Step 9 in Ten Steps to Complex Learning is “analyze prequisite knowledge.”  As with Steps 7 and 8, van Merriënboer and Kirschner are talking about procedural information, the knowledge that you apply in the same way to different problems.

(You can click the image to see a chart with all four components and all ten steps.)

The prerequisites are the things you have to know in order to perform these recurrent skills.  vM&K argue that you have to analyze the cognitive rules (Step 8) in order to find out what the prerequisites might be.

Facts: three levels down

Way back in Step 6 (analyze mental models), Ten Steps discussed domain models for non-recurrent skills (the skills you apply differently to different problems).  One way to think of a domain model is that it’s a high-level abstraction.  As you move closer to the job, you can discern elements like conceptual, structural, and causal or functional models; moving closer still, you get to individual facts.

When you’re talking about recurrent skills, the middle and bottom levels are more relevant to the algorithmic nature of procedural information.  As with cognitive rules, this is a step you might be able to avoid if the rule-based information already exists in manuals, traing programs, and similar forms.

For that middle level, vM&K talk about concepts, plans, and principles. Concepts are descriptions and classifications, like the concept of a field in data entry, or the concept of offsides in soccer.

Plans (another peculiar vM&K term) “relate concepts to each other in space…or in time.”  What I think they mean by plan is a kind of map or arrangement, like an electrical circuit or a standardized format.

One of their examples is how you present the mean and the standard deviation in a research paper: M=x.xx; SD=y.yy.  The idea is that as you go about writing your paper, that arrangement is the plan for that particular item.

Plans can also be scripts, which I take to mean small recipes for accomplishing some task.  The order of sections for your research paper is a kind of script.

Finally, principles related concepts to one another in cause-effect or as part of an overall natural process.  (The difference is that a natural process is continuous and doesn’t have a fixed start point, like the evaporation/condensation cycle.)

vM&K say that learning a principle helps a person move from rote memory to understanding.  If you learn principles for performing subtraction, for example, you don’t have to memorize how to subtract every number from every other number.

Facts and features

Ten Steps takes a side trip into logic, or philosophy, or something.  The chapter suggests that one way to identify a concept is to “list all the facts that apply to its instances” in a “feature list.”  These will be “propositions” with a “predicate” and at least one “argument.”

For example, in word processing, a column is elongated.  “Column” is the argument (the subject), and “elongated” is the predicate (the relationship).

No, I didn’t quite get it, either.  In another example:

A text processor [word processor] may construct columns using the table function.  This is a proposition with three arguments (text processor, which is the subject; column, which is the object; and table function, which is the tool connected with the predicate “construct”).

vM&K say that these propositions are the smallest building blocks of cognition; “there are no facts that enable the learning of other facts.”

Let’s see–let’s take the fact that Paris is the capital of France.  As the authors say, in a sense a fact has meaningless, arbitrary links.  You could say “Paris is the capital of France” without knowing anything about Paris, capitals, or France.  And even if you do know about Paris and France, you’re not necessarily better able to learn other facts about Paris or about France.

Facts and concepts

Concrete concepts may require physical models like schematic diagrams, exploded diagrams, and similar tools to help learners develop better mental models.  Along with the concept of an electrical resistor (opposes the flow of electricity), examples of its physical form can help the learner.

There’s actually an interplay here, and this may be part of that confusing conceptual-model business.  Not all resistors use color-coded bands to indicate the amount of resistance.

As you’ve seen with conceptual rules, vM&K say that prerequisites should be aimed at the entry behavior of the target learners.   You’d think it’d be easy to go too far–think of computer-application training that insists people know what radio buttons are, not just know how to use them on the job.  The authors are also concerned that it’s all too common to overestimate the amount of prerequisite knowledge that learners already have–the familiar curse of knowledge.

Design implications

As with other types of knowledge, learning about prerequisites can benefit from an analysis of misconceptions.  Think of language barriers and George Bernard Shaw’s observation that Americans and Britons are two people separated by a common language.

In the U.K., a “scheme” is a plan; the British government is proposing a scheme for regulating asset-backed securities.  In the U.S., the word “scheme” almost always has a connotation of trickiness or outright deceit, enshrined in “Ponzi scheme.”

The Ten Steps consistently recommends presenting prerequisite information just-in-time, and on a just-enough basis.  In addition, by focusing attention on misconceptions, well-designed materials can help people learn.  I haven’t owned a Volkswagen since I was an undergraduate, but still recall John Muir’s manual for keeping my Beetle alive.  Muir consistently put “front is front” into instructions for dealing with engine problems.

Beetle engines were in the rear of the car.  Muir learned as he helped people work on their cars that they often shared a misconception: “front” to them meant “closer to the outside.”  If he said, “change the front plugs,” they’d start changing the ones closest to the back of the car.

So, “front is front” was a prerequisite piece of knowledge: in this manual, when you’re working on the engine, “front” means “the front of the entire car.”

Other techniques to help learners master prerequisite knowledge:

• Slower fading–in other words, maintain a relatively high level of support during the early learning tasks.
• Multiple representations.  You might provide both a verbal or textual description and a diagram, photo, or illustration.
• Compare/contrast.  As a design element, vM&K urge you to have learners practice applying the new skills.  Working with effective and ineffective concepts helps them better recognize the difference when it matters.

That’s it for Step 9.  Next time, the tenth step (design part-task practice).

CC-licensed images:  not-quite-level steps by R.B. Boyer;
normal distribution with standard deviations from Wikipedia;
automatic flusher sign by tico24.

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