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[Music]

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Hello, I'm Robert Gagne. As
instructional design moves out of its

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infancy, it is important for
instructional designers to be aware of

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the tools which may assist them in their
planning. Accurate planning can support

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the achievement of learner outcomes. One
type of learning outcome is intellectual

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skills. Today we intend to look at
intellectual skills and ways of

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analyzing them by means of learning
hierarchies. This kind of analysis is

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done to reveal the simpler skills of
which they are composed. In other words,

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they are prerequisite skills. But first let
me set the stage by the question: how

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many different types of learning
outcomes are there?

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[Narrator] Instruction may be designed to support five major kinds of learning outcomes.

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These learning outcomes are cognitive strategies: information, motor skills, attitudes, and

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intellectual skills. Learning hierarchies
are applicable to intellectual skills

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and, in their strictly defined form,
they are not applicable to other kinds

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of learned capabilities. They apply to
intellectual skills, the learning of

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rules, concepts, and discriminations. When
a new rule is learned, that is the kind

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of capability which makes possible rule
governed performance, the learning is a

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matter of combining simpler rules or
concepts into a more complex whole.

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This means that the new skill to be learned
has some prerequisites.

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These prerequisites are subordinate skills, or rules that are actually incorporated

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into the newly learned more complex rule.
As a very simple example take for

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instance the skill of adding two place
numbers. As learned by a young child, this

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skill incorporates two prerequisites. One is adding one place numbers; the other is

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the operation of carrying or regrouping.
When the new skill is learned, it

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actually incorporates these two
prerequisite skills. You have already

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been informed that a learning hierarchy
has something to do with prerequisite

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skills with subordinate intellectual
skills that become an integral part of a

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newly learned more complex skill. The
prerequisites of any and every

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intellectual skill can be determined by
analyzing the skill.  Just think for a

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moment of how that can be done if the
question is asked what must the learner

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know how to do in order to learn a new
skill which is a combination of these

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prerequisites. For the example we have
used, you would surely be able to answer

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adding two place numbers. You would say if
this more complex skill is to be learned

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the learner must be able to put together
some simpler skills follow some simpler

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rules
namely adding single place numbers

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identifying numbers with two places and
carrying. The process of analysis is

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carried out by asking the following
question with reference to any new

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intellectual skill to be learned: what is
it that the learner has to know how to

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do in order to learn the new skill?
Strictly speaking, the question is asked

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in the negative.
What subordinate skills must the learner

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already have, the absence of which would
make it impossible for him to learn the

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new skill.
By asking this question one can

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identify the prerequisites of an
intellectual skill. In a theoretical

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sense, the learning of a new skill is a
matter of combining simpler skills which

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have been previously learned, and are
accessible in the learners memory.

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Notice that these subordinate skills may have
been learned a long time ago or they may

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have been learned just minutes ago, but
they must be present in the learners

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working memory at the time the new
learning occurs. Now if one applies this

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analysis to a somewhat more complex
skill some interesting things can be noted.

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[audio corrupted]

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in way each of these is also found to be
composed of simpler skills, rules, or concepts.

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So, if the process is continued,
the result is a diagram which shows not

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only the prerequisite of the original
skill to be learned but also the

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prerequisites of these prerequisite
skills.

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The result is a learning hierarchy. As
shown in the example, the target skill to

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be learned is subtracting whole numbers
of any size. A first analysis of this

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skill shows that it requires three sub
skills having to do with borrowing.

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Number eight is the skill of borrowing
more than once in columns that are not

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jumped. Number nine is subtracting when
borrowing is required in adjacent

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columns. And number ten is subtracting
when double borrowing is required as is

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true when a zero is involved.

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At the same time an even simpler skill
is involved in this target skill, namely

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number 4, subtracting in successive
columns when no borrowing is required.

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Now these subordinate skills themselves
may be analyzed into simpler skills.

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For example, skills 8, 9, and 10 all involved
the simpler skill numbered 7, subtracting

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when a single borrowing is required in
any column. Number 7 in turn requires the

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simpler skills labeled 5 & 6, identifying
the situation in which borrowing must be

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done, and subtracting a one digit number
from a two digit number with borrowing.

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Thus as the analysis is continued, the
skills get simpler and simpler and more

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and more generally applicable. We finally
arrive at the skill of simple

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subtraction required in all the others
and shown here as number one at the

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bottom of the hierarchy. What do the
theoretical aspects of learning

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hierarchies amount to? Remember first
that they apply only to intellectual

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skills, so far as is known, not to the
learning of information or attitudes.

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The prerequisite of any new skill or rule to
be learned are combined into the new

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skill and become a part of it.
This means that provided the subordinate

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skills have been previously learned and
are available in the learners working

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memory, learning the new skill should
take place very readily and rapidly.

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As shown in the illustration, if the
prerequisite skill or skills have been

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mastered, learning of the new skill will
be maximally facilitated.

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That is to say, there will be positive
transfer of the prior learning to the

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new learning. However, if there has been
no prior mastery of the subordinate

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skill, learning of the new skill will not
be facilitated. Positive transfer will

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not occur. You should note that a
learning hierarchy says something

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important about internal conditions of
the learner at the time he learns a new skill.

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It says that certain specific
prerequisite skills should be accessible

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to the learner's memory at the time the
new learning is undertaken. It is perhaps

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equally important to note what the
learning hierarchy does not say.

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It says nothing about the external conditions of
learning. it doesn't tell what the

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instruction is like, whether it be
instruction delivered by a teacher or

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delivered by the learner to himself as
self instruction. So it says only this:

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the prior learning and recall of
prerequisite skills is one essential for

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the learning of a new intellectual skill.
You are perhaps ready for the question

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of what use are learning hierarchies for
instruction? Of course, they are useful

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for the planning of instruction. They
remind us that when a new intellectual

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skill is to be learned, an important
first step is to see whether

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prerequisite skills have been learned. If
they have not it will be a good idea to

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teach them first. If they have, students
should be reminded of them and

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encouraged to recall them so as to be
ready for the new learning.

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In a more comprehensive sense one can
say that learning hierarchies provide a

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basis for the sequencing of instruction.
Observe that they do not suggest a rigid

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sequence, only what may be called an
adaptive sequence, in which what is

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taught next is adapted to the
pre-existing capabilities of the learners.

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If the learner already knows a
prerequisite skill, the hierarchy doesn't

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suggest that he be taught that skill all
over again, merely that he be reminded

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that he already knows it. Another point
about sequence will be evident from the

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diagram of the hierarchy.
notice that the subordinate skill

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labelled Roman numeral seven is
subordinate to eight nine and ten and so

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should be learned or already known
before eight nine and ten are to be

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learned. But no particular sequence is
suggested for eight nine and ten. All of

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them are essential but the hierarchy
does not specify which should be learned first.

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Another important question: can the
sequence of subordinate superordinate

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skills be changed in instruction? Yes it
can, but that involves some further

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consideration of what is really taking
place. Sub skill seven for example can be

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taught before the separate instruction
of sub skills five and six. What is

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actually being done in that case is that
the subordinate skill is being taught

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together with the subordinate skills all
in the same time interval. This can

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easily be done if the learners are
sufficiently capable. The fact that

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sequencing of instruction can be done in
this manner does not negate the basic

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idea of the learning hierarchy.
Since the hierarchy suggests an adaptive

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sequence, it does not deny the fact that
a bright student may skip over the

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learning of some of the intervening
skills by learning them all together

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with a superordinate skill. As for the
scope of applicability of learning

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hierarchies, we have used examples from
mathematics. Mathematics is a precise and

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logical subject composed almost entirely
of intellectual skills, so it provides

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examples which are easy to follow. The
analysis which results in learning

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hierarchies, however, is perfectly
possible of application to the learning

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of language skills: the rules of language
that are employed in composing sentences

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and larger bodies of prose or poetry, and
the rules used for reading and spelling.

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Learning hierarchies can be constructed
to describe specific topics of science,

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since these too are concerned with the
learning of rules and concepts. They are

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also possible for social studies, but one
must be constantly aware that they are

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intended to describe intellectual skills,
not information. How to construct a table

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comparing the exports of several
countries is an intellectual skill in

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the social studies realm. Recounting the
events of the presidential election of

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1932 is not an intellectual skill and
cannot be represented by a learning

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hierarchy. A number of examples of
learning hierarchies are illustrated in

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the book Principles of Instructional
Design, by Gagne and Briggs.

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It is also of some interest to note that
learning hierarchies are applicable to a

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variety of kinds of students of various
ages and various countries.

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Richard White, for example, has carried out some
important studies of validation of the

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learning hierarchies in Australia. He
used particularly a hierarchy of the

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task of learning to find the slope of
curved line graphs. His colleague Link

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showed that the hierarchy White
developed was equally valid in

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describing the learning of students in
New Guinea. So a learning hierarchy, once

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developed in a valid form, appears to
have considerable breadth of

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applicability. Another kind of
application should perhaps be noted.

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Although we have tried here to stick to
the strict definition of learning

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hierarchies as applicable only to
intellectual skills, other people have

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advocated the liberalizing of the idea
and its application to other domains of

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learning. For example, a book by Cook and
Wallbesser entitled How to Meet Accountability

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describes learning
hierarchies for mathematical topics, but

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also other kinds of hierarchies called
topical hierarchies, which they apply to

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the learning of literature and social
science.

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In other words, Cook and Wallbesser are
suggesting that the notion of hierarchy

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is broadly useful for the planning of
instruction and the sequencing of

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instruction. When used in this sense it
would be preferred to call the

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hierarchies they construct instructional
maps. An instructional map is a diagram

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that shows the teacher what students
should have learned and what they have

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yet to learn. If they are indeed as
useful as Cook and Wallbesser

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maintained, we can scarcely object to
them. But it is of some importance to

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emphasize the precise meaning of
learning hierarchies as it is to

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describe various kinds of intellectual
skills. Remember that learning

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hierarchies attempt to describe the
internal conditions for learning

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intellectual skills. They do not describe
the external conditions, the instruction

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itself, nor are they applicable to the
analysis of verbal information or

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attitudes, only to intellectual skills,
such as the example we saw of

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subtracting. What part do learning
hierarchies play in the design of

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instruction? Keep in mind that learning
hierarchies are an adaptive sequence to

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conform to the variables of the specific
situation as well as to the capabilities

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of the learner. Learning hierarchies
allow the designer a basis for

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sequencing instruction to obtain
an intellectual skill. Correct use of

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learning hierarchies will allow you, the
designer, accurate and effective planning

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in the sequencing of such instruction.

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[Music]

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The preceding was an instructional
media production of the instructional

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systems development center, Florida State
University.

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[Music]