Module 2: Invariant Tasks 

Basic Methods of Instruction 
1.Kinds of Learning 
2.Invariant Tasks 
3.Concept Classification 
4.Procedure Using 
5.Principle Using 
7.Generic Skills 

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Principles for Learning Invariant Tasks 
Before you can figure out how to teach an invariant task, it is helpful to know how invariant tasks are learned. Different learning theories provide different perspectives on how they are learned. In this section, we provide a description from the perspective of behaviorist theory, cognitive / information processing theory, cognitive / schema theory, and constructivist theory. Then we provide an integrated view of principles for learning invariant tasks. 

Behaviorist Learning Theory 

There are several kinds of behaviorist learning theories. You may be familiar with "conditioned response theory" developed by Pavlov, whereby a response that already occurs in the presence of one stimulus can be "conditioned" to occur following a different stimulus. This learning theory is very important for emotional learning, but has little relevance to most learning of invariant tasks. 

Far more relevant is "reinforcement theory," first developed by E. L. Thorndike (1913). and further developed by B.F. Skinner (see e.g., 1956) and others. In reinforcement theory, an invariant task is viewed as a "response" and is learned when it becomes "associated" with an appropriate stimulus. For example, "3.14" is a response that should become associated with "Pi". This learning process occurs whenever "reinforcement" follows the response. For example, each time a learner responds with "3.14", a reinforcer such as "Right!" or "Good!" or even just a smile with a nod will increase the probability of the learner responding the same way in the future.  With sufficient repetition of these stimulus-response-reinforcement events, the response will come to occur automatically in the presence of the stimulus. 

Cognitive / Information Processing Theory 

There are at least two major kinds of cognitive theory relevant to learning invariant tasks: information-processing theory and schema theory. According to the information-processing model of learning (see Figure 2.1), there is a series of stages by which new information is learned (Gagné, 1985). Information is received by receptors (such as the eyes and ears), from which it is passed to the sensory register where all of it is held, but for only a few hundredths of a second. At this point, selective perception acts as a filter which causes some aspects of the information to be ignored and others to be attended to. For example, the ears (receptors) receive the sounds comprising "Pi equals 3.14," along with various other background sounds, and all those sounds are passed on to the sensory register in the brain. Then through the selective perception process, some of the information (hopefully the "Pi equals 3.14 part) is attended to." 


Figure 2.1. The Information-Processing Model of Learning 

That information which is attended to is transformed and passed on to short-term memory, which can only contain a few items of information at a time (usually identified as 7+2 items, depending on their complexity). For example, if "Pi equals 3.14" is attended to, it is then passed on to short-term memory, where it might be said to "echo" for a few seconds, and the echoing can be prolonged through rehearsal."  Items can persist in short-term memory for up to about 20 seconds without rehearsal, but with constant rehearsal they can be retained indefinitely. 

Finally, the information may be passed to long-term memory. This process is called encoding. For example, if appropriate encoding processes are exercised to link the "Pi equals 3.14" with prior knowledge, then the information is passed on to long-term memory." It is likely that different types of knowledge are encoded in different ways, which is why they require different methods of instruction. It is typically only this stage which we call "learning", for information which is not passed on to long-term memory is lost (at least, it is not retrievable). It is necessary to turn to other theories, such as schema theory, for descriptions of how the encoding process may occur. 

Cognitive / Schema Theory 

The other major kind of cognitive theory is schema theory. It proposes that, when new knowledge is encoded, it is organized into schemas, which are networks of related pieces of knowledge. For example, an invariant task can be encoded as a new schema, complete with such contextual factors as conditions for its use, in which case it will be at least loosely related to other schemata, or more typically it can be assimilated into an existing schema. But more importantly for instructional purposes, specific elements of the invariant task can often be learned--or more accurately, retrieved--more easily by relating them to certain carefully selected prior knowledge, especially meaningful knowledge. For example, it is easier to remember the colors of the rainbow and their order (red, orange, yellow, green, blue, indigo, violet) by associating them with the name, "Roy G. Biv." 

Constructivist Theory 

Constructivist theory views learning as .... 

An Integrated View 

There are two major degrees of memorization: recognition and recall. In recognition for a list, the name of the list and an item from the list are both presented to the learner, who indicates whether or not the item belongs to the list: "Which of the following were Presidents of the United States: Abraham Lincoln, Fred Washington, . . . ?" For an ordered list, two or more items from the list are presented or performed, and you indicate whether or not they are in the right order. In recall for a list, the name of the list is presented, and you have to retrieve the items from your own memory: "List ten Presidents of the United States below" or "Change the oil in your car." 

Does association learning occur the same way? An association, in its simplest form, has two elements which must be paired together (associated with each other): a stimulus, which is presented to the learner, and a response (either mental or physical), which is provided by the learner. A state with its capital, a person with her name, a painting with its artist, a symbol with its name, and the letters of the alphabet with the finger movement necessary to type each on a standard keyboard are all cases in point. In its more complex forms, an association can have many elements which are all to be associated with each other, such as a person, a place, a date, and (the name of) an event. In this case, you usually have one stimulus and multiple responses. For example, "the discovery of America" might be associated with "Christopher Columbus," "1492," "Queen Isabel of Spain," and "the Nina, Pinta, and Santa Maria." 

In recognition for an association, the stimulus and a response are both presented, and you indicate whether or not they are a correct match, or you match up the correct ones. "Was the Declaration of Independence signed in 1770?" is such an item. In recall for an association, the stimulus is presented, and you have to retrieve the response from your own memory. "When was the Declaration of Independence signed?" is a case in point. 

In spite of these differences, association learning is similar to list learning in that it is a rote (nonmeaningful) form of learning which is committed to memory primarily by repetition. It is also acquired gradually over time with practice, and it can be learned to the point of recognition or to the point of recall. 

Learning a rote procedure may require learning two things: when to do each action, and how to do each action. But in many cases, the learners may already know how to do each action, such as an experienced computer user learning how to use a particular WWW browser to search the Internet. That learner just needs to learn what actions to take when, not how to take them. 

What are the obstacles to memorization? 

Learning psychologists generally believe from hypnosis experiments that getting information into memory is easy, that the only real obstacle is retrieval from memory. The items on a list are thought of as being stored in memory as individual nodes, in this case, one for each President. Retrieval occurs through links among nodes. The links become stronger each time they are used. The challenge, then, becomes one of creating links which are strong enough that retrieval is quick and effortless. This is our first principle of learning for invariant tasks. 

An obstacle to list learning is presented when there are many items to remember on the list--the more items, the harder the task. Would you try to learn the names of all the Presidents at the same time? Or would you divide up the names and work on a few of them at a time until they are mastered before going on to another set of names? George Miller (1956) found that "working memory" has a limit of 7+ 2 items. In other words, you can only productively work on memorizing up to about seven items at a time. Much subsequent research has shown that learning proceeds more easily if a large list is divided into chunks of about 5-7 items and each chunk is mastered before the next chunk is taken on. This is our second principle of learning. 

Two additional things have been found to facilitate remembering. Rote information can usually be remembered better if it is related to meaningful prior knowledge. For example, the meaningful phrase, "Every Good Boy Does Fine", makes it much easier to remember the order of the notes (lines) on a staff (in music): E G B D F. This is our third principle. It is also easier to remember visual images and musical tunes and rhymes than to remember words. For example, presenting a picture of a boy with a halo getting a pat on the back would likely make it easier to remember "Every Good Boy Does Fine". Similarly, the rhyme, "Thirty days have September, April, June, and November....", makes it much easier to remember the lengths of the months.


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This file was last updated on March 10, 1999 by Byungro Lim
Copyright 1999, Charles M. Reigeluth Credit