You probably form an image of a dog in your mind, right? What is that dog like? What color is it? It doesn't really have any color, does it? How big is it? About average height for a dog, right? Unless you have a beloved dog of your own, your image is not of one specific dog. Rather it is of a prototype (which literally means pattern or model). It concentrates on the characteristics common to all dogs and tends to ignore the characteristics which vary across dogs, such as color and size and length of hair. Robert Tennyson has shown that prototype formation is probably the first phase of learning to apply a concept. This is our first principle of learning for concept classification. 

Once a prototype has been formed, we must learn how dogs varyóthat they can be different sizes, colors, shapes, and so on. So we must learn to generalize beyond the prototype. But the other side of that coin, according to Sue Markle and Phil Tiemann, is learning ways that dogs cannot vary. So we must learn to discriminate them from nondogs. 

Discrimination. All dogs have certain characteristics in common, such as being mammals, having a certain type of teeth, a certain type of diet, a certain range of body shapes, and so on. These are called common characteristics. Some of them are easily visible (e.g. body shape) and some of them are not (e.g. diet). Hence, some common characteristics are useful for classifying an animal as being a dog or not, and others aren't. The ones which are useful are called critical characteristics. They are what you need to learn to discriminate dogs from nondogs. This is our second principle of learning for concept classification. 

Generalization. Dogs also have certain characteristics which vary from one dog to another, such as their color, size, and so on. These are called variable characteristics. They are what you need to learn to generalize across all kinds of dogs. This is a third principle of learning for concept classification. Generalization across variable characteristics and discrimination on the basis of critical characteristics are very important aspects of learning to apply concepts. But it is helpful to keep in mind that variable characteristics can have different degrees of variability. Some can be common to almost all of the members of the concept class, while others can be very rare in any of them. The ones that are common to most can sometimes be very useful for classifying. Almost any concept can be broken down into kinds (called "subordinate concepts"), and each of those kinds represents what Joseph Scandura calls a different "equivalence class." The different equivalence classes are sometimes called "dimensions of divergence." 

Some concepts are quite complex. That is, they have many critical characteristics. This can make learning to classify very difficult. Lev Landa has identified a technique which people learn to facilitate the process. They develop an algorithm, or procedure, to follow. It is likely to be something like this: 

First look to see if it has such-and-such. 
If it doesn't, it is not a widget. 
But if it does, look to see if it has either a whatsit or a whosie. 
If it has neither, then it is not a widget. 
But if it has either one, then look to see if . . . ." 

Learning to apply a concept alwaysentails learning an algorithm, but for simple concepts the algorithm has just one step. This is our fourth principle of learning for concept classification. Incidentally, "experts" are usually unaware of the algorithm they use. 

A final important consideration for learning concept classification is prior knowledge. Robert Gagné (1985) has shown that the skill of applying a concept always has some "prerequisite" skills, skills which must be mastered before it is possible to learn any given classification skill. Those prerequisites are the critical (and sometimes variable) characteristics, which are concepts in their own right. This is yet another principle of learning which has important implications for the instructional strategies that will be helpful for teaching concept classification. 

Given all these principles for concept learning, how should one teach a concept classification task?