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Hello, I'm Robert Gagne. As instructional design moves out of its
infancy, it is important for instructional designers to be aware of
the tools which may assist them in their planning. Accurate planning can support
the achievement of learner outcomes. One type of learning outcome is intellectual
skills. Today we intend to look at intellectual skills and ways of
analyzing them by means of learning hierarchies. This kind of analysis is
done to reveal the simpler skills of which they are composed. In other words,
they are prerequisite skills. But first let me set the stage by the question: how
many different types of learning outcomes are there?
[Narrator] Instruction may be designed to support five major kinds of learning outcomes.
These learning outcomes are cognitive strategies: information, motor skills, attitudes, and
intellectual skills. Learning hierarchies are applicable to intellectual skills
and, in their strictly defined form, they are not applicable to other kinds
of learned capabilities. They apply to intellectual skills, the learning of
rules, concepts, and discriminations. When a new rule is learned, that is the kind
of capability which makes possible rule governed performance, the learning is a
matter of combining simpler rules or concepts into a more complex whole.
This means that the new skill to be learned has some prerequisites.
These prerequisites are subordinate skills, or rules that are actually incorporated
into the newly learned more complex rule. As a very simple example take for
instance the skill of adding two place numbers. As learned by a young child, this
skill incorporates two prerequisites. One is adding one place numbers; the other is
the operation of carrying or regrouping. When the new skill is learned, it
actually incorporates these two prerequisite skills. You have already
been informed that a learning hierarchy has something to do with prerequisite
skills with subordinate intellectual skills that become an integral part of a
newly learned more complex skill. The prerequisites of any and every
intellectual skill can be determined by analyzing the skill. Just think for a
moment of how that can be done if the question is asked what must the learner
know how to do in order to learn a new skill which is a combination of these
prerequisites. For the example we have used, you would surely be able to answer
adding two place numbers. You would say if this more complex skill is to be learned
the learner must be able to put together some simpler skills follow some simpler
rules namely adding single place numbers
identifying numbers with two places and carrying. The process of analysis is
carried out by asking the following question with reference to any new
intellectual skill to be learned: what is it that the learner has to know how to
do in order to learn the new skill? Strictly speaking, the question is asked
in the negative. What subordinate skills must the learner
already have, the absence of which would make it impossible for him to learn the
new skill. By asking this question one can
identify the prerequisites of an intellectual skill. In a theoretical
sense, the learning of a new skill is a matter of combining simpler skills which
have been previously learned, and are accessible in the learners memory.
Notice that these subordinate skills may have been learned a long time ago or they may
have been learned just minutes ago, but they must be present in the learners
working memory at the time the new learning occurs. Now if one applies this
analysis to a somewhat more complex skill some interesting things can be noted.
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in way each of these is also found to be composed of simpler skills, rules, or concepts.
So, if the process is continued, the result is a diagram which shows not
only the prerequisite of the original skill to be learned but also the
prerequisites of these prerequisite skills.
The result is a learning hierarchy. As shown in the example, the target skill to
be learned is subtracting whole numbers of any size. A first analysis of this
skill shows that it requires three sub skills having to do with borrowing.
Number eight is the skill of borrowing more than once in columns that are not
jumped. Number nine is subtracting when borrowing is required in adjacent
columns. And number ten is subtracting when double borrowing is required as is
true when a zero is involved.
At the same time an even simpler skill is involved in this target skill, namely
number 4, subtracting in successive columns when no borrowing is required.
Now these subordinate skills themselves may be analyzed into simpler skills.
For example, skills 8, 9, and 10 all involved the simpler skill numbered 7, subtracting
when a single borrowing is required in any column. Number 7 in turn requires the
simpler skills labeled 5 & 6, identifying the situation in which borrowing must be
done, and subtracting a one digit number from a two digit number with borrowing.
Thus as the analysis is continued, the skills get simpler and simpler and more
and more generally applicable. We finally arrive at the skill of simple
subtraction required in all the others and shown here as number one at the
bottom of the hierarchy. What do the theoretical aspects of learning
hierarchies amount to? Remember first that they apply only to intellectual
skills, so far as is known, not to the learning of information or attitudes.
The prerequisite of any new skill or rule to be learned are combined into the new
skill and become a part of it. This means that provided the subordinate
skills have been previously learned and are available in the learners working
memory, learning the new skill should take place very readily and rapidly.
As shown in the illustration, if the prerequisite skill or skills have been
mastered, learning of the new skill will be maximally facilitated.
That is to say, there will be positive transfer of the prior learning to the
new learning. However, if there has been no prior mastery of the subordinate
skill, learning of the new skill will not be facilitated. Positive transfer will
not occur. You should note that a learning hierarchy says something
important about internal conditions of the learner at the time he learns a new skill.
It says that certain specific prerequisite skills should be accessible
to the learner's memory at the time the new learning is undertaken. It is perhaps
equally important to note what the learning hierarchy does not say.
It says nothing about the external conditions of learning. it doesn't tell what the
instruction is like, whether it be instruction delivered by a teacher or
delivered by the learner to himself as self instruction. So it says only this:
the prior learning and recall of prerequisite skills is one essential for
the learning of a new intellectual skill. You are perhaps ready for the question
of what use are learning hierarchies for instruction? Of course, they are useful
for the planning of instruction. They remind us that when a new intellectual
skill is to be learned, an important first step is to see whether
prerequisite skills have been learned. If they have not it will be a good idea to
teach them first. If they have, students should be reminded of them and
encouraged to recall them so as to be ready for the new learning.
In a more comprehensive sense one can say that learning hierarchies provide a
basis for the sequencing of instruction. Observe that they do not suggest a rigid
sequence, only what may be called an adaptive sequence, in which what is
taught next is adapted to the pre-existing capabilities of the learners.
If the learner already knows a prerequisite skill, the hierarchy doesn't
suggest that he be taught that skill all over again, merely that he be reminded
that he already knows it. Another point about sequence will be evident from the
diagram of the hierarchy. notice that the subordinate skill
labelled Roman numeral seven is subordinate to eight nine and ten and so
should be learned or already known before eight nine and ten are to be
learned. But no particular sequence is suggested for eight nine and ten. All of
them are essential but the hierarchy does not specify which should be learned first.
Another important question: can the sequence of subordinate superordinate
skills be changed in instruction? Yes it can, but that involves some further
consideration of what is really taking place. Sub skill seven for example can be
taught before the separate instruction of sub skills five and six. What is
actually being done in that case is that the subordinate skill is being taught
together with the subordinate skills all in the same time interval. This can
easily be done if the learners are sufficiently capable. The fact that
sequencing of instruction can be done in this manner does not negate the basic
idea of the learning hierarchy. Since the hierarchy suggests an adaptive
sequence, it does not deny the fact that a bright student may skip over the
learning of some of the intervening skills by learning them all together
with a superordinate skill. As for the scope of applicability of learning
hierarchies, we have used examples from mathematics. Mathematics is a precise and
logical subject composed almost entirely of intellectual skills, so it provides
examples which are easy to follow. The analysis which results in learning
hierarchies, however, is perfectly possible of application to the learning
of language skills: the rules of language that are employed in composing sentences
and larger bodies of prose or poetry, and the rules used for reading and spelling.
Learning hierarchies can be constructed to describe specific topics of science,
since these too are concerned with the learning of rules and concepts. They are
also possible for social studies, but one must be constantly aware that they are
intended to describe intellectual skills, not information. How to construct a table
comparing the exports of several countries is an intellectual skill in
the social studies realm. Recounting the events of the presidential election of
1932 is not an intellectual skill and cannot be represented by a learning
hierarchy. A number of examples of learning hierarchies are illustrated in
the book Principles of Instructional Design, by Gagne and Briggs.
It is also of some interest to note that learning hierarchies are applicable to a
variety of kinds of students of various ages and various countries.
Richard White, for example, has carried out some important studies of validation of the
learning hierarchies in Australia. He used particularly a hierarchy of the
task of learning to find the slope of curved line graphs. His colleague Link
showed that the hierarchy White developed was equally valid in
describing the learning of students in New Guinea. So a learning hierarchy, once
developed in a valid form, appears to have considerable breadth of
applicability. Another kind of application should perhaps be noted.
Although we have tried here to stick to the strict definition of learning
hierarchies as applicable only to intellectual skills, other people have
advocated the liberalizing of the idea and its application to other domains of
learning. For example, a book by Cook and Wallbesser entitled How to Meet Accountability
describes learning hierarchies for mathematical topics, but
also other kinds of hierarchies called topical hierarchies, which they apply to
the learning of literature and social science.
In other words, Cook and Wallbesser are suggesting that the notion of hierarchy
is broadly useful for the planning of instruction and the sequencing of
instruction. When used in this sense it would be preferred to call the
hierarchies they construct instructional maps. An instructional map is a diagram
that shows the teacher what students should have learned and what they have
yet to learn. If they are indeed as useful as Cook and Wallbesser
maintained, we can scarcely object to them. But it is of some importance to
emphasize the precise meaning of learning hierarchies as it is to
describe various kinds of intellectual skills. Remember that learning
hierarchies attempt to describe the internal conditions for learning
intellectual skills. They do not describe the external conditions, the instruction
itself, nor are they applicable to the analysis of verbal information or
attitudes, only to intellectual skills, such as the example we saw of
subtracting. What part do learning hierarchies play in the design of
instruction? Keep in mind that learning hierarchies are an adaptive sequence to
conform to the variables of the specific situation as well as to the capabilities
of the learner. Learning hierarchies allow the designer a basis for
sequencing instruction to obtain an intellectual skill. Correct use of
learning hierarchies will allow you, the designer, accurate and effective planning
in the sequencing of such instruction.
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The preceding was an instructional media production of the instructional
systems development center, Florida State University.
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