The power of examples

What are some things educators should know about demonstrations?

Most of us have probably heard the phrase, “teach by example.” Teaching by example often means that one models something, behaves in a certain way. “She is a great example of calm demeanor,” or “isn’t he a good example of scholar-athlete?”

Another meaning of “example” in teaching is more akin to instance or demonstration. A teacher might point to an ‘m’ and say, “the sound for this letter is ‘mmm.’” Or the teacher may project an image of a chemical structure onto the screen at the front of the room and say, “That is a carbon chain.”

Because they are very common in teaching, understanding examples is foundational to understanding instruction. This post provides a couple of (well, uhm…) examples of examples for teaching.

An example

Suppose that I hold up a nearly cylindrical object that has a point at one end and a small rubber part at the opposite end. I hold this object, which is about 10 cm long between my thumb and fore fingers, wiggling it slightly. And I tell you, "this is Tove."

I have just given you a demonstration or an example of a concept. The label for the concept is, "Tove."¹

An example of the concept “Tove.” Photo © 2025 by John Wills Lloyd, Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)

Let's contemplate the example of ‘tove.’ Given the demonstration, illustrated in the forgoing image, what are some possible interpretations that learners might derive from the demonstration? Well I’d conservatively estimate there are a few million possible legitimate interpretations. “Tove” might mean

• pencil,

• something held in the fingers,

• something held at an angle,

• something that is blue,

• something that has multiple parts,

• something that the teacher is showing me,

• one,

• cylindrical,

• something that has parts,

• something touched by three digits,

• ….

This can be a fun game! See how many more legitimate meanings you can give to “tove.”²

This little game makes clear that if teachers want to communicate ideas (Concepts!), showing learners one example simply is not going to do the job. A single example admits to uncounted possible interpretations.

Multiple exemplars

Okay, so let’s use additional examples! That’s what we should do to teach effectively. Let’s see how that works.

For this example, instead of ‘tove,’ we’ll use ‘blarp.’ (The video is fewer than 90 seconds long.)

So, there you go! A teaching demonstration with multiple examples.

Uhm, how did you do on the test items? The proof is in the pudding, right?

Probably nearly everyone answered “yes” for the first item. However, the answers on the second and third items are unlikely to have been clear. There isn’t really any telling whether the items are or are not blarp. All of the examples of blarp on the previous slide were in the same orientation³ and were the same color-shading. So, a learner (you!) didn’t get sufficient evidence to make a smart answer (Carnine, 1980a, 1980b; Granzin & Carnine, 1982).⁴

Not examples

To teach about a concept, teachers need more than a single example and more than a collection of similar examples. Some magic happens when teachers use not examples.⁵ A not example shows what a concept is not.

The teacher is holding an example of ‘tove’ in a different spatial orientation and it is still labeled “tove.” “Aha, the learner might think.⁶ It’s ‘tove’ when it’s up and down, too! Oh, and front and back, too. And close or far.” The learner is right! She is interpreting the additional examples the teacher shows as eliminating some of the few million possible interpretations of “tove.” So, the teacher only needs a few-million (minus-70-11) more examples to help the learner eliminate all alternative explanations. Uhmmm....

But, when the teacher throws in a not example, she helps the learners considerably:

1. She holds the blue pencil and say’s “It’s tove,”

2. Then tosses it up in the air and, pointing to it in mid-flight, says, “It’s not tove,”

3. And then catches it in her hand and says, “It’s tove.”

That not example is powerful! (Go back to the earlier bulleted list and see what the not example ruled out.)

Still, just as a single positive example is insufficient to teach, so is a single not example. For learners to get concepts, they need to have demonstrations that contain a carefully curated set of examples and not examples. And “carefully curated” means that the instructional designer must exercise care in selecting and sequencing examples and not-examples in ways consistent with research about those very matters.

That is to say, Dear Readers. that I am not making up this poop.

Research basis

You won’t find the research in the popular discussions of neuroscience or neuropsychology. You don’t need to know about brains structures or blood flow. Those things don’t tell you how to teach. In fact, teaching causes the blood flow that the neuroscientists report.⁷

And you won’t find the evidence about the importance of instructional design in the popular discussions about “direct instruction,” because those folks didn’t examine teaching at a sufficiently fine-grained level to see it. They focused on much broader matters (ask lots of questions, for example) and even on the “cognitive” level of those questions (“lower-order” fact based questions vs. “higher-order” open-ended questions). They (e.g., Rosenshine & Mesiter, 1995) did not, however, examine the actual questions (meaning the selection of examples and not examples.⁸

There’ve been mucho studies about selection and sequencing of examples in instruction. I’ve just grabbed a few and dropped them into the bibliography for this article. Readers will surely recognize names in the list. It’s not exhaustive, but it will give one a start.

If one want a serious education on the topic of design of instruction, of course, one should read Theory of Instruction by Zig Engelmann and Doug Carnine (1982).

So, all you folks who advocate roll-your-own teaching: I recommend doing some homework (and I mean serious study) about examples in teaching. It’ll help you to design and execute more effective lessons, I’m pretty dang sure.

Why does this matter?

Oh, yes. those Dear Readers who are saying, “This is pretty esoteric poop, John,” are right. This topic is way down deep in the proverbial weeds. But it matters for our kids. If our kids get shoddy instruction, they are likely to latch onto faulty understandings. If the Tier-1 instruction is ill-developed, it’s our kids who are at risk of getting hurt. And if teachers of our kids at other levels (Tier 2 or 3) are using instructional practices that are not carefully controlled, I fear that our kids will, once again, be left in a cloud of dust.

We really need to ensure that our kids get the very best instruction that they can get. If they still have trouble, then we can look for new and groovy magic.

Coda: One more applied example

Jeff Sprague and Rob Horner examined the effects of using different examples in teaching adolescents to use vending machines. They compared how rapidly the students learned to use machines under three different conditions: “(a) a single vending machine, (b) three similar machines, or (c) three machines that sampled the range of stimulus and response variation.” They found that the students performed best on generalization probes when they received training on varied training machines.

Bibliography

Carnine, D. (1980a). Relationships between stimulus variation and the formation of misconceptions. Journal of Educational Research, 74(2), 106-110.

Carnine, D. (1980b). Three procedures for presenting minimally different positive and negative instances. Journal of Educational Psychology, 72(4), 452-456.

Carnine, D. W., & Stein, M. (1981). Organizational strategies and practice procedures for teaching basic facts. Journal of Research in Mathematics Education, 12(1), 65-69.

Engelmann, S., & Carnine, D. (1982). Theory of instruction: Principles and applications. Irvington.

Granzin, A. C., & Carnine, D. W. (1977). Child performance on discrimination tasks: Effects of amount of stimulus variation. Journal of Experimental Child Psychology, 24(4), 332-342.

Jitendra , A. K., & Kame’enui, E. J. (1994). Review of concept learning models: Implications for special education practitioners. Intervention in School and Clinic, 30(2), 91-98.

Klausmeier, H. J., & Feldman, K. V. (1975). Effects of a definition and a varying number of examples and nonexamples on concept attainment. Journal of Educational Psychology, 67(2), 174-178.

Markle, S. M., & Tiemann, P. W. (1970). “Behavioral” analysis of “cognitive” content. Educational Technology, 10(1), 41-45.

Rosenshine, B., & Meister, C. (1995). Scaffolds for teaching higher-order cognitive strategies. In A.C. Ornstein (Ed.) Teaching: Theory into practice. Allyn & Bacon.

Tennyson, R. D., & Park, O. (1980). The teaching of concepts: A review of instructional design research literature. Review of Educational Research, 50(1), 55-70.

Sprague, J. R., & Horner, R. H. (1984). The effects of single instance, multiple instance, and general case training on generalized vending machine use by moderately and severely handicapped students. Journal of Applied Behavior Analysis, 17(2), 273-278. https://pmc.ncbi.nlm.nih.gov/articles/PMC1307940/pdf/jaba00032-0149.pdf

Williams, P., & Carnine, D. (1981). Relationships between range of examples and of instructions and attention in concept attainment. Journal of Educational Research, 74(3), 144-148.

Footnotes

1. I’m stealing from Ludwig Wittgenstein here. Professor Wittgenstein taught philosophy in the first half of the 1900s. His work has been celebrated as the basis for study of human understanding of language (for example), including labels that people use for concepts. Readers who would like to trace my understanding can consult “The Blue Book,” a version of his lectures from his time at Oxford.

2. It can even turn in on itself: Readers might legitimately consider it an example of giving an example.

3. The orientations were the same except for the two that were close together and moved a bit.

4. So, don’t get the idea that you suffer from some mystical, neurodiversity that inhibits you answering correctly. The problem was in the instruction, the examples I used.

5. I say “not examples.” Some folks say “non-examples.” I use the former because I’m not talking about examples that are non existent. The examples I’m talking about show what the concept is not, not what it’s non.

6. Sorry to go all cognitive on your here. I’m just using these “might thinks” as a shorthand about “rules” the learners might “develop,” “construct,” or “generate.” Markle and Tiemann (1970) offered a very sensible explanation of such cognitions.

7. In fact, we should remember that it is the teaching that causes the blood flow in the brain. I’ve made this point previously (see, e.g,, the DI Keynote of 2023). and will, no doubt, return to it again.

8. B. Rosenshine and I corresponded over the years. He wrote a chapter for a book I edited. We discussed the idea of how his model overlooked instructional design. I should go back to that correspondence and write a post about his views of what he called “master designers.”