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
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
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 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 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
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.