# Pros/Cons of using a single story in multiple examples to demonstrate different points

Judea Pearl, in his book "Probabilistic reasoning in intelligent systems" uses a handful of stories over and over again, each time to demonstrate a different point. (His "Alarm" story comes to mind)

I assume that the perceived advantage of such a strategy is that students gain familiarity with the example and so no time and mental effort is wasted in understanding the story each time, making it easier to focus on the actual point. But surely there's also something to be gained from going over different examples, showing, for example, the applicability of the taught methods in different situations.

What are some other advantages/disadvantages of this approach? When is it recommended?

(I'm mainly interested in undergrad level courses)

I agree that the advantage of a repeated story is a familiarity with the context so that cognitive load is minimized. Cognitive load theory describes different types of load, and while you cannot minimize some types of cognitive load, for example the intrinsic difficulty of the topic that you are teaching, you do have control over other types, such as extraneous load of instructional details like problem contexts and material choice/design. One way to do that, as you point out, is to reuse similar contexts.

### Abstraction & Transfer Learning

An advantage in changing-up the context is in helping students to abstract by de-contextualizing problems. A significant goal in education is transfer learning, or the ability of students to re-apply knowledge in new but similar contexts. This is also an area of research in machine learning. When we write our curricular units we are required to identify "transfer knowledge", or what it is that students will be able to use across multiple domains.

It is helpful for students to understand concepts by examples, but also by non-examples. We want them to "know" a concept both by what it is and by what it is not. To me, that is a significant advantage of seeing a concept in a variety of contexts. Seeing only the same context repeatedly can be risky if students might attribute an unrelated piece of the context to the concept or vice versa. For example, I once created an awful lesson on Law of Sines where I kept using similar side ratios for all of the examples, so students ended up learning the ratios of that particular triangle very well without really understanding Law of Sines.

Really, I don't think "transfer learning" exists! I think we either develop new schema or we map/project new contexts onto existing schema. Ok maybe that's exactly what transfer learning is... Brains are weird.

### Caveat of Contexts

Contexts often are not distinct, and there tend to be subcontexts. So it is possible to see different contexts within the same story. I'm not familiar with "Probabilistic Reasoning in Intelligent Systems", but it may be that Pearl repeats the same stories while at the same time creating new contexts of understanding. Maybe it's similar to how a show can have different problems in different episodes while maintaining characters and settings.

Didactic stories should be simple, clear, and short. Think Aesop’s fables. If they become more complex, at some point they become case studies. (Case studies are good to use, but it’s a separate question.)

Why repeat them? I don’t know Pearl’s book, so I am not familiar with his purposes in repeating stories. So I’ll offer reasons why I sometimes repeat them.

First let’s note that short stories and fables themselves often repeat a story within the tale, usually the magic number of three times, each time with variation. Repetition makes the story (or the lesson) easier to remember. The variations advance our understanding of the problem presented in the story, usually with the third time being the charm. And repetition makes the lesson easier to remember.

A story that teaches a fundamental principle might be repeated as often as the fundamental principle is applied. It being a fundamental principle, it will probably be applied relatively often in different contexts. Learning to apply it in such contexts must be an important goal in the course. Richard Hamming in “The Art of Doing Science and Engineering: Learning How to Learn” tells a story of two people, one who makes a random walk and one whose directions of motion somewhat line up. The first makes progress at an average rate proportional to $$\sqrt{n}$$ and the progress of the second will be proportional to $$n$$. Over time, the second person will outstrip the first. He revisits this story several times in examining examples of engineers who had successful careers and those who had stunted careers. It is one of the fundamental points of his course: Making decisions according to your career goals will advance your career more successfully than making them without any direction in mind. It must be effective because I read that book over fifteen years ago. It’s also a geeky parable, which for his audience and for me makes it easier to remember.

The following reason for repetition probably is not what Pearl does. Here variation is used in the repetitions to illustrate significant differences when elements are changed. I don’t really know a “story” per se that does this, but I can think of calculus examples. For instance $$(\sin x)/x$$ has three types of limits, but some students memorize, literally, “the limit of $$\sin x$$ over $$x$$ is $$1$$.” And they may very well write that no matter whether $$x$$ is approaching zero, infinity, or a nonzero number. @Carter’s answers also points out the importance of variation to help keep students from associating irrelevant elements of context to an example and from ignoring important elements.

Now for a reason not to repeat a story. A story that can be repeated multiple times, each time to illustrate a different fundamental principle, is probably too complicated to tell even once. Without a specific example, I might be going out on a limb. They apparently retold the Iliad many, many times in ancient Greece, and Aristotle draws several different lessons from it. It would be hard to do that in a semester-long class, though.

• Moral +1. Liked the Hamming story. – guest Feb 18 at 18:42