Definitions are abstract by design — that’s what makes them apply to many situations at once. It’s also what makes them slippery to remember and even harder to recognize in a new problem. “Diminishing returns,” “opportunity cost,” “a function is injective if it never maps two inputs to the same output” — each of these is precise, and each of them is close to meaningless until you attach it to something specific. The fix is simple to state and consistently skipped: for every abstract concept you study, generate at least one concrete example yourself.

Why abstract definitions don’t stick on their own

A definition has almost no retrieval cues attached to it. If you’ve only ever encountered “opportunity cost” as a sentence in a textbook, the only path back to that sentence in your memory is… the sentence itself. If you forget a few words of it, there’s nothing else to reconstruct it from.

A concrete example changes that. “Opportunity cost is what you give up when you choose one option over another — if you spend Saturday studying instead of working a paid shift, the opportunity cost of studying is the money you didn’t earn.” Now the concept is attached to a scenario you can picture, which gives you multiple ways back to the idea even if you’ve forgotten the textbook phrasing entirely.

This is part of why dual coding works too — a concrete example often comes with an implicit picture (a calendar, a paycheck, a trade-off), even without drawing anything. This pattern is sometimes called the generation effect: information you produce yourself is retained better than information you simply read.

Generate your own — don’t just read the textbook’s

Textbooks provide examples, and reading them is better than nothing. But there’s a meaningful difference between reading an example someone else constructed and generating one yourself. Producing your own example requires you to retrieve the definition, hold it in mind, and search your own experience for something that fits — which is itself a form of active recall, layered on top of the concrete-example benefit.

A useful habit: after reading a definition, cover it and ask “what’s a situation — ideally from my own life or something I already know about — where this applies?” If you can’t think of one, that’s often a sign the definition hasn’t fully landed yet, which is useful information on its own.

Using examples across subjects

  • Math/SAT: For a formula like the slope of a line, don’t just memorize “rise over run” — pick two actual points, plot them (even roughly), and calculate the slope yourself. When a word problem later describes a real-world rate, you have a concrete scenario to map it onto rather than a bare formula.
  • IELTS grammar: For a rule like “use the present perfect for an action that started in the past and continues now,” generate your own sentence about your own life: “I have lived in this city for three years.” A self-generated example tied to something true about you is far stickier than a textbook sentence about a stranger.
  • Science concepts: For “negative feedback loop,” find an example from something you already understand well — a thermostat, your own body regulating temperature — before trying to apply the term to a new system you’re learning about.

The common mistake: studying examples passively

The failure mode looks like progress: you read three worked examples in a row, nodding along, each one making sense as you read it. But reading someone else’s example and generating your own test different things. You can follow a worked example without being able to produce a new one — which is exactly the gap that shows up on an exam, where you’re given a new problem with no example attached.

If you’ve just read a worked example, the next step isn’t to read another one — it’s to close the book and try to construct a new example of your own, even a rough one.

FAQ

How many examples does a concept need? One self-generated example is far better than zero. If the concept is one you’ll be tested on repeatedly (a formula, a recurring grammar rule), two or three varied examples — covering slightly different situations — help you see the boundaries of when the concept applies and when it doesn’t.

What if I genuinely can’t think of an example? That’s useful information: it usually means the definition hasn’t connected to anything you already know yet. Go back to the source, but instead of re-reading the definition, look specifically for how the source itself uses the concept — then try to generate a second, different example based on that.

How does this relate to dual coding? Concrete examples and dual coding both work by giving an abstract idea something tangible to attach to — one through a scenario, the other through a visual. Combining them (sketching your own example) often works better than either alone.