the learner can manipulate and transfer.
12. Mathematics: concrete examples should make the quantity relationship explicit
Suppose a learner is studying fractions. A pizza is concrete, but it can mislead if slices are unequal or if the learner treats “three shaded pieces” as three quarters regardless of the whole.
Use multiple wholes, orientations and partitions. Keep the defining relationship constant: the whole is partitioned into equal parts, and the numerator counts selected parts of that whole.
Then move into diagrams and symbolic notation while asking what each number refers to.
13. Science: concrete examples should not be mistaken for proof
An everyday example can make a scientific idea intuitive.
But one familiar event is not automatically evidence sufficient for a general scientific claim. A puddle disappearing can introduce evaporation. It does not, by itself, establish every factor affecting evaporation rate.
Use the example to enter the mechanism, then return to controlled evidence and scientific language.
14. English: examples should reveal language in use
A vocabulary definition becomes stronger when paired with several sentences showing collocation, register and contrast.
A writing technique becomes stronger when learners compare two paragraphs and identify what the technique is doing for the reader.
The example should expose function, not simply provide a sentence to memorise.
15. Learner-generated examples are powerful tests
After instruction, ask the learner to create a new valid example.
This reveals the boundary they believe the concept has. An inaccurate example is valuable evidence because it exposes overgeneralisation or undergeneralisation.
Then ask for a non-example and an explanation of the difference.
16. Examples should change as the learner changes
Early examples can reduce entry difficulty. Later examples should increase discrimination.
A novice may need a clear prototypical case. A developing learner needs variation. An advanced learner needs edge cases, misleading surfaces and examples that require choosing among competing models.
Example design should therefore evolve with expertise.
17. The most memorable example can become the biggest trap
When learners remember “the candy experiment,” “the pizza question” or “the train problem,” ask what concept the example was supposed to represent.
If the answer is vague, reconnect the example to the abstraction. Then use a second example from a different domain to break the surface association.
Memory for the episode is useful only if it retrieves the right relationship.
18. The final receipt is a concept that survives a new example
Remove the original example.
Give a new case with changed surface details. Ask whether it belongs, why, and which feature controls the decision.
If the learner can recognise the structure without relying on the original story, the concrete example has become a bridge rather than a cage.
What concrete examples are not
- A vivid example is not automatically a useful example.
- One example rarely establishes the whole concept boundary.
- Concrete and abstract representations are not opposing camps.
- Realism can add irrelevant complexity.
- The example must be explicitly connected to the concept.
- Concrete supports should fade where independent abstract use matters.
- An everyday example is not automatically scientific evidence.
A concrete-example diagnostic map
| What adults see | Possible issue | Useful next move |
|---|---|---|
| Remembers the story but not the concept | Surface dominates structure | State the mapping explicitly and add a different example |
| Only succeeds in one familiar context | Undergeneralisation | Vary context while preserving the relation |
| Applies the idea too broadly | Boundary too loose | Add near-misses and non-examples |
| Manipulates symbols without meaning | Abstraction detached from concrete referent | Map symbols back to several cases |
| Gets lost in realistic details | Example overloaded | Simplify to the smallest useful concrete world |
| Cannot invent a new example | Concept not operational | Generate example, non-example and justification |
A practical concrete-example cycle
- Name the abstract idea.
- Choose a simple concrete example.
- State exactly how the example maps to the concept.
- Change irrelevant surface details.
- Add a second example from another context.
- Compare the two.
- Identify the invariant relationship.
- Add a near-miss.
- Move towards a more abstract representation.
- Test a fresh case without the original support.
For parents
- “What idea is this example supposed to show?”
- “Which part of the story does not matter?”
- “Can you give me a completely different example of the same concept?”
- “Can you give me something that looks similar but is not an example?”
- “Can you explain the idea without using the original story now?”
For students
- Use examples to understand, not only to remember.
- Collect examples with different surfaces.
- Write why each example belongs.
- Add near-misses.
- Move between concrete and abstract forms.
- Test yourself on a new example without labels.
How do we know concrete examples are working?
- The learner can explain the mapping to the abstract concept.
- Different-looking examples are recognised as members of the same class.
- Surface features control answers less often.
- Near-misses are rejected for the right reason.
- Abstract representations become meaningful rather than merely symbolic.
- New examples can be generated independently.
- The original example can disappear without the concept disappearing.
The complete concrete-example chain
ABSTRACT IDEA → CONCRETE CASE → EXPLICIT MAP → VARY → COMPARE → IDENTIFY INVARIANT → CONTRAST → FADE → TRANSFER
Research and evidence boundary
The Learning Scientists include concrete examples among six widely taught evidence-informed study strategies and stress the importance of multiple examples and explicit links to the abstract idea. The U.S. Institute of Education Sciences recommends connecting concrete and abstract representations and rates the recommendation as supported by moderate evidence. Research does not justify a universal rule that concrete or abstract instruction is always superior; example design, prior knowledge and transfer demands matter. The Learning Scientists: Concrete Examples; IES Practice Guide.
