In recent years there has been an increased focus on
the role of education and training, and on the effectiveness and efficiency of
various instructional design strategies. Some of the most important
breakthroughs in this regard have come from the discipline of Cognitive Science,
which deals with the mental processes of learning, memory and problem
Cognitive load theory (e.g. Sweller, 1988; 1994) is an
instructional theory generated by this field of research. It describes learning
structures in terms of an information processing system involving long term
memory, which effectively stores all of our knowledge and skills on a
more-or-less permanent basis and working memory, which performs the intellectual
tasks associated with consciousness. Information may only be stored in long term
memory after first being attended to, and processed by, working memory. Working
memory, however, is extremely limited in both capacity and duration. These
limitations will, under some conditions, impede learning.
tenet of cognitive load theory is that the quality of instructional design will
be raised if greater consideration is given to the role and limitations, of
working memory. Since its conception in the early 1980's, cognitive load theory
has been used to develop several instructional strategies which have been
demonstrated empirically to be superior to those used
This paper outlines some of the basic principles of
cognitive load theory. Examples of the instructional design strategies generated
by cognitive load theory are also provided.
2.1 Remembering information
Some people believe that we remember
information by 'capturing' it on something like a video tape in our minds. This
is not the case. What we see and remember depends more on what we already know,
than on what is actually presented.
Look at each of the following, and
note what you see.
In the first example most
people read 'THE CAT', even though the centre symbol in each word is the same.
The context of reading provides information which we use to help interpret the
In the second example most people will read each symbol as an
example of the letter "a", even though no two symbols are identical. We can read
an infinite range of symbols as the letter "a", even most peoples' hand writing,
although we have never seen their handwriting before. We are able to do
so because of our knowledge of what constitutes the letter
Similarly, we are also able to recognise literally millions of
different trees, as trees, even though no two are identical.
examples demonstrate that we cannot help but to impose meaning on things that we
sense. Humans are able to behave and think in 'intelligent' ways because of
their ability to quickly identify meaning in presented stimuli.
knowledge and skills in activities as diverse as reading, driving, mathematics
and gardening all derive from the knowledge base which we hold more-or-less
permanently in long-term memory.
2.2 Chunking information
When presented a "large" set of elements
to remember, it is often helpful to combine the elements to form a smaller
number of groups. Each of the groups is referred to as a "chunk" of
For example, it is common practice to combine the digits of
a phone number into two or three chunks of several digits each, rather than
listing all digits in one long sequence. The phone number 3476 - 2980 may be
easier to remember than the sequence 3 4 7 6 2 9 8 0.
Chunking does not
need to be based upon any underlying meaning or logic that can be identified
within the elements of the to-be-learned information. However, if an underlying
meaning or logic can be identified and is used to define the chunks,
then remembering is greatly enhanced.
For example, remembering a shopping
list where elements are chunked into like groups, such as:
is much easier to remember
than a list of identical elements which are chunked into groups without any
underlying structure, such as:
Look at each of the following
statements in turn for just a few seconds, and try to memorise the sequence of
letters and spaces.
The first statement is
difficult to memorise. The series of letters and spaces appears to be random. If
we are unable to identify any form of pattern or meaning then we are reduced to
a strategy of memorising individual letters in turn. If, however, we are able to
identify the "scrambled" meaning, then our strategy for remembering becomes one
of trying to remember the location of the spaces.
The second statement is
easy to memorise because the spaces are located in a way that promotes meaning.
Consequently we need only memorise a few ideas (All fish, enjoy, clean
When what we already know enables us to identify or impose
meaning on a new piece of information because it connects with
information held in long-term memory, then it is relatively easy for us to
remember it because we can "build it into" our existing knowledge base in a way
that makes sense for us. The new information becomes an integral part of our
overall knowledge, held in long-term memory.
2.3 The modal model of memory
It is now widely accepted that we
have, and use, more than one type of memory.
A modal model of memory
distinguishes between three distinct memory types (modes). These are sensory
memory, working memory and long term memory.
Each mode has its own
characteristics and limitations.
These three modes are integrated to
define an information processing model of human cognitive
2.4 Sensory memory
Sensory memory deals with incoming stimuli from
our senses. These are sights, sounds, smells, tastes and touches. A separate
partition of sensory memory exists for each of the
Sensory memories extinguish extremely quickly.
(About half a second for visual information, 3 seconds for auditory
information). In that time, we must identify, classify and assign meaning to the
new information or it will be gone forever.
While looking at the picture
below, quickly shut your eyes, and keep them shut for a few seconds. Repeat this
soon as you shut your eyes you may have noticed an image of the picture
remaining for a split second "somewhere in your mind". This demonstrates the
operation of the partition of your sensory memory that deals with visual
perceptions. This is not restricted to blinking at pictures. Look at anything
around you and it will still work.
2.5 Long term memory
Long term memory refers to the immense body of
knowledge and skills that we hold in a more-or-less permanently accessible
Our name, date of birth, the letters of the alphabet, how to read,
how to write, how to drive, swim, play chess, catch a ball and everything else
that we "know" is all held in our long term memory awaiting
Activation will occur as a direct result of our working
memory querying long term memory for specific factual information (through our
consciousness). Once a query has been made activation (and the 'answer') is
Knowledge and skills that are activated with
extremely high regularity, such as walking and talking, may be activated
'automatically' without the need for high levels of conscious attention, even
though the task itself may be a complex one. (Automation is discussed further in
Consider each of the following questions.
Question 1: What is your
You will be able to answer this quickly. It's no surprise since it
is referred to frequently and consists of only a few words. Note how quickly you
can provide the answer.
Question 2: What are the letters of the
Again, you will be able to answer this quickly but this is a
more interesting question than the first. Here there are 26 items in the answer
and virtually everyone presents the 26 items in the same order. Our long term
memory holds the letters of the alphabet in alphabetical sequence. If you try to
say the letters of the alphabet in a random order, then you will find it an
extremely difficult, probably impossible task.
Question 3: Who won the
lottery in 1992 at Wattle St., Sydney, Australia?
Most people will
quickly realise that they do not know the answer to this question. They
recognise almost immediately that this is information that is not currently held
in their long term memory. Generally, people "know that they don't
2.6 Working memory
Working memory is the part of our mind that
provides our consciousness. It is the vehicle which enables us to think (both
logically and creatively), to solve problems and to be
Working memory is intimately related to where and how we
direct our attention to "think about something", or to process
The biggest limitation of working memory is its capacity to
deal with no more than about seven elements of information simultaneously
Working memory capacity may be expanded slightly by
mixing the senses used to present information. That is, it is easier to attend
to a body of information when some of the information is presented visually and
the remainder of the information is presented auditorily than it is when all of
the information is presented through a single sense (either all visually or all
If the capacity of working memory is exceeded while
processing a body of information then some, if not all, of that information will
Consider answering both of the following questions without using
pencil and paper.
For most people
Question 1 is quick and easy to solve as an example of mental
In many ways Question 2 is nothing more than a 'larger'
version of Question 1, yet it is almost impossible to solve mentally.
role of long term memory is effectively the same for these two questions (to
recall the rules of addition).
The difference is that in Question 2 our
working memory capacity is exceeded. It cannot cope with the large number of
elements (in this case the numerals) that need to be attended to simultaneously
in order to solve this problem.
The use of pen and paper aids solution to
Question 2 because it effectively relieves the burden placed upon working memory
by giving us a means of recording elements in a 'permanent' form once we have
finished processing them.
3.1 Definition of learning
Learning may be defined as the encoding
(storage) of knowledge and/or skills into long term memory in such a way that
the knowledge and skills may be recalled and applied at a later time on
Humans have a great capacity for learning and tend to spend their
lives doing so. They learn not only how to walk upright, but also how to talk,
read and write. Many people today learn how to drive a car, operate a microwave
oven, and use a computer. Some even learn how to perform a heart transplant
operation. For all of these tasks (and just about every other task you care to
mention) the role, capacity and qualities of sensory memory and working memory
remain effectively unchanged. The driving force behind all skilled performance
is the knowledge base that has been acquired within long term memory.
capacity of our long term memory to acquire knowledge appears to be unlimited.
No-one ever "runs out of space", although with age there may be an overall
deterioration in the performance of our memory system.
It should also be
noted that virtually everyone can learn how to drive a car, operate a
microwave oven, use a computer or even perform a heart transplant operation,
provided that they are given sufficient time and training to enable them to
acquire the necessary knowledge and skills.
The next diagram
presents part of an information network for cars for you to complete, or at
least think about. There are no right or wrong answers.
Spend a few
minutes writing down in point form some information about cars. Some ideas have
been included for you to work from but you are free to add anything you like.
For example, details about their use, cost, construction, road rules, impact on
the environment, history of development, principles of combustion engines, how
to change gears, how to replace spark plugs.....and so on.
writing down ideas as soon as they come to you. If you spend more than a few
seconds "stuck", then begin another branch.
Everyone living in modern
society holds an enormous amount of knowledge regarding cars, their use, road
rules, and so on. This knowledge base is held in a well structured information
network which is itself connected to other networks. Networks such as those for
'transport' or 'modern society' are higher order concepts, while networks for
'seat belt', 'spark plugs' and 'accelerator' are lower order concepts. Knowledge
about procedures is also held (for example, how to park and how to change
These hierarchical information networks are referred to as
"schemas". Schemas build in detail and complexity as more extensive knowledge is
acquired in a content area. The network in the diagram above is part of your
schema for cars held in your long-term
Individual differences exist in the nature and
details of schemas. Someone who is employed as a mechanic and spends their
pastime rebuilding vintage cars will have more detailed and complex schemas for
cars than most people.
Schemas that are well learnt may be recalled and
applied with relative ease. For example, someone learning to drive a manual car
needs to concentrate intently on the knowledge and skills required to coordinate
the movements of the clutch, gear stick and accelerator, in order to change
gears smoothly. After several years of driving, however, most people are able to
change gears "automatically". As automation develops, there is a reduction in
the need for concentration.
3.2 Process of learning
The previous section (Section 3.1) argued
that when we say that "something has been learnt", we mean that is has been
successfully encoded into long term memory and can later be recalled on
The next question to be considered is 'how does information
become encoded into long term memory?' While the factors which contribute to
encoding may vary from one situation to another, there is one factor that is
always present. To be encoded, information must first be attended to, and
processed by, working memory . If for any reason, working memory is unable
to attend to a body of to-be-learnt information, then learning will be
This has important implications for instructional design
because the limitations of working memory may impede the learning process. This
forms the basis of cognitive load theory.
Try to learn the following
rhyme without paying attention to it.
..........Twinkle twinkle little
star, how I wonder what you are.
In all likelihood you had not proceeded
past the word 'star' before you became aware that you already knew this rhyme.
Indeed, you could probably add a few more lines of the rhyme without
You were instructed to learn this rhyme without paying
attention to it . The fact that you "recognised" the rhyme as one that you
already know, shows, however, that you did attend to the information. Perhaps
you feel that this is due to the fact that a well known rhyme was used. Try the
Try to learn the following rhyme without paying attention to
..........Emus and elephants into the stew, rub turns your until it
If you were aware of any grammatical problems with this
statement, then you have again been paying attention to it. Once again, you
could not help yourself.
Working memory, as the embodiment of our
consciousness, cannot be "turned off" or "by passed" while we are
3.3 What a novice needs to learn to become an expert
For any given
cognitive domain (algebra, crosswords, astrophysics, chess, electronics) we
think of novices in that area as not knowing much and for their performance to
be slow and error prone. In contrast we view experts as knowing almost
everything and assume their performance to be quick and error
Contrary to popular belief, expertise does not appear to be due to
anything as robust as "intelligence". Nor does it appear that experts are more
"thoughtful" than novices.
The only two distinguishing features of
1 . the expansive schemas (information
networks) that experts hold, and
2 . the high level of
automation (ability to perform tasks without concentrating) that experts
Schemas and automation appear to explain
all other expert/ novice differences.
Experts, because of their
expansive set of schemas, have effectively seen almost every possible situation
in the content domain before. Moreover, they have learnt what response is
required for each situation and can carry out the required responses
automatically, without the need for high levels of concentration. Experts are
effectively just going through a set of routine exercises. It is no surprise
then that experts are so fast and accurate in their
Novices, on the other hand, have relatively few schemas.
They have trouble recognising anything but the most basic and common situations
as ones that they have encountered previously. Novices are presented with a
"problem" almost every time they venture into the content domain (problem being
defined as not knowing what to do or how to do it). Novices must "solve" almost
every situation presented to them. To make matters worse, even when they realise
what response is required, they may have difficulties in performing the
response. They need to concentrate intently if they are to avoid making
Consider the task of reading this page of printed material.
Presumably you may do so with little effort. While you need to concentrate on
the arguments being presented, it is likely that you do not need to
concentrate on the actual task of reading, that is, on the interpretation of all
these squiggles which represent letters of the alphabet, which are sequenced to
form words, which are sequenced to form sentences, and so on.
The task of
reading is incredibly complex yet we use written documents as an easy and
efficient way to communicate ideas.
All this changes, of course, if the
reader is young (say five years old).
And what chance would a typical
three year old have of reading even one line of this page? None.
three year olds can recite the letters of the alphabet. They can also identify
many, if not all, of the letters in written form. However, lower case letters
may present some difficulties, and running writing may be virtually impossible
for them to handle. If a three year old can spell his or her name (or simple
words like 'cat' or 'dog'), then the adults around the child express praise and
By the age of five a child is likely to have developed
more refined schemas for letter recognition, and perhaps even for recognition of
some words (their name for example). However, there is a general absence of
automation in reading. Reading is slow, error prone, and needs high levels of
concentration (mental effort). It is likely that in "reading" the child will
sometimes sound out the letters of each word in a sentence, but not actually
comprehend the sentence as a whole. This is because their attention needs to be
fully focussed on each word in isolation.
Contrast this to your reading
skills. You no longer need to attend to individual letters or individual words.
It is likely that you can process the text as quickly, if not faster, than you
can say the material aloud. The only times that you need to slow your reading
speed will be when reading becomes "difficult".
One source of difficulty
lies in physical factors such as tiredness (low levels of attention), loud music
(distractions), tiny text or poor lighting (inability to
The more interesting difficulties, however, arise when
something presented on paper fails to fit into your schemas and/or level of
automation. Uncommon or technical words such as 'einstellung' or 'xanthoma', or
misspelt words such es thiis werrd may cause your attention to be directed to
the individual word, perhaps even the individual letters.
The irony about
tasks such as walking, talking and reading is that they are among the most
difficult that humans ever master, yet we are able to perform each of these with
extremely low levels of mental effort. Our schemas in these areas have become so
complete, and our level of automation so high, that we now find each of these
tasks to be almost trivially easy.
A well known proverb states that
"familiarity breeds contempt". In the context of education and training this
should perhaps be modified to read "familiarity breeds
4: Cognitive Load Theory
4.1 Definition of cognitive load
Cognitive load refers to the total
amount of mental activity imposed on working memory at an instance in
The major factor that contributes to cognitive load is the number
of elements that need to be attended to.
Look at each of the following
statements in turn for just a few seconds, and try to memorise the sequence of
digits. Note that you do not need to remember all statements at once. Give all
of your attention to each statement in turn.
For this activity we may use
the number of digits (the elements) to be remembered as a simple measure of
cognitive load. Consequently:
Note that the measure used
for cognitive load does not equate mathematically to task difficulty. That is,
even though statement 2 has twice the number of digits as statement 1, it is
almost as easy to remember.
In contrast, statement 4 has twice the number
of digits as statement 3, yet seems more than twice as difficult to remember.
While statement 3 can be remembered with effort, statement 4 is impossible for
most people to remember without some form of practice or memory aid.
4.2 Reasons why some material is difficult to learn
activity (Activity 4.1) used a digit span task to demonstrate that human working
memory has a threshold of somewhere between 4 and 10
For the previous activity this means that:
the total number of digits to be remembered is four or less then the task is
trivially easy for most people.
2..... when the total number of digits to
be remembered is between five and nine then the task is achievable for most
people if they exert 'some' mental effort.
3.....when the total number of
digits to be remembered is ten or more then the task is difficult for most
In many ways, however, this task is artificial. People are rarely
required to memorise sequences of random digits. After all, even telephone
numbers and post codes may have an underlying logic.
Most of the
information that we are required to learn in our lifetime is far more complex
than a simple sequence of objects (whether they be digits in a telephone number,
or items on a shopping list). Content areas such as mathematical calculus,
biochemistry and computer programming are considered to be "difficult" to
master. One of the reasons for this is undoubtedly the sheer volume of
information that must be acquired (and built into schemas) before an expert
knowledge base is held in the area. But there is another critically important
quality that is evident in these content areas: that of 'high element
Element interactivity is defined as the degree to which
the elements of some to-be-learned information can, or cannot, be understood in
isolation. While the nature of element interactivity is difficult (and often
subtle) to comprehend, a simple example may assist in describing this
Example 4.2 - Element
Consider the task of learning a
foreign language. Most people can quickly learn some simple, everyday words, but
will have difficulty in generating grammatically correct sentences, even when
all of the words used in the sentence are known.
Vocabulary is an example
of low element interactive material. Although there may be literally thousands
of words to be learnt, most words may be learnt in isolation to all of the other
To build sentences that are grammatically correct, however, one
must attend to all of the words within the sentence at once while also
considering syntax, tense, verb endings and so on. Grammar is an example of high
element interactive material because to learn it, many elements must be
Determine if either of the following
statements could be true.
.....1. My fathers' brothers' grandfather is my
grandfathers' brothers' son.
.....2. My fathers' brothers' grandfather is
my grandfathers' brothers' father.
Although each of these statements
requires only a few elements (people) to be considered, the activity is
extremely difficult because there is a need to also attend to the relationships
between the elements. This is an example of "complex" information where
elements interact with each other. As a consequence of the high element
interactivity, the cognitive load induced exceeds the resources of working
The cognitive load associated with this material can be greatly
reduced if the information is presented pictorially. Elements which interact
with each other often have the potential to be presented in pictorial form,
where the picture itself holds (and conveys) some of the information, reducing
the need for it to be held in working memory.
The partial family tree
presented below shows that statement 2 is logically possible.
4.3 Elements held in working memory are schemas
This paper has
argued that the limited resources of working memory mean that only a few
elements of information may be attended to at any given time.
previous section (Section 4.2) demonstrated that to-be-learned information which
has a high level of element interactivity imposes a cognitive load over and
above that imposed by the elements themselves, due to the need to attend also to
the relationships between elements. Consequently, high element interactive
material exacerbates the difficulties which result from working memory
All of this begs the question "what is an element?" The
short answer is "that it depends". It depends on the schemas held by the person
who is required to attend to some body of to-be-learned information because
generally, elements are schemas. What is a single element consisting of a single
schema for an expert may be several elements consisting of sub-schemas for a
Consider again the contrast between statements of the type
represented by 1. and 2. below.
The first statement presents
itself as a random sequence of letters and spaces. It is without meaning and
consequently each letter and each space is a separate element which working
memory needs to attend to.
In contrast, the second statement contains
obvious meaning. Each cluster of letters forms a meaningful word, and the words
combine to form a meaningful sentence. Here the number of elements for an expert
reader, who knows a little about the behaviour of dogs and cats, may be as few
as one. After all, it is a grammatically correct sentence, and it is well known
that dogs do chase cats.
Schemas not only provide the ability to combine
'many elements' into a single element. They also have the capacity to
incorporate the interactions between elements. This means that information which
consists of several elements, all of which interact with one another, may be
embodied into a single schema.
For example, a professional fibre glasser
holds a schema for 'mixing resin' which takes into account not only the ideal
ratio of resin and catalyst that need to be mixed, but also, automatically,
considers interacting factors such as the air temperature, air moisture, and
purpose of the mixture. It is likely that a novice in this area would not even
know that if environmental factors such as temperature and moisture are not
taken into account, then a defective mixture may result.
4.4 Intrinsic and extraneous cognitive load
load Intrinsic cognitive load is due solely to the intrinsic nature
(difficulty) of some to-be-learned content. Intrinsic cognitive load cannot be
modified by instructional design. For example, content which is high in element
interactivity remains high in element interactivity regardless of how it is
Extraneous cognitive load Extraneous
cognitive load is due to the instructional materials used to present information
to students. Teaching materials addressing a concept such as continental drift,
for example, will be more effective if it makes an appropriate use of graphics
rather than a text only presentation.
By changing the instructional
materials presented to students, the level of extraneous cognitive load may be
modified. This may facilitate learning.
1. When intrinsic cognitive load is
low (simple content) sufficient mental resources may remain to enable a learner
to learn from "any" type of instructional material, even that which imposes a
high level of extraneous cognitive load.
2. If the
intrinsic cognitive load is high (difficult content) and the extraneous
cognitive load is also high, then total cognitive load will exceed mental
resources and learning may fail to occur.
the instructional materials to engineer a lower level of extraneous cognitive
load will facilitate learning if the resulting total cognitive load falls to a
level that is within the bounds of mental resources.
4.5 Principles of cognitive load theory
Cognitive load theory
focuses on the role of working memory in the learning process.
fundamental principles of cognitive load theory rest upon the following
1. Working memory is extremely
2. Long term memory is essentially
3. The process of learning requires working
memory to be actively engaged in the comprehension (and processing) of
instructional material to encode to-be-learned information into long term
4. If the resources of working memory are
exceeded then learning will be ineffective.
4.6 Applying cognitive load theory to instructional design
fundamental principles of applying cognitive load theory to instructional design
rest upon the following argument.
1. Excessively high
levels of cognitive load may result directly from the instructional materials
presented to students.
2. Redesigning instructional
materials to reduce the levels of extraneous cognitive load may enhance
3. Content areas that are most likely to
demonstrate beneficial results from improved instructional design are those that
deal with "complex" information where the elements of to-be-learned information
interact with one another (therefore imposing a high level of intrinsic
Summary 4.6 - Applying cognitive
load theory to instructional design
theory states that learning will be maximised by ensuring that as much of a
learners' working memory as possible is free to attend solely to encoding
5: Effects Generated by Cognitive Load Theory
5.1 The different effects
Cognitive load theory has been used
successfully to develop several instructional techniques which facilitate
.....the goal free effect
worked example and problem completion effect
.....the split attention
.....the redundancy effect
5.2 Benefits for learning
Each of the effects listed above in
Section 5.1 has been shown empirically to provide strong benefits to learners
when used appropriately. In each case the benefits include all of the
.....reduced training time
on test problems (similar to those seen during training)
performance* on transfer problems (those which are dissimilar to problems seen
during training but requiring the same rules for
Note : Enhanced performance* means both
shorter times to complete problems, and fewer errors.
The fact that
students spend less time learning, yet return superior performances when tested,
is a powerful finding that has considerable implications for education and
Of special importance is the increased performance on transfer
problems. This shows that the learning which results from each of these effects
is at a level of true understanding that enables students to solve a wider range
of problems than those students taught using "conventional" instructional
5.3 Generating a measurable effect
Each effect has been developed
by the argument that engineering a cognitive load which falls within the
limitations of working memory facilitates learning.
The specifics which
determine when and how each of the effects operate for a given set of learners
on a given set of to-be-learned content, may be found in the original research
Of particular importance to the successful generation of these
effects is the expertise of the learner relative to the to-be-learned
When learners hold high levels of expertise in the content
area then the elements which their working memory may attend to are each, in
and of themselves , large complex knowledge networks (high level schemas).
Consequently, their working memory need only consider a few elements in order to
hold all of the to-be-learned information in mind. Ample cognitive resources
thus remain for the process of learning. Instructional design manipulations for
this group of learners will be ineffective because their working memory capacity
is not being exceeded.
In contrast, when learners hold a low level of
expertise in the content area then only simple elements (low level schemas) have
been acquired (perhaps almost none in the case of true novices). Consequently,
working memory needs to attend to many elements in order to hold all of the
to-be-learned information in mind. Here, cognitive resources are stretched
beyond their capacity and insufficient cognitive resources remain for the
process of learning. Instructional design manipulations for this group of
learners will be effective if the reduction of cognitive load results in a level
that is within the capacity of working memory.
The dynamics of generating
any of the effects thus depends on obtaining a group of students whose relative
level of expertise to content difficulty is ripe for instructional design
manipulations. (See Cooper & Sweller, 1987, for details on how student
ability impacts upon the generation of a measurable effect.)
5.4 Conventional problems
Before presenting information detailing
the effects generated by cognitive load theory a brief overview describing
conventional problems, and the process by which novices solve conventional
problems, will be presented. This is because both the goal free effect and the
worked example effect are based upon the finding that the method employed by
novices to solve conventional problems (means-ends analysis, which is discussed
in the next section) imposes a relatively high level of cognitive load (Sweller,
Conventional problems are those which present students with a set
of given data (the known information) and a well defined goal (specifies what
needs to be found). Moreover, the answer may be objectively determined to be
correct or incorrect by applying rules (such as formulae) in an algorithm based
Conventional problems are typically found in all topic areas of
mathematics and science, and in all subject areas that make use of mathematical
principles (for example engineering, accountancy and computer
If y = x +
6, x = z + 3, and z = 6, find the value of y
A particle starts from
rest and is accelerated at 12 m/s2 for 4.5 seconds. What is its
For the right triangle shown, determine the length of the
5.5 Using means-ends analysis to solve problems
is a problem solving heuristic (strategy) which is widely used to solve
conventional problems by people who are not highly familiar with the specific
problem type (Larkin, McDermott, Simon & Simon, 1980; Simon & Simon,
Means-ends analysis is based upon the principle of reducing
differences between the current problem state (which begins at the problem
givens) and the goal state. In practice, this procedure often results in a
problem solver working backwards from the goal to the problem givens, before
then working forwards from the givens to the goal.
While this strategy is
very effective in obtaining answers (assigning a value to a goal state) it has a
necessary consequence of inducing very high levels of cognitive load. This is
because the nature of the strategy requires attention to be directed
simultaneously to the current state, the goal state, differences between them,
procedures to reduce those differences and any possible subgoals that may lead
to solution. Full details of how means-ends analysis operates, and its
consequences for working memory, are presented in Sweller
If y = x + 6, x = z
+ 3, and z = 6, find the value of y .
A novice problem
solver (using means-ends analysis) would first focus on the goal state (find the
value of y).
Rereading the question s/he would note that the value of "y"
is provided by the equation "y = x + 6", so finding the value of "x" becomes a
Similarly, a further rereading of the question would show that
the value of "x" is provided by the equation "x = z + 3", so finding the value
of "z" becomes a subgoal also.
Rereading the question yet again s/he
would identify that the value of z is provided as given information (z = 6).
This value may now be substituted into the equation "x = z + 3" to obtain the
value "x = 9".
A true novice at this point may forget why the value of
"x" was required. After all, their working memory has been heavily taxed
attending to many elements of the problem.
Nevertheless, he or she will
eventually identify that the value of "x" was calculated so that it could be
substituted into the equation "y = x + 6". Doing so yields the value of "y =
15", which is the goal state.
As can be seen by this example (and this is
just a simple problem), means-ends analysis is very cumbersome, and requires
large amounts of cognitive resources for the strategy to be implemented
successfully. Problem solvers using means-ends analysis may successfully solve
"many" problems of an identical type, yet effectively learn nothing from the
activity (Sweller & Levine, 1982)
5.6 The goal free effect
Means-ends analysis operates on the
principle of reducing differences between the goal state and problem givens.
Consequently, means-ends analysis may be rendered inoperable by redefining the
problem goal so that no obvious goal exists (for example, "find what you can").
This is the principle behind the generation of goal free problems.
problems are "goal free" then a problem solver has little option but to focus on
the information provided (the given data) and to use it where ever possible.
This automatically induces a forwards working solution path similar to that
generated by expert problem solvers. Such forward working solutions impose very
low levels of cognitive load and facilitate learning (Owen and Sweller, 1985;
If y = x +
6, x = z + 3, and z = 6, find what you can.
focus on "z = 6" as this is the only variable specified as a numerical
Rereading the question it would be identified that the value of "z
= 6" can be substituted into the equation "x = z + 3". Doing so provides "x =
Rereading the question it would now be identified that the value of
"x =9" can be substituted into the equation "y = x + 6". Doing so provides "y =
Nothing else remains to be found.
It can be seen that this
solution path is far simpler than that generated by means-ends analysis in
starts from rest and is accelerated at 12 m/s2 for 4.5 seconds. Find
what you can.
the right triangle shown, Find what you can .
5.7 The worked example and problem completion effect
subjects such as mathematics and science have been taught using the following
Step 1 :Introduce a new topic.
Present background knowledge, principles and rules.
2 :Demonstrate, using a few worked examples, how to apply the
principles and rules.
Step 3 :Have the students
"practice" how to apply the principles and rules by solving many ,
conventional, goal specific problems.
Section 5.5 described how the use
of means-ends analysis to solve conventional problems imposes high levels of
cognitive load, and thus impedes learning. It is therefore likely that the
emphasis given to "practice problems" described above will not result in
While the use of goal free problems
provides an effective alternative to conventional problem solving its
application is limited to situations where the problem space is "small". As the
size of the problem space becomes "large" the increasing number of alternatives
faced at each step in a solution render the technique impractical for teaching
An alternative technique may be found in reconsidering the
nature and purpose of worked examples. Worked examples are presented to students
to show them directly, step by step, the procedures required to solve different
problem types. Worked examples contain explicit information that equates to
schemas and automation.
That is, worked examples promote the acquisition
of knowledge and skills required to: .....identify problems as being of a
particular type, .....recall the steps (in sequence) needed to solve each
particular type, and .....perform each step without error.
worked examples imposes a low level of cognitive load because attention need
only be given to two problem states at a time and the transformation (rule
operator) that links them.
A successful method for placing emphasis on
worked examples is to present them with conventional problems in an alternating
sequence (example type A, problem type A, example type B, problem type B and so
on). Students are informed of the paired nature of the material and instructed
to study each example closely because they will not be allowed to look back at
it once they begin the associated problem.
Students thus focus their
attention on the problem type and the associated steps to solution (the
schemas). In solving the associated conventional problem they are testing
themselves to determine if they have learnt the procedure. This may be a more
genuine form of "practice problem solving".
- A worked example format for teaching algebra.
the numbered sequence, first study the worked example, then cover it, and
attempt to solve the associated problem.
For each of the following, solve
problem completion procedure has a similar rationale and effect
to the use of worked examples (see Paas, 1992; Van Merrienboer and Krammer,
1987). Instead of providing an entire worked example followed by a problem,
students are just provided with partially completed worked examples. For
instance, in example 1 above, they may be provided with the first two lines and
required to complete the third line themselves.
The specific details regarding the number of
example-problem pairings or completion problems to present, the range of
examples to present, the rate at which the orbit of problem type is increased
and so on, depends on the complexity of the material relative to the expertise
of the learners. The greater the relative expertise, the quicker the pace of
increase in problem types.
Worked example techniques have been
demonstrated to be highly effective at facilitating learning across a wide range
of mathematically based content (see Cooper and Sweller, 1987; Zhu and
Simon,1987; Pass and Van Merrienboer, 1994).
5.8 The split attention effect
Many instructional materials require
both a pictorial component and a textual component of information.
Conventionally a graphic has been presented with the associated text above,
below, or at the side. Such instructional presentations introduce a split
attention effect where the student needs to attend to both the graphic and the
text. Neither the graphic, nor the text, alone, provide sufficient information
to enable understanding. The instructional material can only be understood after
the student has mentally integrated the multiple sources of information. The
portion of working memory that needs to be used in integrating the graphic and
text is unavailable for the learning process. Consequently learning is
Consider this conventional mathematics based example, taken
from Sweller, Chandler, Tierney & Cooper (1990).
5.8.a - Split instructional format for teaching co-ordinate
The presentation may be
restructured to improve learning by physically integrating the solution into
the graphic to produce a single source of instructional information. This
eliminates the need to split attention between the graphic and the text. The
association between the text and the graphic is clearly
Example 5.8.b - Integrated instructional
format for co-ordinate geometry.
The split attention
effect is not limited to worked examples in mathematics. It is demonstratable in
all contexts where a graphical and a textual presentation are both necessary to
Consider the instructional material presented below
dealing with electrical testing. (Taken from Chandler & Sweller,
Example 5.8.c -Split instructional format for
teaching a procedure. INSULATION RESISTANCE
TESTS a) CONDUCTORS IN PERMANENT
Test : To test Insulation Resistance from conductors to
How conducted : i ) Disconnect appliances and busways during these
tests. Make sure mainswitch is "on" and all fuses are "in". Remove main earth
from neutral bar and set meter to read insulation. Connect one lead to earth
wire at MEN bar and take first measure by connecting the other lead to the
active. Take next measure by connecting the lead to the neutral.ii) If
resistance is not high enough in either of the two tests in i) then measure each
Results required : i) At least One Megaohm ii)
Same result as i) above
Again, by reformatting
the material so that the instructions are integrated into the graphic, learning
is enhanced. In fact, in this study, evidence indicated better performance
resulted on both theoretical and practical
Example 5.8.d - Integrated instructional
format for teaching a procedure.
TESTS a) CONDUCTORS IN PERMANENT
5.9 Sources of split attention
The examples presented in Section
5.8 (the split attention effect) focussed on the need to eliminate split
attention effects which result from separate textual and graphical components of
instructional materials. Appropriately integrating the text into the graphic
Split attention, however, will result
whenever a learner needs to simultaneously attend to two or more
sources of instruction or activities.
Multiple sources of purely text
based instructional materials will induce a split attention effect if two or
more sources must be considered simultaneously. For example, this is likely to
occur when cross referencing documents, or even cross referencing within a
Chandler and Sweller (1992) provided evidence that a
split attention effect occurs when reading conventional experimental papers
because the results section and the discussion section are reported separately,
yet need to be considered simultaneously to understand the complex of results
and their implications. Here the split attention effect may be eliminated and
intelligibility increased, by restructuring experimental papers to integrate the
results and discussion sections.
A split attention effect may also result
from mixing activities. For example, when learning to use a software package it
is common practice for the learner to simultaneously refer to a hard copy
tutorial (or manual) and the computer. The tutorial provides
step-by-step instructions for performing each task and the learner attempts to
carry out each step on the computer. While this may seem to be an obvious way of
learning a software package, experimental investigations have shown that far
more effective learning strategies are available.
modification is to eliminate the use of the computer in the learning phase and
replace it by appropriate pictures and diagrams. Provided the manual contains
all of the relevant information, then students who study the manual alone
outperform students who perform each step in sequence on the computer based upon
the manual instructions. The irony here is that the manual-only-group complete
their "training" without ever having used the software package, yet in testing,
on a computer with the real software, they perform better than the group who has
already spent time using the software package. See Chandler and Sweller (1996)
Another alternative is to develop a computer based training
package which integrates text based instructions into a computer simulation of
the target computer package. When this is done the manual may be eliminated from
the training process, leaving students to focus their attention wholly on the
computer screen. This eliminates split attention and facilitates learning. See
Cerpa, Chandler & Sweller (1996).
Summary 5.9 -
Sources of split attention
Split attention occurs whenever a
learner needs to attend to more than one source of information, or more than one
activity. A common source of split attention is the need for a learner to
perform a search. Searching a graphic to locate a component, searching a
document to find a reference and searching software pull-down menus to find a
function referred to in a manual are all examples of split
Redesigning instructional materials to eliminate search and
other sources of split attention facilitates learning.
5.10 The redundancy effect
Sections 5.8 and 5.9 described the
benefits which result from integrating mutually referring textual and graphical
sources of instruction.
Caution needs to be exercised, however, to ensure
that both sources of instruction truly are necessary for the to-be-learned
information to be intelligible.
In situations where a source of textual
instruction, or a source of graphical instruction alone provides full
intelligibility then only one source of instruction should be used (either the
textual or the graphical), and the other source, which is redundant, should be
removed completely from the instructional materials. In these contexts a single
source of instruction returns higher levels of learning than either an
integrated format (text integrated into the graphic), or a dual format (both
text and graphic presented in parallel).
Cognitive load theory explains
this result by focussing on the levels of cognitive load imposed upon the
learner who needs to process the varying instructional
Attending to both textual and graphical sources of instruction
requires more mental resources than attending to a single source. Attending to
both textual and graphical sources of instruction, therefore, results in a
reduced portion of working memory being available for the process of
Maps, whether their purpose is to locate countries (an atlas),
indicate the steepness of terrain (a topographic map) or to show the way to get
from A to B (a street directory) are examples of graphically based sources of
instruction that are fully self contained. Provided the user has the skills to
read and interpret a map, then there is no need for any associated body of
Similarly, many instances of textual instruction
have no need for graphics. Arguments of litigation, analysis of history and the
use of a dictionary or thesaurus are fully intelligible in a text-only format.
The use of graphics in these situations actually reduces the level of learning
that results from the use of these documents.
5.10.a - Redundant textual information in a dual
5.10.b - Redundant textual information in an integrated
This example, dealing with the functions of the heart, is
taken from Chandler and Sweller (1991). Note
The graphic contains labels to indicate parts of the heart, and arrows
to indicate the flow of blood.
The textual statements which are
integrated into the graphic do nothing other than restate the parts and the flow
of blood. On this basis the textual statements are redundant and should be
deleted from the instructional material.
Students presented a graphic
only instructional format learn more than students presented either an
integrated format or a dual format.
5.11 The modality effect
All of the effects discussed so far in
this paper have emphasised the need to reduce cognitive load because of the
limitations of working memory.
While information processing models of
learning have historically emphasised the "fixed" limits of working memory,
there is evidence (Pavio, 1990; Baddeley, 1992) that under some conditions, an
expansion of working memory may be achieved.
Consequently, rather than
attempting to reduce cognitive load, an alternative strategy, that of expanding
working memory, may be pursued as a means of facilitating learning.
work by Pavio and Baddeley indicates that at least some portions of working
memory appear to be sensory mode specific. That is, some portion of working
memory is dedicated to attending to visual information only (especially
diagrammatic information) and some other portion of working memory is dedicated
to attending to aural information only (especially verbal information). (Note,
however, that the majority of working memory appears to be in the form of a
central resource which may be allocated to any type of sensory
Partitioning to-be-learned information so that some
information, such as graphics, is presented visually, while other information,
such as text, is presented auditorily enhances learning (see Mousavi, Low and
Sweller, 1995; Jeung, Chandler and Sweller, 1997; Tindall-Ford, Chandler and
Sweller, 1997). The modality effect holds the potential to impact upon the multi
5.11 - Mixed mode instructional format
This example is
taken from Jeung, Chandler and Sweller
(1997). Notes: 1. The graphic is presented
visually but the text is only presented auditorily. 2. Screen
highlights (flashing) were used to identify the components of the graphic
referred to by each auditory statement to eliminate screen search.
two parallel lines intersect with a third line, four pairs of corresponding
angles are equal. In the diagram, two parallel lines, AB and CD, intersect with
a third line, XY. The following four pairs of angles are corresponding
Section 6: Summary and Discussion
Cognitive load theory displays
strong consistencies with current knowledge regarding memory, thought, learning
and problem solving.
It is a theory which views the limitations of
working memory to be the primary impediment to learning. Reducing total
cognitive load imposed by a body of to-be-learned information increases the
portion of working memory which is available to attend to the learning process.
This may only be achieved by engineering reduced levels of extraneous cognitive
load through instructional design.
It is interesting (and important) to
note that the effects generated by cognitive load theory often "fly in the face"
of standard practices. This attests to the strength of the theory. The table
below outlines this observation.
The effects generated by
cognitive load theory should be viewed as "rules of thumb" rather than absolute
"laws of instruction". The bottom line, according to cognitive load theory, will
always be the need to reduce total cognitive load, and the need to maximise
cognitive resources available to be utilised in the learning process. If for
some reason cognitive load increases rather than decreases, then learning will
For example, the worked example effect will not occur if
the examples used actually increase, rather than decrease, extraneous cognitive
load. This is the case for examples which impose a split attention effect.
Redesigning the format of the examples to eliminate split attention returns the
educational benefit of the use of the worked examples.
The success of
cognitive load theory in developing strategies and techniques which result in
both reduced training times and enhanced performance is of paramount importance
to the education and training industries.
Any fears that the application
of instructional design techniques generated by cognitive load theory may result
in a "poorer" quality of student or worker who is less able to think and act
independently in unusual or unforeseen situations are totally unfounded. Over
the last ten years a large body of evidence has been acquired to show that
students taught using cognitive load generated materials are actually more able
to deal with such unusual or unforeseen situations as attested to by their
superior performances on transfer problems (those that differ to problems seen
during training, but requiring similar rules for their solution).
should also be noted that current research projects have provided preliminary
evidence for four additional effects generated by the application of cognitive
load theory. These are (1) the procedural learning effect, (2) the imagination
effect, (3) the colour coding effect and (4) the interaction effect. These
effects are not discussed in the current paper as the results are not yet
published (at December 1998). However, the effects appear to be real and promise
to deliver further strategies for instructional
wish to pursue further readings in cognitive load theory then try: 1. Sweller
(1991), a very short, non technical description of how educational practice is
often based upon myths rather than empirical research, and then 2. Sweller
(1994) which presents a more detailed (though still non-technical) review of
cognitive load theory and the effects generated. 3. Sweller, Van Merrienboer
& Paas (1998) which presents a detailed (and partially technical) summary of
human cognitive architecture and the implications for instructional
After that you may wish to go to the original journal papers.
Ayres, P. (1993).Why goal free problems can facilitate
learning. Contemporary Educational Psychology, 18 ,
Baddeley, A.D. (1992). Working memory. Science, 255,
Cerpa, N., Chandler, P., & Sweller, J. (1996). Some
conditions under which integrated computer-based training software can
facilitate learning. Journal of Educational Computing Research, 15,
Chandler, P., & Sweller, J. (1991). Cognitive load theory
and the format of instruction. Cognition and Instruction,8,
Chandler, P., & Sweller, J. (1992). The split attention
effect as a factor in the design of instruction. British Journal of
Education Psychology, 62, 233-246.
Chandler, P., & Sweller, J.
(1996). Cognitive load while learning to use a computer program. Applied
Cognitive Psychology, 10, 151-170.
Cooper, G., & Sweller, J.
(1987). Effects of schema acquisition and rule automation on mathematical
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Jeung, H. J., Chandler, P., & Sweller, J. (1997). The role
of visual indicators in dual sensory mode instruction. Educational
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