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Forgetting curve
The forgetting
curve illustrates the decline of memory retention in time. A related concept is
the strength of memory that refers to the durability that memory
traces in the brain
. The
stronger the memory, the longer we can remember it. A typical graph
of the forgetting curve
shows that humans tend to halve their memory of newly learned knowledge in a matter of days
or weeks unless they consciously review the learned material.
We can roughly
describe forgetting with
where is memory
retention, is relative strength of memory and is time
.
The speed of forgetting
depends on a number of factors such as the difficulty of the learned
material (e.g. how meaningful it is), its representation (see: mnemonic
), and physiological factors
such as stress
and sleep
. Interestingly, the basal forgetting rate differs little between individuals.
The difference in performance (e.g. at school) can be explained by mnemonic representation
skills. This means that some people are able to "imagine" memories in the right way while
others
are not.
Basic training
in mnemonic techniques can help overcome those differences in part. The best
methods for increasing the strength of memory are:
Each repetition in learning increases the optimum interval before the next repetition
is
needed (for near-perfect retention
, initially repetitions may need to be made within days,
but later then can be made after years)
The first significant
study in this area was carried out by Hermann Ebbinghaus
and published in
1885 as Über das Gedächtnis (later translated into English as Memory. A Contribution
to
Experimental Psychology). Ebbinghaus studied the memorisation of nonsense syllables, such as
"WID" and "ZOF". By repeatedly testing himself after various time periods and recording
the
results, he was the first to describe the shape of the forgetting curve.
The forgetting
curve is steepest for nonsensical material such as that studied by Ebbinghaus. On
the other hand, it is nearly flat for vivid or traumatic memories. The flatness of the curve is not
necessarily evidence for the decrease in the forgetting rate
, but can be taken as evidence of
implicit repetition (e.g. reliving memories) that indefinitely restores memory traces.
In a typical schoolbook
application (e.g. learning word pairs), most of students show the
retention of 90% after 3-6 days (depending on the material). This means that, in this period, the
forgetting curve "falls" by 10%.
Organization and
Retrieval in the Long Term Memory (top
)
Organization
When does Wednesday
come after Thursday?
Clustering
Items recalled
from long-term memory are clustered or grouped.
The clustering
is based on some logical association between the items.
What is the first
word that comes into your mind when you hear the word "red"?
Collins & Loftus
(1975) proposed the well-known semantic network model.
In this model,
each concept is linked with a set of others, which are in turn linked to still others.
A specific iten
can be linked with a category (rose®bush) or vice-versa (flower®daisy).
An object can be
linked with a characteristic (knife®sharp), and vice-versa.
A place can be
linked with an activity (classroom®sleep), and so forth.
The concepts and
their links form a network.
Some linkages are
stronger than others.
When a concept
is activated, the activation can spread to linked concepts, activating them.
The shorter and
stronger the chain of linkages, the more quickly one concept leads to another.
Retrieval Cues
Retrieval is the
process of putting the contents of long-term memory into working memory.
Retrieval often
depends on a retrieval cue, a hint or prompt that triggers the memory.
When you are unable
to recall information due to missing, inadequate or inappropriate cues you
are experiencing retrieval cue failure.
Very often the
unrecalled information is in fact in LTM.
Have you ever had
something on the tip of your tongue? The tip-of-the-tongue phenomenon
occurs when you have the feeling that you know a piece of information but you can't quite recall
it at the moment. These experiences have been studied by a number of memory researchers.
Usually some part of the information can be recalled.
About half the
time, people can recall the first letter of the word or name they are looking for
and often they know the length of the word (in syllables).
Often people produce
similar sounding, looking or meaning words.
The recalled bits
may serve as cues to retrieve the missing piece.
The missing word
usually comes to mind some time after you stop trying to think of it.
Tip-of-tongue experiences
highlight that retrieval is not a simple all-or-none process.
There are different
types of recall:
Recall or free
recall is the retrieval of information with no cues.
Cued recall is
the retrieval of information in response to a cue (complete the sentence).
Recognition is
simply identifying a piece of retrieved information (as on a multiple choice test).
Serial effects:
Serial recall is
the retrieval of information in order.
It doesn't do you
much good to remember the directions to a friends house unless you
remember them in order: "I know how to get there. You take six lefts and four rights."
Sometimes each
list item cues recall of the next: I remember students more easily in alphabetical
order.
The serial position
effect refers to the relative ease of recalling items at different positions on a
list.
primacy effect:
items at the beginning of the list are more easily recalled
recency effect:
items at the end of the list are more easily recalled
The Encoding Specificity
Principle
Recreating the
original learning conditions improves retrieval.
I remember students
names more easily if they don't move around in the room.
The Context Effect
An encoded memory
may include more than the specific piece of info that was being learned,
such as environmental stimuli present at the time of learning.
These stimuli can
serve as cues to aid in the retrieval of the learned information.
I have an easier
time remembering students' names in class than in the grocery store.
There seems to
be a hierarchy of contexts: the closer the context to the original, the easier it is
to recall (I recently saw a student on Block Island, although he looked familiar, it took me
several minutes to realize that he was a student; I couldn't recall his name for about a half hour).
Students do better
on exams when tested in the room where they learned.
State-Dependent
Learning
A memory may include
not only external cues (as in the context effect) but also internal cues.
Free recall of
things learned while intoxicated is slightly better when done intoxicated (though
overall, learning and recall is worse when you are intoxicated).
Mood Congruence
When you feel good,
you have happy memories; when you are blue, you have sad memories.
Flashbulb Memories
Where were you
when you heard that OJ Simpson had been found not guilty?
A flashbulb memory
is proposed to involve the retrieval of a number of details surrounding a
rare and striking event.
Neisser & Harsch
(1992) carried out an experiment on flashbulb memories:
Immediately after
the Challenger disaster, students wrote down what they had been doing
when they heard the news. Three years later, they were asked to recall the same things.
Most of the students
were very confident of their recollections, but about a third were wrong.
Seeing the proof of their errors, these students still felt confident that their memories were
correct.
The work of Ebbinghaus
is a good place to begin considering revision. Ebbinghaus1was
a 19th
Century German psychologist who studied memory and is famous for his forgetting curve (see
Figure 2
). This work has been reproduced in a variety of contexts. Most of us would believe it to
be true from our own experience.
Attention
Attention is the
focusing of your consciousness on a specific activity. There are different types
and levels of attention, which can be focused on one or more things. Sometimes attention is
involuntary, being drawn from an intensive stimulus. Intensive stimuli usually elicit an orienting
response (sudden captivation and the switching of attention towards the stimulus). However, if
the stimulus is repetitive or continuous, attention will slowly be turned away from it and towards
something else, due to habituation. Attention is not required for some types of activities, such as
registering the general features of your surroundings. Also, over time, some activities that
initially required your full attention may become so automatic that they no longer require you to
focus your attention on them.
Research into which
sections of the perceptual process are influenced by attention culminated in
Donald Broadbent's Filter Theory. This theory proposed that a large amount of sensory
information can be absorbed at once, and that a selective "filter" reduces the input for one
source while the brain is processing the information from another source. The information
placed on hold may later be perceived if it is deemed to be important. Broadbent showed that
an unfocused state of mind allows some learning to take place, but that motivation or interest
may be required to activate these memories.
Dividing attention
between multiple tasks becomes more difficult when the tasks involve the
same abilities. For example, most people can listen to music and read at the same time, while
few people can listen to two people talking to them at the same time. It is believed that this is
due to the anatomical separation of the brain centers that perceive different types of sensations.
Concept Formation
A concept is any
idea that includes a description of the important properties of a category.
Someone who has formed or attained a concept can easily fit new ideas into a category,
thereby acquiring an effective thinking device. While on the surface it appears as though things
in our world form natural groups and categories, concepts are simply the names that people
learn to associate with them. This summary of concepts does not address the fact that concepts
can be false, and neglects that the human mind may impose as well as discover it.
Traditionally,
everything in a category must have some characteristics in common. Thus,
concept formation and attainment is learning what these defining characteristics are. However,
categories do not always need to have something in common, but rather may have a
resemblance structure, where the category members share similar properties but are not
sufficient to firmly place them in the same category. For example, most birds fly, sing, and build
nests in trees. However, ostriches do none of these things, yet they are still birds. So while
ostriches belong in the "bird category", they are not necessarily put into this category when
someone bases their "bird category" purely on resemblance structure.
Research into cognitive
psychology has suggested that concepts are more than just lists of
characteristics. An individual's knowledge and theories in the organization of concepts are also
important. People may demonstrate a bias by assuming that categories have defining properties
and then theorize about what exactly those properties are. Theories such as these may fall
between the ideal properties and the actual properties, leaving the structure of that person's
concepts to be imposed and discovered via the interaction of the mind and world.
Habituation
Habituation is
a decrease in responsiveness to unimportant stimuli or stimuli that do not provide
appropriate feedback. In other words, habituation is learning not to respond to a certain
stimulus. Sometimes when a stimulus is first encountered, the response is immediate and
vigorous. However, if the stimulus is presented many times, the elicited response to it gradually
decreases and may eventually disappear altogether. If the stimulus is withheld for a period of
time after habituation, the response may reappear if the stimulus is later presented. This is called
sensitization.
Habituation is
an important aspect of learning since it increases efficiency. Birds learn not to
waste energy by taking flight at the sight of every leaf blowing in the wind. Squirrels learn not to
respond to the alarm calls of other animals if these calls are not followed by an actual attack.
This may also help us understand why animals avoid predators (since they are rarely seen),
while ignoring common, harmless species.
Imprinting
Imprinting is an
aspect of learning which occurs at an early age. An example of imprinting is
how young geese follow their mothers. But how do the young geese know whom to follow?
Konrad Lorenz addressed
this question in several experiments which led him to discover that
newly hatched goslings would follow whatever moving object they saw first, and would
continue to identify with this object throughout their lives. Lorenz divided a nest of goose eggs,
leaving half with the mother and putting the rest in an incubator. The geese raised by their
biological mother showed normal behavior, following her around during their youth and growing
up to interact with other geese. When the incubated eggs hatched, the goslings spent their first
few hours with Lorenz instead of their mother. From then on, these goslings followed Lorenz
around, showing no recognition of their own mother or even adults of their own species. As
adults, these geese continued to prefer humans over members of their own species. Lorenz's
experiment showed that geese have no instinct telling them who their mother is, or who is of
their species. Instead, they respond to and identify with the first moving object they encounter.
There are two features
that distinguish imprinting from other aspects of learning. First, what is
learned from imprinting is irreversible. Second, imprinting must occur within a critical period,
which is a limited phase in an animal's development during which learning a particular behavior
can occur. For example, Lorenz discovered that goslings isolated from any moving object for
the first two days after hatching failed to imprint on any parent figure afterwards. So for these
geese, the critical period for parent imprinting was two days.
Imprinting has
traditionally been thought of as only involving very young animals rather than
short critical periods. However, it is now known that similar learning processes occur in older
animals, and that critical periods may be of various durations. Not only do young birds require
imprinting to recognize their parents, but the adults also require imprinting to recognize their
young. For the first day or two after their young hatch, adult herring gulls will accept and defend
another chick introduced to their nest, even if it is of a different species.
Memory
Memory is the ability
to remember something that has been learned or experienced. It is also a
vital part of the learning process, since if you were unable to remember anything from the past
you could not learn anything new.
Little is known
about how memories are stored in the brain. Storing memories seems to involve
chemical changes in the brain's nerve cells as well as changes in their physical structure.
Research has shown that these changes seem to occur in a small area of the brain called the
hippocampus. The hippocampus is part of the cerebral cortex, which controls most higher brain
functions (such as problem solving and language). It is believed that memory is acquired via a
series of event in the brain which consolidate and then store the information.
Although there
are many types of memory, they are usually divided into three main groups:
sensory memory, short-term memory, and long-term memory.
Sensory memory
is our instantaneous memory, which is only held for an instant as something is
experienced. For example, when looking at a photograph, sensory memory occurs as the
image of the picture enters your eyes and is transmitted to the brain. This entire process takes
less than a second.
Short-term memory
can hold a piece of information for as long as you actively think about it.
For example, short-term memory is used when looking up and dialing a telephone number. As
long as you are focusing on this information, you are utilizing short- term memory. However,
about twenty seconds after you stop repeating this information to yourself, it will begin to fade
unless it is transferred to long-term memory.
Long-term memory
can last a lifetime. Information enters long- term memory due to either
repetition or intense emotion. So, for example, friends and family will be remembered for a long
time, while someone you only meet once will not. Similarly, the events surrounding a traumatic
experience are remembered, while the typical day-to-day events leading up to it are usually not.
Memory is accessed
by recall, recognition, and relearning. Recall involves thinking of a past
event and trying to list as many details of it as you can. Recognition is isolating accurate details
from more facts than are relevant. Most people tend to recognize more facts than they can
recall, which is why students tend to perform better on multiple-choice tests than on long-
answer tests. Relearning involves memorizing details after you supposedly forgot them. People
tend to relearn information faster than they learned it the first time, depending on how much of
the original learning they actually remember.
There are many
reasons why people forget things over time. The primary explanations include
interference, retrieval failure, motivated forgetting, and constructive processes.
Interference occurs
when remembering certain facts block the memory of other facts. For
example, if one of your friends moves, initially you may not be able to remember his new
telephone number. The old phone number may keep coming to mind, interfering with your
ability to remember the new number. However, after you have thoroughly learned the new
number you may not even be able to remember the old one. When previously learned
information hampers the ability to remember new material, it is called proactive interference. On
the other hand, learning new facts may interfere with old memories, and is called retroactive
interference.
Retrieval failure
is the inability to remember facts that have been stored in long-term memory. A
prime example is when you are unable to think of a name, place, or event, even though it seems
to be "on the tip of your tongue". Often later, when you are no longer thinking about it,
the
information will suddenly come to you.
Motivated forgetting
is the loss of memory due to conscious or unconscious desire. We forget
many things simply because we want to forget them. Motivated forgetting is also called
repression if it involves forcing unpleasant feelings or experiences into the unconscious mind.
Constructive processes
involve the unconscious invention of false memories. When trying to
remember an event from several months or years ago, only a few details may be recalled. The
gaps in those facts are filled with details that seem logical, but may be untrue. Constructing facts
to tell a complete story is called refabrication. Refabricated memories often seem real, and are
almost impossible to distinguish from the memories of the events that actually occurred.
Perception
Perception is the
way we receive and interpret the information we are presented with.
Understanding of our surroundings is perceived by our sense organs. Light and radiation
stimulate our eyes; sound waves and air vibrations stimulate our ears; tastes stimulate our
tongues; and smells stimulate our noses. Our skin is also a sense organ, perceiving pressure,
pain, and temperature.
Through perception,
we learn to associate certain things as being known objects, events, or
people. However, perception does not tell us about the objects, events, or people themselves.
Our brains must organize and interpret what our sense organs perceive, converting
environmental stimuli into information about the world.
There are three
factors that make up perception:
1. Detection: Sensing the stimulus.
2. Recognition: Identifying the stimulus.
3. Discrimination: Differentiating between stimuli (such as different musical notes).
Receptors are important
to perception. Sensory systems (such as vision and hearing) each have
specialized receptors which are sensitive to certain types of stimuli. They receive the
environmental stimuli, and send information to the brain via nerve impulses. For example, the
human eye has two types of receptors in the retina: rods and cones. The rods respond to the
intensity of light, resulting in detailed black- and-white vision. The cones respond to the
frequency of light, perceiving color. Rods allow us to have detailed vision even in dim light,
while the cones enable us to perceive color and vivid detail in bright light.
Many factors (including
experience, expectations, and physical, emotional, and psychological
influences) affect what we perceive. Personal experience, emotion, and motivation are also
important in determining our perception. Experiments have shown that the perception of form,
color, pain, and touch differ between cultures and age groups. Therefore habits, customs, and
education also influence perception. Emotions can prevent perception entirely, such as when an
emotional shock causes someone to temporally lose their hearing. We are also more likely to
perceive stimuli that are related to our motivation. Motivation affects the characteristics we
observe in people, objects, and events, such as when a highly anticipated day seems to take
forever to arrive while the day of an exam seems to rapidly approach.
While many people
believe that an illusion is a false perception, it is actually defined as anything
that is inconsistent with other perceptions. Since perceptions do not impart information about
objects or events themselves, no sensory system is better than another at receiving truthful
perceptions.
Closure is a general
principle of perception that allows us to perceive general or incomplete
things as being complete. Our experience and knowledge allows us to use closure to fill in parts
of a perception that may be missing, or associate a general perception with a known one. On
the other hand, constancy is the principle stating that despite changes that may occur, we tend
to perceive objects as being constant in their physical properties (such as size, shape, and
color). For example, under different kinds of light, we tend to perceive an apple as being red
despite not actually seeing that color. The opposite of constancy can also occur, when an
object stays the same but we begin to perceive it differently. M C Escher's art involving optical
illusions is a prime example of this.
Problem-Solving
A problem exists
when someone has a goal and an idea as how to solve it, but does not know
how to proceed. Problem- solving deals mainly with intellectual problems: those which can be
solved mentally or by manipulation. Problem-solving uses three main methods:
1. Examining what has been said about the problem.
2. Experimenting with the problem.
3. Working through the problem.
Research into problem-solving
has shown that this process is not entirely open to
consciousness. A person may begin by using conscious reasoning, but the solution is often
found suddenly, as if it came out of nowhere. Graham Wallas described the general problem-
solving sequence as containing four distinct stages:
1. Preparation - The problem is defined and possible ways to approach it are explored.
2. Incubation - Attention is turned away from the problem, and towards other things.
3. Illumination - The solution suddenly become apparent.
4. Verification - The solution is checked to confirm that it works.
The first studies
into problem-solving were carried out by Gestalt psychologists, who
emphasized the difference between solving a problem by understanding its structure and finding
the solution by a blind application of known rules. Karl Duncker applied this type of analysis to
multiple-step problems. He discovered that every phase of a solution tends to be a slight
variation of the original problem. Duncker coined the term "functional fixedness" to describe
a
common source of difficulty: if the solution to a problem requires a concept to be used in an
unfamiliar way, a fixation on the familiar usage may prevent the new one from being discovered.
Mathematician Gyorgy
Polya introduced the idea that there are general techniques which can
be applied to solving problems. He called these techniques heuristics: procedures that can help
solve a problem, but cannot guarantee success. One well- known heuristic technique is working
backwards when the answer is known.
Since the 1960s,
computers have been an important contribution to problem-solving. A recent
computer approach involved memory-based reasoning, in which a program compared new
data to previously solved problems and tried to make decisions based on similar cases.
Although computer systems examine the possible solutions more quickly, even the most
complex computer system cannot match the complexity of human reasoning or incorporate
human experience into their problem solving methods.
Reasoning
Reasoning is a
process of directed thinking. We may reason with a specific goal in mind (such
as finding the solution to a problem) or more generally (such as to deal with inconsistencies in
thought).
Reasoning is often
treated as a process that follows the rules of logic, building formal arguments
from fixed conditions in order to reach a valid conclusion. Reasoning can be viewed as a loose
combination of mental processes which are focused towards finding a more coherent view of
an issue. Feelings and sensation may contribute to this process, and the underlying logical
structure can be abandoned if required. Such reasoning is referred to as cognition, concept
formation, problem solving, or thinking. The approach to reasoning can be divided into three
main categories: clinical, learning, and developmental.
The clinical approach
to reasoning studies the ways in which people reason. Sigmund Freud is
well known for distinguishing between the two thought processes believed to be involved: the
primary process (which responds to internal and biological interactions) and the secondary
process (which responds to social and environmental interactions). This conscious and rational
approach to psychoanalysis served to approach the principles of predicting events and
understanding the world.
The learning approach
to reasoning studies apparent behavior and stimulus-response
connections. These behaviorists believe that problem solving involves gradual, continuous, and
automatic behavior changes, and that these general processes form the basis of intelligence and
creativity.
The developmental
approach is based upon four stages. The first stage is sensory-motor
thought, characterized by physical interactions with objects and the idea that objects exist
independently of one's perception of them. The second stage is pre- operational thought, where
the thought process is based upon an internal representation involving symbols that are limited
to the interpretation of appearance. Concrete operational thought, the third stage, is
characterized by reasoning based upon logic and independence from appearance. The fourth
stage, formal operational thought, is based upon systematic, formal, deductive thinking fully
independent from appearance.
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Classification
People who are
gifted are usually defined as having an unusually advanced level of intellectual,
artistic, or academic ability. Most people who are gifted are socially, emotionally, physically,
and creatively successful. The most common diagnostic criterion is an IQ score of at least 130,
accounting for two to four percent of the population. Someone with an IQ score between 130
and 145 is usually labeled as moderately gifted; 145-160, highly gifted; 160-180, exceptionally
gifted; and over 180 profoundly gifted. However, people can be gifted in certain areas while
not others, or have a learning disability. This makes it more difficult to identify certain people as
being gifted.
Characteristics
Although people
who are gifted vary in talents and abilities, most show several of these
characteristics:
Management
Gifted individuals
are usually fortunate in that they can readily adapt to any situation they are
presented with. Their interests, ability, and motivation usually mean that they are self-starters
and require little assistance, academically or otherwise.
Even without special
programs, many gifted students will excel academically while developing
their own interests and abilities. However, academic enrichment within a regular or segregated
classroom can help develop gifted students' abilities. One form of this enrichment is subject-
acceleration, where students progress at their own pace without regard to grade levels. Total
academic acceleration allows students to advance through the grade levels at their own pace,
matching students to the classrooms that are most appropriate in terms of their abilities. Project-
based learning allows students to work on meaningful projects that enhance their learning while
developing non-academic skills. Guided independent study allows students to explore their own
academic interests independent of normal classroom constraints. Special classes and programs
of study are often established, allowing schools to maintain a set curriculum while allowing
students to pursue higher-level study in the subjects they excel in.
Although there
are many alternatives available to gifted students, the main goal is to foster and
encourage the students' emotional and cognitive development. Many gifted students are not
challenged in a normal classroom environment, and enrichment is required to allow these
students to reach their potential. |
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18.1 Introduction
Chapter 15, "Quantitative
Analysis Techniques", introduced the concept of the learning curve.
(Cost improvement is also used to refer to learning curve theory.) Learning curves are useful
both to cost estimators and analysts. While estimators may concentrate on deriving a learning
curve, analysts focus efforts on critiquing a learning curve submitted by a contractor. The
fundamental concepts do not differ, only the application of concepts differ.
This chapter explores
the theory of this learning curve in more detail and will focus on its
applications. Section 18.2 explains the fundamental concepts of learning curves. Sections 18.3
and 18.4 describe both common and special learning curve applications. Section 18.5
discusses criteria that can be used to evaluate learning curves.
18.2 Fundamental
Concepts
The learning curve
was adapted from the historical observation that individuals who perform
repetitive tasks exhibit an improvement in performance as the task is repeated a number of
times. Empirical studies of this phenomenon (Wright, T.P.; Asher, H.; and Boston Consulting
Group) yield three conclusions on which the current theory and practice are based:
Consistency in
improvement has been found to exist in the form of a constant percentage
reduction in time required over successively doubled quantities of units produced. The constant
percentage by which the costs of doubled quantities decrease is called the rate of learning.
The slope of the learning curve is 100 minus the rate of learning. For example, if the hours
between doubled quantities are reduced by 20% (rate of learning), it would be described as a
curve with an 80% slope.
When plotted on
ordinary graph paper with rectangular coordinates,
becomes hyperbolic.
This is because the amount of cost reduction is not constant. Rather, the
amount of decline continually diminishes as the quantities double. With very large quantities, the
decline trickles off to a very insignificant amount, as depicted by the tapering off of the graph in
Figure 18-1. This happens as workers approach a "standard cost" for a process. With
continual change in the process or product, this point can be delayed. Several research studies
of manufacturing operations in the steel, auto assembly, apparel, and musical instruments
industries have described this phenomenon as "plateauing" (Baloff.)
FIGURE
Figure 18-1.
80% Learning Curve on Linear Graph
Although the actual
amount of decline in cost over time is a decreasing one, the amount of
change in cost over the "doubling" period has been observed in empirical studies to be a
constant percentage (Wright, T.P.; Boston Consulting Group.) Constants are helpful because
they simplify the estimation. This type of constant percentage decline in one variable for a
constant decline in another (the doubling of quantity) can be modeled using an exponential
equation. Exponential equations can be solved by using logarithms. In the jargon of the cost
estimating trade, it is common to speak of plotting the learning curve on "log-log" paper--a
reference to bygone days when estimators plotted the learning curve by hand on graph paper
with a logarithmic scale. Plotting learning curve data (such as in Figure 18-1) on a logarithmic
scale causes the points to lie on a straight line, which allows for easy projection of future costs.
Today, computers have replaced log-log paper.
18.3 Unit
and Cumulative Average Theory
Specific types
(i.e., mathematical models) of learning curves have often been named after the
men who proposed them or companies that first used them. They include Wright, Crawford,
Boeing, and Northrup curves. All of these names refer to one of two mathematical models
generally agreed to best describe how costs or labor hours decrease as the quantity of an item
being produced increases. These two models are most commonly referred to as the unit curve
and cumulative (cum) average curve. The equations underlying the models appear to be
identical. However, because of the differences in the definition of the dependent variable, they
predict different results even with identical first unit (also known as Theoretical Unit 1 (T1 for
short)) and slope values. Consequently, an analyst must be aware, before evaluating the slope
used to predict costs, of whether the unit or cum average curve was used to derive the slope.
Learning curve
theory states that as the quantity of items produced doubles, costs decrease at a
predictable rate. This predictable rate is described by Equations 18- 1 and 18-2. The
equations have the same equation form. The two equations differ only in the definition of the Y
term, but this difference can make a significant difference in the outcome of an estimate.
Equation 18-1 describes
the basis for what is called the unit curve. In this equation, Y
represents the cost of a specified unit in a production run. If a production run has generated
200 units, the total cost can be derived by applying Equation 18-1 200 times, for units 1 to 200
and then summing the 200 values. This is cumbersome and requires the use of a computer or
published tables of predetermined values.
Equation 18-2 describes
the basis for the cumulative average or cum average curve. In
this equation, Y represents the average cost of different quantities (X) of units. The significance
of the "cum" in cum average is that the average costs are computed for X cumulative units.
Therefore, the total cost for X units is the product of X times the cum average cost. For
example, to compute the total costs of units 1 to 200, an analyst could compute the cumulative
average cost of unit 200 and multiply this value by 200. This is a much easier calculation than in
the case of the unit curve.
 There are also
important similarities between the two formulations of the learning curve. Both
are exponential functions. This is important information, because the solving of exponential
equations requires the use of logarithms. According to Donald Stancl in Mathematics for
Management and the Life and Social Sciences (page 815), "the method of solution is to take
the logarithm of both sides of the equation and then use the fact that ln Xb = b* lnX to ‘get b
out of the exponent.’" For convenience, it is typical to use the natural logarithm (usually
referred
to as ln in math books and electronic spreadsheets). Knowing the mechanics of how to solve
the learning curve equations using logarithms will help the reader to use electronic spreadsheet
tools effectively.
Taking the natural
logarithms of both sides of the equation reduces the equation mathematically
to a straight line equation of the form ln Y = T1 + blnX or more commonly Y=aX +b. Straight
lines are useful for analysts because a straight line is easy to extend beyond the range of the
data--if you fit a least squares regression line to a data set, it is easy to extend that straight line
and estimate from that line. A curved line, by contrast, is tougher to extend because the precise
angle of the curve is unclear outside the range of the data set. To summarize, the cum average
learning curve equation can be rewritten as Equation 18-3.
Both the unit and
cum average learning curve equations describe and model the observation
that costs decrease by a constant percentage every time the quantity doubles. This is reflected
in the curves through the b value, a constant reflecting the amount of the decrease for every
doubling of quantity. The b value for both curves is computed by Equation 18-4.
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A change in slope can be caused by many factors. The following factors should
be considered
in deciding which slope to use:
The above factors which can cause a slope change also can cause a change in the
theoretical
first unit cost. In other words, it may be more appropriate to adjust the unit cost upward or
downward to account for certain changes, for example where there is a deletion or addition of
a component. If the process has not changed much, but a component is being deleted, there
may not be a change in the learning curve slope, but an adjustment in the T1. Technical experts
(industrial engineers or other engineers likely to understand the process for which an estimate is
being made) should assist in deciding on whether to adjust the slope or T1. An analyst armed
with the right questions, such as those just described, is likely to find technical experts willing
to
give useful input on appropriate learning curve adjustments.
Changes (additions,
deletions, substitutions of components) may be expressed as a percentage of
original effort, as a percentage of effort, or in terms of a specific number of hours or dollars of
effort. The approach to be presented on how to deal with changes implies that changes are
discrete (e.g., the addition or removal of a component such as a radar). However, all modifications
are not necessarily this straightforward. Instead, they may involve such things as the movement of
components, supporting structures, and peripheral devices from one place to another; re-routing of
cabling; additional milling or machining requirements due to design changes; etc. Thus, the form in
which the change is expressed through the learning curve will be driven to some extent, by the
nature of the change itself. For a more complex modification, it may well be that the slope changes,
since slopes are generally steeper for more complex processes. However, the examples in the next
issue are based on the assumption that the change involves a discrete component. Both deletions
and additions of components will be demonstrated, since both cause a "step" in the learning
curve.
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Additions
Whenever a new
component is added to an assembly that is already in production or
installation, several key factors must be considered when analyzing the impact of the addition. It
is logical to assume that the addition of a new component to an assembly already in production
or installation will require additional hours of effort to incorporate the new component.
However, two general assumptions can be made about the nature or behavior of these
additional hours in relation to effort completed prior to the addition:
-
The rate of "learning"
for the added component may be the same as for the rest of the
unit because, under most circumstances, the components will be similar and the work
environment (e.g., company policy, management attitudes, etc.) stable enough that the
same rate of "learning" can be expected.
- Previous "learning," for the
unit being modified does not apply to the added
component. A T1 for the new component must be developed.
From the above,
it can be inferred that an addition should be treated as a new learning curve
having the same slope or rate of improvement as the original unit.
Deletions
A deletion, in
its simplest form, involves the removal of a component from an item that is
already being produced. However, it may be concerned with changes other than the removal of
a discrete component. For example, it could entail such things as a deletion of work,
implementation of less stringent specification requirements, etc. Again, it should be expected
that this type of change will have an impact upon the cost of the item being produced.
However, in this instance, costs should decrease because less effort is required for each
modified unit. In other words, there is not as much work to be performed on each unit as there
was before the deletion occurred.
Human Memory Encoding, Storage, Retention, and Retrieval
Memory is retention
of information over a period of time. Ebbinghaus studied memories by
teaching himself lists of nonsense words and then studying his retention of these lists over
periods of hours to days. This was one of the earliest studies of memory in psychology.
Contents:
-
Short Term Memory
- Working Memory
- Long Term Memory
- Spreading Activation Model
- Practice and Strength
- Depth of Processing
- Elaborative Processing and Text
- Forgetting: Gone or Inaccessible?
- Forgetting: Decay or Interference?
- Retrieval and Inference
- Other Facts about Memory
Short Term Memory
While Ebbinghaus
studied retention over long intervals, later experiments studied memory loss
over periods of seconds to minutes. Short term memory was postulated to explain temporary
retention of information as distinct from long term retention of information . Short term memory
acts to also store current sensory information and to rehearse new information from sensory
buffers. It has limited capacity (Miller's 7 plus or minus 2). The probability of encoding in Long
term memory has been directly related to time in short term memory.
It is now believed
that the loss of information stored in short term memory has the same
characteristics as loss of information stored in long term memory. It happens quicker because it
involves information that is not learned as well. What we call the learning process is transferring
information from short term to long term memory and is a physiological process. The shape of
the memory loss curves are the same. Hence we don't need to postulate a special type of
memory. Instead, we need a theory of:
Working Memory
Here we address
why we can rehearse only limited information at a time.
Articulatory
Loop Rehearsal limitations are due to limits in how long it takes verbal material to
decay, not how many items we can store. Hence, the faster we can rehearse, the more we can
store (Baddeley, 1986). Experimental support: word length effect. How long it takes to read
words predicts how many words will be remembered. Articulatory loop is called the
phonological loop due to evidence that it involves speech. We can rehearse about 1.5 seconds
of verbal material before it decays. Time in the loop is not related to probability of coding in
long term memory. Baddeley's model proposes that we have a visual/spatial sketchpad as well
as the phonological loop. These hold information for use by a central executive. There is
evidence that a particular area of the frontal cortex is involved in working memory.
Long Term Memory
A simple observation:
we often need to recall information that we learned long ago.How
quickly and reliably we recall it depends on:
Experimental
Evidence: (Anderson 1976) - Subjects learn some sentences. Some sentences
are studied twice as long as others. Subjects must discriminate sentences they learned from
distracters. They are tested for each sentence more than once, with varying intervening
sentences. Results: Both amount of study and how recently the information was accessed
affect speed of response. However amount of study matters only if the information was not
recently accessed (an interaction effect).
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Delay
(number of intervening items)
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Degree
of Study
|
|
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Less
Study
|
More
Study
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Short
(0-2)
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1.11
seconds
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1.10
seconds
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Long
(3 or more)
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1.53
seconds
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1.38
seconds
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Spreading Activation Model
When information
becomes easier to access as a result of having been used recently, we say it
is more activated. This activation spreads between semantically related concepts.
Empirical Evidence:
Implication:
Text is easier to read if semantically related words are used.
Practice and Strength
We've seen that
speed of recall of information from long term memory depends in part on how
recently that information has been activated. However, what about the fact that speed of recall
also depends on amount of practice? Activation changes quickly over time. The effect of
practice decays much more slowly over time (witness Ebbinghaus, the alphabet). Thus these
are believed to be distinct processes.
Power Law of
Learning
A very robust result:
the effect of practice in a wide range of different tasks fits a power law
Reaction Time equals
C * Practice Time K where C and K are constants that depend on the
task.
Practice helps
a lot at first, then provides decreasing gains as you reach the limits of your
performance ability.
Long-Term Potentiation
- There appears to be a neural basis for this law of learning. Neural
pathways in the hippocampus (known to be involved in learning) become increasingly sensitive
when stimulated. The change in sensitivity follows a power law relationship.
Depth of Processing
Craik and Lockhart
(1972) proposed that strength of memory depends on how deeply
information is processed, not on how long it is processed
Experimental support:
Memory for words not improved by merely repeating them for a longer
period of time (Glenberg et al. 1977). A large number of studies support the depth of
processing conclusion. It applies to subject matter learning as well as laboratory situations.
Subsequent work focused on what constitutes deep processing.
Processing Meaning:
Some lab studies
compare tasks that require processing meaning of words versus form (e.g.,
what letters do they have).
Elaborative Processing and Text
Studies show benefits
of connecting the items to be remembered to other related information
(e.g., elaborating on sentences to be remembered, or rhyming). Intention does not matter.
Subjects in deeper processing conditions do better regardless of whether they know they will
need to remember the processed items.
Implications
for study habits and method.
-
Preview the material
- Make up questions
- Read, trying to answer the questions
- Reflect while you read. think of examples,
relate it to what you know.
- Recite the information in each section
after you've read it. Re-read what
- you can't recall.
- Review the major points and the answers
to your questions at the end.
- Question generation is at least as beneficial
as question answering.
- Questions generated before the material
rather than after may be more beneficial
Forgetting: Gone, or Inaccessible
Do we forget because
the information is gone, or do we forget because we can't access
information that is still there? It is difficult to distinguish the two. However, there is evidence
that
we retain more than we can retrieve.
Experiment: (Nelson
1971) - Learn paired associates (numbers to nouns). Tested 2 weeks
later to see which were remembered. Then given new material to learn that had some of the
forgotten numbers, both with and without their original nouns.
Results:
Subjects relearned the original associations faster (in spite of the fact that they could
not recall them). Subjects relearned the original associations faster (in spite of the fact that they
could not recall them). This suggests that some associative information was retained. One
possible interpretation: strength of memories decay gradually. If these strengths fall below a
certain threshold, we can't recall the information, but the remaining memory trace is still there to
facilitate relearning.
Forgetting: Decay or Interference?
Is forgetting due
to decay of unused information, or to interference of new information with old
information? Different kinds of evidence are offered for each position.
A survey of forgetting
research concluded that the rate at which we forget information usually
conforms to a power law: we forget a lot at first, but over time the rate of forgetting diminishes.
Decrease in long-term
potentiation follows a similar power law. These facts are interpreted by
some as evidence for a physiologically determined decay rate.
Interference
Experiments Typical Experiment (A-D C-D paradigm):
Typical Results:
Experimental subjects take longer to learn their second set of associations
than controls, and make more errors on the A-B test. Experimental subjects take longer to
learn their second set of associations than controls, and make more errors on the A-B test.
These results are interpreted as evidence that learning new associations to stimuli causes
forgetting of old associations. However, interference does not happen with factual material
when the additional facts are redundant with (e.g., causally related to) the original facts.
Fan Effect (a model)
- Interference effects can be modeled as weakening of spreading
activation over multiple links in a propositional network.
Stimulus activates
concept nodes.- Fixed (limited) amount of activation spreads from activated
nodes over associative links, divided equally between links. (Hence the more links, the less
activation per link.) Activation converges at propositional nodes (candidate responses) until one
emerges as the answer. Time to identify the response is inversely related to level of activation.
Decay or Interference?
Some claim that interference can produce the appearance of decay
although it appears, both mechanisms are involved in forgetting or memory loss.
Retrieval and Inference
It is well established
that people make inferences during retrieval, and believe that they saw or
heard things that they in fact did not. People are more likely to erroneously think they read a
sentence if it is an implication of something they read.
Effect of Prior
Knowledge - People add other knowledge they have about the material
studied.
Effect of Question
Wording - Subjects shown film of automobile accident. Subjects asked:
Did you see a broken headlight? or Did you see the broken headlight? (There was actually
none.) Results: Subjects more likely to respond yes to the broken headlight. Implications for
courtroom testimony!
Other Facts about Memory
Organization
of Material
Retrieval of information
is better if the information is organized in some manner supporting
systematic search, such as in hierarchies.
Method of Loci
The ancients remembered
things by imagining taking a familiar walk, and placing the things to
be remembered at locations along the way. This method works because it organizes the
material to be remembered and it encourages elaborative processing and memorable imagery.
Context-Dependent
Learning
Physical and emotional
context may be inadvertently coded as retrieval cues, along with the
intended cues.
Consistent with
this idea, various studies show that recall is better when tested in the same
context (physical or emotional) as in which learning took place. Some benefit has been found
studying for important exams in the same room as they will be taken. However these results are
variable.
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Retrieval
from Long-Term Memory
Retrieval Cues: stimuli associated with information
stored in memory that help us remember.
There are 2 types:
1. Context-Dependent Memory- recall is better
when remembering takes place in the
same setting in which learning occurred.
2. State-Dependent Memory- it os often easier
to recall information when the
internal state is similar to that at the time of
learning.
Conclusion:
Squire’s
Taxonomy of Long-Term Memories
THE BIG PICTURE: Types of Information in Memory
Storing
Information in Episodic Memory
Models that propose ways in which knowledge
may be mentally represented and
organized:
Tulving (1972, 1983) proposed that there
are 2 distinct yet interacting memory systems:
Important Storage Effects: Rehearsal,
Organization, & Imagery
Levels
of Processing Approach
Depth of Processing: Memory is determined
not by how long information stays in the system,
but by how the person processes it.
1. Shallow processing leads to poor LTM traces.
2. Deep processing leads to strong LTM traces.
Indicates that the greater the effort expended in
processing information, the easier it will be to
recall.
This approach highlighted problems with the 3 Storage
Model of Memory:
Proposed a Processing Theory of Memory (Craik & Lockhart,
1972)
Core ideas of Levels-of-Processing:
Experimental Evidence:
Hyde & Jenkins (1969)
Four groups of subjects were presented with a list
of 24 words.
S's were then given a surprise recall memory
task.
Results:
Craik and Watkins (1973) “G” study.
The orienting task:
Is it an animal? DOG Is it in upper case? table
Dog requires semantic processing; table does not.
So, people will remember the word “dog” better
than the word “table”.
Craik & Tulving (1975)
Standard Incidental Learning Paradigm:
Subjects perform "perceptual judgment tasks"
which vary in depth.
S's were then given a surprise recognition memory
test.
Results:
Conclusion: People do not remember
what is "out there" in the world. What they remember is
what they did/how they thought about it at encoding!
WHY does analyzing semantic meaning improve
memory?
A.
Elaboration?
Craik & Tulving's Elaboration Experiment: An
incidental learning expt w/ sentences varying in
complexity.
~>
As sentence elaborateness increased, memory increased.
More
on elaboration: What is the most elaborate set of knowledge you have?
Probably your knowledge about YOURSELF.
B.
Distinctiveness?
The suggestion here is that the more unique
the way a stimulus is encoded in memory,
the better the memory will be. Examples?
This may be because:
Challenges to Depth of Processing: Is
this a circular explanation for performance? (Baddeley, 1978)
Effects using recognition instead of recall. The
Congruity effect (better memory for “yes” over “no”
words, even if both were processed deeply).
Food for thought:
Can you have imageless thought? what exactly is a
visual image? how is it stored in LTM? how are
images and words stored in relation to one another? how would you even study/measure visual
imagery?
History
Anecdotal Observations
IMAGERY & MEMORY - The mental picturing
of a stimulus that affects later recall or recognition.
How are images and words stored in relation to
one another? Similarities...differences
A test of memory for words and pictures:
Shepard (1967)
Schnorr and Atkinson (1969):
 Paivio's Dual-
Coding Theory According to Paivio's Dual-Coding hypothesis
information can be represented in either a verbal or a
nonverbal system.
1) Two independent but interacting system; Material
can be processes in one or both
systems
Two codes increase the likelihood of later
retrieval.
this image
is adopted from the web site designed by Stephen R. Schmidt, Ph.D. @ Middle Tennessee
State University
Effects of Imagery on Memory
Basic Result: Paivio (1971)
Explanations:
1) The Imagen system has superior memory abilities
to the Logogen system.
2) Representing ideas in both systems is superior
to representing ideas in only one system.
How do you test which of these explanations
is correct?
You could compare:
Results: Across all these situations,
the evidence consistently supports the claim that having two
representations leads to superior memory.
Tulving & Thomson (1973) -- The Encoding Specificity Hypothesis
They used a simple Paired-Associate Learning
Paradigm
Often used to study pro and retroactive interference.
A list of stimulus terms is paired item by item with
a list of response terms.
After learning, the stimulus terms are used as cues
for the response terms.
Sample Paired Associate Lists
Factors in
Retention
In the last two
modules we have been concerned with the problems of reaming and the process
by which behavior is acquired. We will now study the closely related phenomena of forgetting
and retention.
As you read through the text, keep the following questions in mind.
LONG-TERM VERSUS SHORT-TEAM MEMORY
In recent years, evidence has been growing to support the idea of a two- stage
memory process. The two stages are short- and long-term memory, sometimes called
primary and secondary memory. We have all had experiences in which we ask
someone for a phone number. We dial it and get a busy signal. If we try to redial it just
a few seconds later, we usually have to ask for the number again. The number was
stored in short- term memory and was quickly lost. If we wish to commit the number
to long-term memory, we must either practice it or code it by some associations.
The fastest drop in retention occurs immediately after learning
Research on short term memory was conducted by Peterson and Peterson (1959).
Items were presented for a brief period of time. Subjects were then asked to recall the
items at intervals that varied from three to 18 seconds immediately after exposure.
Results were dramatic. After three seconds, immediate recall was high, but after 18
seconds less than 10% of the subjects were able to recall the item.
According to one theory, the effects of short-term memory are due to neural traces
in
the brain resulting from presented stimuli (Hebb 1949). These traces quickly decay
over time, making the item less available for immediate retrieval. The theory holds that
in long-term memory, permanent traces are formed when stimuli are presented
repeatedly.
THE COURSE OF FORGETTING
Forgetting and retention are inverse concepts. Retention refers to the amount
of original
learning that is still effective, while forgetting refers to the amount lost. Figure 5 shows a
typical retention curve.
F igure 5. Forgetting
and retention compared
As the graph indicates,
by far the greatest amount of forgetting takes place in the first few
moments after learning. Thereafter, the curve levels off. The amount retained after 5 hours is
only slightly greater than after 15 hours.
The form of the
retention curve depends in part on what measure is used. The three most
frequently used measures are recall, relearning, and recognition.
82
RECALL
We find different
retention rates depending on how we test for recall
In recall, the
subject is asked to reproduce the original response in some form. In experimental
work the subject often responds vocally or may even be asked to write his response in a blank.
There is little prompting in recall testing. Often the student is simply instructed to remember as
many items from a list as possible. As might be expected, a test of recall generally yields the
lowest measure of retention.
RELEARNING
Relearning is sometimes
called the savings method. Using this method, the subject first learns
some material and, after various lengths of time, relearns that same material to the same
criterion level. The number of trials to relearn the material is always fewer than the number
required to learn it the first time.
The formula for
relearning expresses the percentage of practice time saved.
The relearning
score = 100 x (original trials minus relearning trials) divided by original trials
For example: If
it took ten trials to learn the material originally and only four trials to relearn it,
the relearning score would equal 100 x (10-4)/10 = 60%
Relearning usually
reveals more retention than recall because more stimulus conditions are
present in both the original learning and the relearning. ,
RECOGNITION
Recognition is
the type of retention measured by a multiple choice question. The learner is
required to choose the correct alternative from among several. In an experimental situation, the
subject would be required to point out the correct answer from among many.
With recognition
measures, even weak retention is revealed. The presence of the correct
response among the choices is a prompt for the correct choice. In addition, subjects (and
students) can eliminate some incorrect choices on the basis of length, position, incorrect
grammar, etc. This increases the chance of making the correct selection. Responses which
were previously associated with stimuli similar to the test stimuli are more likely to be selected
erroneously. The phenomenon of false recognition can be seen in the familiar feeling that one
has been in a certain situation before. This feeling, called deja vue occurs when enough aspects
of the immediate situation resemble a previous situation. We incorrectly identify the past with
the present.
THE FORM OF
THE RETENTION CURVE
Each of the three
measures of retention yields different results.
If we used all
three measures of the retention of a learning task, the results would typically
resemble those shown in Figure 6, where Recognition is the top curve, relearning is next, and
recall (on the bottom) shows the lowest amount of retention over time.
Figure 6. Retention
curves for three measures of retention. The top curve is "recognition." The
middle curve is "relearning. The bottom curve is that of "recall."
FACTORS AFFECTING RETENTION
Making material
meaningful to the subject aids retention
1. Meaningfulness:
An important factor in retention is the meaningfulness of the material. In
experiments where material has been presented in prose form or where there is a "theme,"
retention is improved. .
Mediating associations
are especially useful for long-term retention
2. Mediating
Associations: A second variable is the use of mediation al elements. Memory
experts have long advocated the use of associations and mnemonics in aiding recall.
An example of
a well-known mnemonic device is the "On Old Olympus Towering Top, a
Finn And German Viewed A Hop," used by medical students to memorize the names of
the twelve cranial nerves. The student memorizes the verse and then uses the initial
letters to prompt himself to say. "Olfactory, Optic, Culotte, Cochlear," and so on.
The assumption
underlying the use of mediation is that if the learner is unable to recall the
desired response, he might be able to recall the mediator, which in turn would act as a stimulus
for the recall of the response.
For example, suppose
you wished to learn an S-R pair like dog-plant. You could put the
stimulus word on a flash card and its response on the back. Then you could use the method of
anticipation to eventually learn the pair by rote. You could, however, use an alternate strategy.
You could find a common association between the two words dog and plant such as house
(dog-house, house-plant).
In an experiment
by Toast (1967), one group of subjects learned a series of 12 word pairs. A
second group of subjects was told only to find some common association between each of the
two words. These tasks were followed by a test of immediate recall. The subjects were
presented with the first member of each pair and asked to recall the second member. Initially
the subjects in the rote- learning group were slightly superior to those in the association group.
However, after a two-week interval, the association group showed almost no further loss while
the rote group showed a typical loss in retention over time.
Some over learning
increases short- and long-term retention dramatically
3. Overlearning:
Overlearning results from practicing beyond the point when the material has
been mastered. For example, suppose it takes a subject five trials to learn a list of items. If we
now require him to complete five additional trials, we say that 100 percent overlearning has
occurred. In a study by Krueger (1929), subjects were required to learn a list of nouns. One
group reamed with 0 percent overleaming; in other words, they mastered the list, and then were
given no more practice. Another group learned with 50 percent and a third with 100 percent
additional practice trials beyond mastery.
The data in Figure
9 clearly indicate that greater overlearning leads to increased retention.
However, the improvement in retention from 0 percent to 50 percent overlearning is much
greater than the 50 percent to 100 Percent overlearning, indicating that a point was reached
beyond which returns from the increased effort diminished.
SUMMARY OF FACTORS
AFFECTING RETENTION:
It is interesting
to note that almost all,"'memory systems" recommended by experts require you
to (1) practice by reading or reciting beyond mastery (overlearning) (2) study the material in
logical blocks which are related by a theme rather than in small disconnected pieces (increased
meaningfulness), or (3) attempt to find as many associations or "reasons" to remember as
possible (mediation). These recommendations are obviously in accord with the experimental
data.
Human Memory:
Encoding and Storage
Cognitive Psychology and Its Implications: Chapter 6
Anderson
§ “Research on human memory has had a long history but has greatly intensified
since the end of
the behaviorist era.”
Hermann Ebbinghaus
(1850-1909)
§ One of the great pioneers in psychology remembered for developing a means of studying
memory
while minimizing past associations (i.e, the nonsense syllable).
§ Most significant:
• Careful control of experimental conditions.
• Quantitative analysis of data.
• The finding that time to learn is a function of the number of items.
Ebbinghaus
§ He was the first to investigate learning and memory experimentally.
§ He made the study of associations objective:
• The study of formation of associations as they occur, not post hoc.
• He rigorously controlled the conditions of acquisition and recall
Ebbinghaus
§ He provided quantification of learning, memory, recall, forgetting.
§ He also examined:
• overlearning
• associations between lists
• reviewing material
• time between learning and recall
Research with nonsense syllables
§ Ebbinghaus: “meaningless series of syllables”
§ Mistranstlation: “series of nonsense syllables”
§ Usually consonant-vowel-consonant
§ Discovered that meaningless material was 9 times harder to learn than meaningful
material.
§ Demonstrated that longer material requires more repetitions.
What is the “forgetting curve?”
§ Retention decreases as the retention interval (the time between initial learning
and the retention
time) increases, but the rate of forgetting slows down.
Overview
§ The Rise and Fall of the Theory of Short-Term Memory
§ Rehearsal and Working Memory
§ Activation and Long-Term Memory
§ Practice and Strength
§ Levels of Processing
§ Encoding versus Retrieval
The Rise and Fall of the Theory of Short-Term Memory
§ What is the model of memory involving an intermediate short-term memory?
• “A once-popular view in cognitive psychology was that information had
to be rehearsed in a limited-
capacity short-term memory in order to be deposited in long- term memory.”
The Rise and Fall of the Theory of Short-Term Memory
§ What kinds of data supported the existence of short-term memory?
• Apparent difference in the rate of forgetting.
– Now believed that rate of forgetting is a function of how well the information
is learned.
• Rehearsal controls amount of information transferred to long-term memory
– “Depth” of processing more important than amount
– Passive rehearsal does not result in better memory
Rehearsal and Working Memory
• “Baddeley proposed that we have an articulatory loop and a visuo-spatial
sketchpad whose use is
controlled by a central executive.”
§ How does Baddeley’s view differ from short-term memory?
• Information does not have to spend time in the phonological loop to get into
long- term memory.
§ Frontal Cortex and Primate Working Memory
• “Different areas of the frontal cortex appear to be responsible for
maintaining different types of
information in working memory.”
Activation and Long-Term Memory
• “Speed and probability of accessing a memory is determined by its level
of activation, which in
turn is determined by how frequently and how recently we have used the memory.”
§ Spreading Activation
• “Activation spreads through a network from presented items to activate
associated memories.”
Associative Priming
§ Meyer and Schvaneveldt (1971)
• Associative spreading of activation through memory can facilitate the rate
at which words are read.
Practice and Strength
• “As a memory is practiced, it is strengthened according to a power function.”
§ Long-Term Potentiation and the Power Law
• “Long-term potentiation is a form of neural learning which appears to
follow a power law.”
Levels of Processing
§ Elaborative Processing
• “Good memory for material results when it is processed more elaborately.”
§ Meaningful versus Nonmeaningful Elaborations
• “More elaborate processing will result in better memory even if that
processing is not focused on
the meaning of the material.”
Levels of Processing (continued)
§ Incidental versus Intentional Learning
• “Level of processing, and not whether one intends to learn, determines
the amount remembered.”
§ Elaborative Processing and Text Material
• “Study techniques involving question generation and answering lead to
better memory for text
material.”
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The Learning Curve
It is a cliché
today to refer to a “steep learning curve” to indicate that something is difficult to
learn. In practice, a curve of the amount learned against the number of trials (in experiments) or
over time (in reality) is just the opposite: if something is difficult, the line rises slowly or
shallowly. So the steep curve refers to the demands of the task rather than a description of the
process.
As the figure of
a fairly typical learning “curve” shows, it does not proceed smoothly: the
plateaux and troughs are normal features of the process.
In the acquisition
of skills, a major issue is the reliability of the performance. Any novice can get
it right occasionally (beginner’s luck), but it is consistency which counts, and the progress
of
learning is often assessed on this basis. The following stages are an adaptation of Reynolds’
(1965)
model. She also points out that learning skills is largely a matter of them “soaking in”, so
that performance becomes less self-conscious as learning progresses, and that the transition from
one phase to another is marked by a release of energy, in the form of the freedom to concentrate
on other things. (The horizontal line represents a notional threshold of “competence”)
She also suggests
that the final phase (which I have referred to as “Second Nature”) is
characterised by an ability to teach the skill. At earlier stages, the learner is not confident
enough to analyse their own practice thoroughly enough to be able to teach it: there is a feeling
of mystique and fragility —if I examine it too closely I might not be able to perform as well
again.
There is an
interesting distinction to be drawn between learning which follows this
pattern, and that in which increasing sophistication and expertise is characterised by
increasing reflection
— in the one case the better you get the less you think about it (as
in driving or typing), in the other the better you get the more you think about it (as in
teaching, or perhaps selling). I suspect that it is not the skill itself which draws this
distinction, but the degree of uncertainty in the immediate environment.
Linked to the Reynolds
idea is the popular progression of competence model:
-
Unconscious incompetence
- Conscious incompetence
- Conscious competence
- Unconscious competence
— which of
course assumes that the last is the most desirable state.
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Two Dimensions
of Practice
James Atherton
Based
on a paper given at the University of Humberside
(now University of Lincoln) in 1992
People from politicians
to managers seem to have great faith in training, and even sometimes in
education. We are told that it is a panacea: it will improve competitiveness, it will go a long way
to reducing unemployment, it will improve health and safety, and it will even stop child abuse. It
has become very big business, but despite the investment of time and money, it seems
sometimes to yield rather poor dividends.
Possible reasons
for that will be found throughout this site, but I want to start with a model of
working practice, rather than of training as such. The argument is simple: there are some
aspects of practice which can readily be improved by training, and there are some which can
not: those need different kinds of intervention, and although you could perhaps dilute the notion
of “training” until it covers all of them, that would be a semantic trick, not a reflection
of the real
world. Moreover, working with these different forms of practice places different demands on
the teacher.
This model of practice
suggests that it can be rated on two dimensions, which are independent
of each other, yielding four categories. The first dimension assesses the extent to which practice
accords with the values or perhaps the preferences of the practitioner: the second is about
understanding the rationale of practice and its effects.
Willing and Unwilling Practice
Most practice in
most occupations is undertaken fairly willingly. That is not to assert that most
of us enjoy what we do, but that we have a fairly clear idea of what we ought to be doing, and
we act in accordance with that idea. In contrast, there are occasions on which we are forced to
act in ways at variance with what we have learned is best practice, which we shall refer to here
as practising “unwillingly”.
The reasons for
unwilling practice are many, and for present purposes it makes little difference
what they are. Lack of resources and unreasonable demands are probably two of the most
common. As a teacher, I may want to spend time getting to know the individual needs of every
person in my class, but the number of students and the constraints of time may well mean that I
have to treat them as if they were all the same. As a doctor, I may want to talk to my patients
and find out what is behind the complaints which keep them coming back for more sleeping
tablets, tranquillisers or anti- depressants, but the waiting-room is full again, and so I just write
a repeat prescription. As a manager, I may believe it important to consult with my staff about
impending changes, and involve them in decision-making, but I am under pressure to get things
done and so I just issue directives. All of us are familiar with these everyday compromises.
A variant of unwilling
practice may also stem from lack of time to think, where the practitioner
“knows better”, but regresses to survival-oriented practice by “reflex”: the
earlier learning is so
firmly established that when there is no time to reflect, it surfaces although it may be instantly
regretted. At a trivial level, I have tried to train myself not to cross my hands on the steering
wheel while driving. I am fully persuaded that this is desirable for better control. I remember to
do it when I am concentrating and approaching a corner in a planned fashion, but the moment I
am distracted or have to swerve in an emergency I cross my hands again.
Witting and Unwitting Practice
“Witting”
is not a word we use very often, although “unwitting” is fairly common. Just like other
words which we only encounter in the negative — such as "kempt", "couth" "ept"
and "ert" — it
is easy to deduce its meaning [Digression].
Witting practice is knowing practice, when you
understand why you are doing something and what its likely consequences will be. Unwitting
practice is when you simply go through the motions or obey orders without full understanding of
the whys and wherefores.
Four kinds of Practice
Put these two dimensions
together, and we have four kinds of practice:
-
Witting and Willing
- Witting and Unwilling
- Unwitting and Willing
- Unwitting and Unwilling
It should be pointed
out that these are kinds of practice rather than kinds of work; that is, they
relate to the ways in which particular individuals do parts of their jobs at different times. Any
given task or procedure might be carried out in any of the four forms, so it does not make
sense to attempt to use these categories for the purpose of job analysis, although it may make
sense to use them for appraisal.
Intentional (Witting and Willing) Practice
Most training
programmes operate on the assumption that this is the only kind of
practice there is. The practitioner is doing what she set out to do (willing), and in full
knowledge both of the reasons for doing so, and what is likely to follow from the action. She
can therefore be held fully accountable for that practice. If management wishes to modify it, all
they have to do is to issue a new set of regulations, brief or train her to use them, and other
things being equal, practice will change. All this is patently obvious, but it needs to be spelt out
a little to provide the background for the other categories.
Survival (Witting and Unwilling) Practice
As in the examples
quoted above, here we have a practitioner who knows what he ought to be
doing, but finds that he can’t do it. In all the examples cited, the problem is basically lack
of
time, but it might equally be not having the right equipment. Try to change the situation with
regulations or even by offering further training, and you will get protests: “It’s all very
well telling
us to spend more time with our students/ patients/ clients/ staff, but if I do, who’s going to...?”
Very often witting
and unwilling practice is the product of rough and ready prioritisation which
necessitates taking short- cuts. There is a rush order in the machine-shop, so a tool is set up
without using the full safety procedure, for example. It can easily become institutionalised: there
is a common form of industrial protest known as “working to rule”, in which work is slowed
almost to a standstill by an insistence on following all procedures to the letter. The very fact that
this slows things down is testimony to required standards being routinely ignored. This raises
serious questions about a culture of management accountability which trades on issuing
regulations which cannot practicably be applied; but for present purposes the important
consideration is that witting and unwilling practice cannot be rectified by issuing more such
instructions, or simply by training in isolation.
Instead, there
is a prior need to examine the circumstances under which witting and unwilling
practice occurs, and to ensure that the opportunities are available for working without short-
cuts. Staff need to be convinced that there is a realistic assessment of the situation before
training itself is any use at all.
The consequences
of such an analysis may be profound for management. They may require a
review of staffing levels and pay policy, for example. But there is also an issue for trainers
asked to participate in a training effort to rectify such practice. Their efforts may be in vain —
which does not augur well for the re-employment of a consultant trainer — but their credibility
in the eyes of the recipients of training may also be compromised. It is important to most
practitioners that those training them represent both high standards of practice and also close
acquaintance with real-world problems. Failure to convince course members of this severely
undermines the effectiveness of training practice.
Not all survival
practice is related to external pressures, however. Staff in stressful occupations
develop defences to enable them to cope with the pressures. The most explicit study of this is
Menzies’ classic “Case-study in the Functioning of Social Systems as a Defence against
Anxiety” (1967, in Menzies-Lyth, 1988
), in which she examined how the structure of nurse
training had evolved (up to the time of her study) in order to inculcate values and practices which
preserved young and relatively immature entrants from the emotional onslaught of dealing with
seriously ill patients. Here, the survival practice had become institutionalised. Practical experience
on wards was based on a rapid rotation, for example, so that student nurses would not get to
know the patients too well or feel involved with them. Work was organised on the basis of “task-
lists”: a nurse would be assigned to do all the bed-pans on the ward, and then perhaps to take
round all the mid-morning drinks, ensuring that the contact with any given patient was brief and
business- like. The level of dissatisfaction was high, but it was implicitly accepted as being
preferable to nurses getting “over- involved”, and potentially burning out. The pattern
of nurse
training in the UK has changed considerably since the study, but a number of nurse trainers have
commented that while one set of defences has been stripped away, insufficient attention may be
given to how to cope with the pressures, which do not go away.
Such survival sub-cultures
are not confined to nursing: studies by a school of sociologists
known as ethnomethodologists — generally renowned for the obscurity of their writings —
have shown similar systems of “typifications” or stereotyping of clients, in a variety of
service
agencies. They have been studied in the juvenile justice system by Cicourel (1968)
, in coroner’s
services by
Garfinkel (1967)
, in nursing and the police by Sudnow
(1965,
1967),
in hospital
records by Garfinkel (1967), and in social work by
Zimmerman (1969)
. In each case — when
you get behind their own pretentious and obfuscatory jargon — they examine how an informal
system of categorisation of cases “for all practical purposes” grows out of the practical
pressures
of doing the job. One effect is to dehumanise the client, but they persist because they help the
practitioner.
There may also
be more personal factors which lead to the development of survival practice.
Transmitting bad news is an aspect of several jobs which is notoriously done badly: but then
given the tendency of members of the public to blame the messenger, this is perhaps not
surprising. Either fear or a genuine desire not to hurt someone’s feelings can lead to the
information being fudged, or to a brusque “hit and run” approach in which the news is blurted
out, and then the messenger escapes. Although there used to be a medical tradition of not
telling someone that he had cancer, for example, that is fairly long gone, and practitioners
talking about how they ought to act are usually fairly clear about it. Nevertheless, in the heat of
the moment they may regress and act on the basis of survival rather than good practice. Argyris
and Schön (1974)
developed the useful distinction between “theories-in-use”, rather than
“espoused theories” to discuss this discrepancy, in the context of negotiating skills. More
moralistically, and less helpfully, it may be referred to as “hypocrisy”.
This discussion
suggests that tutors have an uphill struggle in trying to work with survival
practice. Unless they (and the learners’ group) can create an accepting and trustworthy
environment, such practice rarely emerges for discussion. Everyone knows what they ought to
be saying and doing, but may be very shame-faced about what they actually do say and do.
Given that such survival practice is often only a small part of their overall pattern of work,
however, it is possible to get through to it with care (and time).
-
The more the members
of a course own the training, the more effective it is likely to be.
They need to be consulted at each stage of its commissioning and design, and their
agenda needs to be acknowledged in the construction of the sessions. Tutors and
managers may feel that the members have got it all wrong, but nothing useful at all will
be achieved if they cannot identify with the task of the training.
- A contract with the course members does
not of itself create the appropriate culture,
but it can help. If the tutor can give an undertaking of confidentiality (usually with
specific exceptions — they are not only realistic, but indicate that it is taken seriously),
learners may be more prepared to “open up”. Be aware, however, that contracts
themselves can be experienced as oppressive, especially if formulated too piously, or
their construction is dominated by the politically correct members of the group. Further,
a contract will be tested, and if it fails you will end up further back than when you
started.
- On the one hand, role-play is often a good
method of exposing such survival practice:
on the other, that is precisely why some people find the technique very threatening. It
needs to be conducted in a constructive environment, and often simple techniques like
suggesting that first of all, people demonstrate how to do something “as badly as
possible”, facilitate the creation of such an atmosphere. Work up to state- of-the-art
good practice slowly, giving critical feedback if necessary on just one aspect of
performance at a time.
- Make use of evidence and anecdotes from
other settings with which course members
might identify.
- It sometimes helps to use a “package”,
by which I mean an established theoretical
framework which provides a “container” within which survival practice can be
discussed. One of the most popular packages for such purposes is Transactional
Analysis (see Stewart and Joines 1987
, inter al.). Overall, I have my doubts about some
of the claims made for TA, but it is eminently teachable and usually greatly enjoyed, and
the framework of “games” encourages group members to talk about their own
experiences — often of survival practice — and to ask “What game is that?”
- But most important of all is to take seriously
the reluctant but powerful emotional
investment people have in their survival practice. After all, it helps them to keep on
doing a difficult job day in day out for years. No-one can just take it away without
showing that the alternative is better.
Shallow (Willing and Unwitting) Practice
Shallow practice
is not be confused with surface learning (Marton, Hounsell and Entwistle, 1997
): it is more analogous to the seed sown on rocky ground in the parable of the Sower (St. Mark
4:16-17). Another term might be "ignorant" practice. There are basically two forms
of such
practice; where staff are simply unaware of its potentially deleterious (or even beneficial) effects,
and where they have just been trained to operate a set of procedures without knowing the
reasons, and are thus unequipped to deal with any variations from the norm. Naturally, these
forms overlap.
One of the clearest
areas in which it is found is that of equal opportunities. As I write this, I am
preparing to teach part of a course on post-compulsory education, one of the objectives of
which specifies an understanding of equal opportunities in adult education. As part of the initial
learning contract, students have been asked to rate themselves on their pre- course
understanding or competence in relation to these objectives. I have just had tutorials with a
series of students who have asked, in one form or another, “what is there to know about equal
opportunities?” They protest that they are not prejudiced against anyone and they treat all their
students the same, so that must be all there is to it. As they go through the module, they will (or
at least should) discover that many of their well-intentioned practices are discriminatory, simply
because they are unwitting about their impact on members of minority groups. I recollect the
catering lecturer who was nonplussed by the reaction of a Jewish student who objected to
preparing chicken Kiev, the IT teacher who could not understand why a visually-impaired
student wanted to learn DOS-based rather than Windows packages, the tutor who took it as
evidence of lack of motivation that women adult returners to learning were regularly late for his
9.00 am class, as well as the numerous teachers who have identified dyslexia with lack of ability.
Equal opportunities
is not the only area of shallow practice, of course. The trainers engaged in
the fruitless task of working with the survival-oriented practitioners discussed in the previous
section might also be in the same position of ignorance about the consequences of their work.
But so, in a much more positive sense, are some of the naive teachers who wonder why their
students like them so much, when they are prepared to look over a draft of an assignment: they
are surprised to learn that not everyone would be prepared (or have time) to do it. But they are
not merely ignorant of common practice, they are blissfully unaware of how much it means to
some students that they are prepared to take such an interest.
The other form
of practice is exemplified by the shop assistant who asked me for my address
when I was making a cash purchase, and then could not explain to me why he needed the
information: he protested that no-one had ever asked before, but he would get into trouble if he
did not get it. I find myself in the same position in relation to some of the questions on our
standard university enrolment form: the name of the school someone attended 20 years ago
might be quite irrelevant, but I know that if the box is left blank, a bureaucrat will reject it. But
I
can’t really be bothered to make a fuss about it or even find out why someone wants to know.
These examples overlap with the first category in that they are about seeking irrelevant
information and thus constitute an unwitting invasion of privacy, but they are also in the second
category because of their "Their’s [sic] not to reason why, Their’s but to do and die"
philosophy.
The implications
for training are considerable. There is a danger for example that competence-
based training programmes can, themselves unwittingly, promote shallow practice. If each
component of the job is divided into competences, and elements, and performance criteria,
there is a danger that the sum of the parts will be less than the whole. Each component of the
programme needs to be contextualised, so that its relationship to the whole can be seen, and
informed decisions can be made about when to apply a particular approach. A number of
National Vocational Qualifications (such as those in health and social care) have taken this to
heart, with the introduction of core competences which are primarily about the application of
appropriate values to the task; but the model does not lend itself readily to such an approach.
Similar concerns have been expressed about the ability of a competence-based model to equip
practitioners (in all fields) to deal with situations of uncertainty, and hence to provide an
adequate basis for training at NVQ Levels 4 and 5.
In practice, of
course, almost any kind of curriculum can suffer from the same problems, partly
because the assessment of practice has to focus on simplified models of the real world. Even
case-studies, valuable though they are, have limitations. Even more intractably, the knowledge
base of the subject may be unwitting about some of its consequences. The medical curriculum,
for example, has changed in quite important respects in recent years, not only because of the
discovery and development of new methods, but because of a recognition that tried and trusted
approaches to the treatment of routine conditions either do not work or have side-effects which
are worse than the illness. Only recently have environmental concerns been taken on board in
the modelling of industrial processes. Here the issues border on the political.
How far does one
go in contextualising the curriculum? There is a point at which one goes so
far that it is no longer possible to devote sufficient attention to the particular skills or knowledge
learners are supposed to be acquiring. (A colleague in Further Education, currently devising a
course in servicing electronic goods, complains that so much emphasis is being put on the
“customer care” requirements of the course that the technical parts are being squeezed out.)
It
is also possible to render learners impotent, by engaging with issues over which they have no
control. A few teachers would maintain that engineering staff working on a product with military
applications need to be aware of who is buying it, but most draw the boundaries much more
narrowly, pointing out simply how important engineering tolerances are for the “safe” operation
of the product. Despite the ethical and political problems, however, it is reasonable to trace the
potential effects of specific bits of practice within the defined boundaries of a system — the
political question is about the drawing of those boundaries.
Driven (Unwilling and Unwitting) Practice
This fourth category
is the most difficult to describe, although you may recognise it when you
see it. It is also the most difficult to address. I call it “driven” because there is a
sense of
compulsion about it, or at least of not being aware of any alternative. It may well be an
expression of a personality trait with which someone is not comfortable, but says, “It’s
just me,
I’m afraid ...” It may be compulsive talking, it may be impatience, it may be shyness. Try
to
make the person aware of it, and they may try to change, but fail because it is so much a part of
themselves. Very often they have some slight idea of its impact, so it is not totally unwitting, and
they may well admit that they “wish I could listen/be so tolerant/let go/be as organised as you,”
but never really having had the experience of being other than they are, they remain substantially
unaware of what their practice would be like if they were different.
If you are familiar
with the personal development literature of the 1960s and 70s, you may have
come across the “Johari window”
, which like the present model, uses two dimension (in this
case “known/unknown to others” and “known/unknown to self”) to yield four quadrants.
This
Driven practice may well correspond with the “Blind self” (known to others but unknown to
self),
or the “Unknown self”.
As the “Blind
self” notion suggests, it is much easier to see this form of practice in other people
than it is in ourselves, but everyone has their areas of it. For myself, I know that one area is a
failure to say exactly what I mean (I’m better at writing what I mean than I am at saying it,
although you may not believe that!): I set out to say one thing and somehow by the time I have
finished I have said something different. I also come across to others as a bit of a “cold fish”.
It
has taken quite a lot of reflection and feedback to realise these quirks, and I am not
comfortable with them, but my insight is impotent. I also know that one of my defence
mechanisms when anxious about my teaching is to retreat into the role of academic show-off,
and pontificate about a subject at great length. And if I use the word “actually” too much,
I do
not know what I am talking about ... Ask my colleagues and they will no doubt be able to list
other features of which I am as yet unaware.
More than that,
I have only the vaguest idea of how my practice would be different if I did not
have these failings _ or even if they really are failings. How would my students react if I were
more approachable? Would my tutorials be different? Would my former counselling practice
have been different? I think I was quite effective as a counsellor at an intellectual and decision-
making level, but would I have got more emotional responses if my body language had been
more relaxed? Would that have been a good thing? Would I have helped some people less
than in fact I did? A colleague tells me that I produce polarised reactions in students — some
think I am a brilliant teacher (well, he did not actually say “brilliant”), whereas some
find me
profoundly irritating or downright incomprehensible (including my partner, who was once a
student of mine). Few are neutral.
Apart from the
understandable reaction of asking who this guy is who has the cheek to
pronounce on teaching and learning issues when he is so self-evidently incompetent himself,
there is a serious point to all this confession. Training as such is not going to address this kind
of
practice. The restrictive solution is to say that anyone so flawed should not be in a particular
job _ they are quite unsuited. Occasionally that may be true, but it applies to all of us. The
perfect practitioner, in whatever discipline, has not yet been invented. The enabling solution is
the aforementioned process of feedback from others and reflection by yourself, perhaps
abetted by such devices as video recordings of yourself in action, and a commitment to work
through your limitations (and to capitalise on your strengths, because some of this driven
practice may just include your greatest talents).
Training may be
ineffective but more important, it may be intrusive and exceed its authority.
There is a well-known side- effect of adult education, which has been termed “perspective
transformation” (Mezirow, 1978).
This occurs when the experience of learning goes beyond an
incremental change in a person’s knowledge, skill or understanding, to a wholesale re-ordering
of
the way they think about themselves and their position in the world. Willy Russell’s play and
subsequent film, “Educating Rita”, dramatises this awakening; and Paolo Freire’s objective
of
“conscientisation” as a product of literacy education is an explicit embrace of it as a
desired
outcome (
Freire, 1972
). It is not dependent on success in learning what the teacher set out to
teach. I have been confronted on several occasions by students who have claimed that even a
vocational day-release programme has, for example, given them the courage to leave their
partners. This is embarrassing and even rather frightening for the teacher who is credited with
the transformation: but at least it was accidental. It was a side-effect of showing people they
could do more than they thought they could, of raising their self-esteem and (waffly jargon)
“empowering” them. There is no way in which (at least now), I would presume to set out to
interfere to that extent in their private lives. (I say “at least now”, because many years
ago I
worked on a rather psychodynamically -oriented social work course about which we used to joke
that we took the students to pieces and then put them back together again — and last year we
had enough parts left over to make two more students!)
The problem is
that to address driven practice is to venture into this therapeutic area, and it is
difficult to know when one is crossing a very indistinct line. Yes, I want to support a student
who is upset by some aspect of the learning. Yes, I want to give feedback on performance so
that he can reflect on it and change if he wishes and is able to. Yes, I will try to help someone
whose learning is adversely affected by external pressures. But students (and trainees in an
occupational context) do not contract for a psychological makeover when they join a course.
When I taught on
another social work course a few years ago, the external examiner
commented at one point that he was concerned that despite the extent and intensity of emphasis
on anti-racist and anti-discriminatory practice on the programme, the work he had read
indicated that the students were not actually using it in their assignments. I found this disturbing,
and tried to think through what was going on, including asking some of the students who had
completed the programme (including some of the black students). Their comments indicated
that they experienced the teaching as a sort of ritual obeisance to political correctness on the
part of the staff. They did not doubt staff sincerity, they just thought it was not much practical
use: so they made similarly token references in their assignments, just enough to meet the
explicit marking criteria related to anti-discriminatory practice. I was not sure what to make of
this. We could reasonably expect that they should combat race, gender and disability
discrimination in their practice, and this was explicitly assessed on their practical placements:
but could we — should we — legislate for what they should believe? Overall, I think not.
I
think they had got it right and we had got it wrong. |
|
|
The goal is not so much to see that which no one has
seen, but to see that which
everyone sees, in a totally different way. --
Arthur Schopenhauer
|
The problems in
education are not only complex and multidimensional, most of them get their
start outside the walls of schools. Ironically, realizing that the problems in education are not
solely problems of education, clarifies the situation. Today’s educational difficulties are actually
part of a larger cultural change affecting western and perhaps global civilization. Before parents
and educators can settle on what needs to be done in schools, they must first understand what
needs to be done in the larger whole.
The Rise of
Integral Society and the Web View of the World
The contour of
this larger change is already easy to see. Cultural sea changes are marked by a
shift in the underlying metaphor the society uses to explain “how the world works” and today
our metaphor is migrating from “machine” to “web” (interconnectedness). The
emerging web
view is witnessed by everything from environmental awareness and holistic alternatives in health
to the global economy and the World Wide Web. The reasons for this restructuring are also
obvious. The crisis in education is but one of a growing list of threats to social well-being that
includes environmental degradation, community disintegration, economic inequity (and
instability) and democratic processes dominated by moneyed interests. Ominous signs floating
in from many directions over many years has built a huge pool of pressure. Most people say
they are struggling to create a sustainable civilization, but the official name for this stage of
civilization is integral society (Ray, 1996).
Contours, however,
are not enough to build a new society. The best way to understand integral
needs is through the comprehensive new science which is rising alongside the new society.
Thanks to the popular press, many people know one or more pieces of web science, say Gaia,
chaos, complexity, quantum mechanics or system theory. To unify web discoveries, however,
one needs a scientifically sound story of why various facets and ideas connect. The only story
capable of making such connections is a story of evolution. The best way to form an intelligible
picture out of many scientific pieces, therefore, is to use the broad new story of evolution
(dynamic evolution) rising with the new science (Goerner, 1999).
Dynamic Evolution
as a Unifying Thread and a Framework for Understanding
The new story of
evolution shows how pieces connect and why civilizations change. It suggests,
not only that we are bound up with everything else on earth, but that human beings and all living
and non-living systems are partners in a encompassing process of self- organizing development
and change (evolution). The whole process is driven and linked by energy flow. It follows
regular patterns.
The new story of
evolution also leads to a scientifically sound, but radically new vision of the
human condition. In particular, it shows how the three main threads of evolution—organization,
collaboration and intelligence—lead to both the cultural situation we now face and the tapestry
of human history that we already know.
The backbone of
evolution, the “organization” thread (structure), describes how energy pushes
systems to emerge, grow and then develop toward increasing “intricacy” (that is, toward
a tight,
lacework of organizational fabric.) The overall process follows three basic themes:
Figure 1 Boiling
Water as an Example of Self-organization and Increasing Intricacy
Energy's penchant
for creating organization and driving developmental change can be seen
clearly in a simple fluid experiment called the Benard cell—or more colloquially, boiling water.
So, imagine a container with water in it. When you turn up the heat, the water molecules begin
moving faster. They keep moving faster until they quite literally cannot go any faster in their
current pattern (random collisions). Since, heat (pressure) still pushes for more, an invisible
crisis sets in. The system becomes unstable and the context becomes ripe for change. Small,
naturally-occurring in homogeneities (diversity) in the system begin to have a new effect. In this
case, little pockets of relatively hotter molecules have been randomly coming together and
moving apart. These little pockets are a type of “diversity,” because they have unique
characteristics which nature soon puts to use. (In this case, hot collections are lighter and more
buoyant than their cooler surroundings.) Now pockets of hot molecules begin to float upward.
Eventually one pocket rises all the way to the top, loses its heat and sinks back down pulling
other molecules in its wake. This triggers a comprehensive “reorganization.” Suddenly, the
entire region erupts into a coherent, circular motion. The name for this process is “self-
organization.” Still, the story isn’t over. If the heat continues, the whole process will
repeat.
Molecules will move faster in the new circular motion until they can go no faster. The system
becomes unstable. Naturally occurring diversity will seed a new, faster cycle. The system will
reorganize itself into a more “intricate” pattern, something like a figure ‘8.’
It is more intricate in
that it consists of smaller, tighter, inter-linked circles.
 Figure 2 The
S-Curve.
If the horizontal
axis is time and the vertical is speed of energy flow, then one can also think of a
newly “self-organized” circle (seen in Figure 1c) as following a standard cycle of development
which leads either to a new more “intricate” organization which can handle new pressures
or
else regression or collapse ensues. Super-purified fluid demonstrate the calamitous alternative.
When you purify a liquid, you remove all the “diversity” along with the “impurities.”
Then, when
the system reaches a crisis point, it explodes instead of reorganizing. In the case of human
systems, there are three alternatives: (a) Increase intricacy—reorganize into a new pattern
which answers the new demands while also restoring the strength of internal bonds; (b) Recede
to a safe niche—find a less pressured environment, where the system can get by in its current
pattern; (c) Regression or collapse—if the system fails to do (a) or (b), it must either shrink
in
size or it will collapse.
 Figure 3: The
Embryo: An Example of Increasing Intricacy
A developing embryo
provides a perfect example of how intricacy evolves. An embryo starts
as a single cell that gets bigger. As the cell grows, however, the forces holding it together get
stretched thinner. Nature’s solution, seen in the embryo, is to divide into two smaller cells
that
then stick to each other. The process then repeats. Each cell grows, reaches its limits, divides
and rejoins its fellows, now for a total of four cells…then eight, sixteen, and so forth. After
each
round of dividing, the embryo is made up of more cells and smaller ones. The system is now
stronger because each cell is smaller and thus stronger in itself. Linking together then gives the
strength of “many bound as one.”
One can see these
organizational themes playing out in the co-evolution of the other two
threads, intelligence and collaboration.
The Co-evolution
of Intelligence and Collaborative Communities
Intelligence started
when the first single-celled organisms began responding to little patterned
trails of energy which led to food. In doing so, they were responding appropriately to
“information.” Over time, living organisms also became more complex, primarily by forming
collaborative communities based on the principle of “specialize and integrate.”Like everything
else in evolution, collaborative enclaves were driven into being by pressure, this time to work
together so everyone could survive better. The end result was multi-cellular organisms (like
ourselves) whose cells take on specialist tasks (lung, gut, leg, etc.) to create a more complex
whole.
Having many cells,
however, made intelligence more difficult. Multi-cellular organisms still
needed to respond to information to get their food (survive), but to do so they also had to
circulate information (signals) inside to stay in sync. As multi-cellulars got bigger, however, they
grew apart (internally) and information circulation broke down. This created evolutionary
pressure to restore internal coherence and collaborative communication. The result was first
nerves and then brains. (See Figure 4.)
Figure 4: Growth
Crises: From Multi-cellular Clusters to Nerve Cells
Though nerves and
brains were mainly mechanisms to stay collaboratively connected, the result
was ever-increasing intelligence and behavioral complexity. In short, living organisms became
more and more amazing—from planaria to human beings—because of the way intelligence,
collaboration, and organizational growth blend together.
Growth brings recurrent
pressures to stay intelligent by staying collaboratively connected. We
are the cutting edge of this evolutionary process. It is basically a universal learning process, as
well as one of developmental change.
Humankind as
a Collaborative Learning System that Still Faces Growth Crises
Dynamic evolution
gives educators a great gift: a scientifically sound explanation of why human
societies are collaborative learning systems (a “society of mind” in scientific terms).
Because we
now have a better understanding of the basic principles which drive organization and change,
we also have a better understanding of what makes our collaborative learning systems flourish
or fail. The list of implications is long. For example, we now see why we must nurture diversity
if we hope to evolve seamlessly, without catastrophe in between. We see more clearly why
well-knit community fabric is crucial to social intelligence. We also learn that punctuated change
is nature’s way and that context and timing play a huge role in all that exists. No theory or
mental map will last forever. If we collaborate well, however, our maps will get better.
To understand the
particularly large crisis in our own time, we need to understand how these
same principles play out in the evolution of human societies. It is actually easy to see:
-
Periodically growth
pulls social fabric apart and human collaborations begin to fail.
The resulting pressure has led to a succession of developmental stages with
accompanying social (behavioral), economic and organizational shifts. Covering
nearly a million years of evolution, these stages are: 1) loose foraging pods, 2)
organized hunting bands, 3) agricultural villages, and 4) war-centered hierarchical
civilization. New stages rise on the shoulders of older patterns which never
completely go away. See Figure 5.
- The last big organizational shift 5000
years ago, brought hierarchies. Hierarchies were
crucial when they first arose because they added coherence and the ability to mobilize
group resources and energies in focused ways. Now, however, the pace of change
and level of complexity of a 21st century world is too much for this ancient command-
and-control system. Bonds break vertically and absurdity is common. Various kinds
of exploitation and abuse of power are also common because the culture which arose
with hierarchy was based on imperialism (war for profit, power and empire-
building). This culture may or may not have been necessary, but it is now clearly
behind many (perhaps most) of the convoluted calamities we now face: from
materialism, inequity and environmental degradation to democratic processes
dominated by monied interests.
- It appears, therefore, that war-centered
hierarchies have reached their limit. The
slowness and rigidity of this organizational structure and the many calamities that the
accompanying culture brings are now generating huge pressures and a vast number of
upstart alternatives (a bubbling pot of diversity). If these bubbles of reform do
coalesce, civilization as a whole will start changing much faster and more coherently
than before. It will do so because blocked energy will be surging through the new
paths, driving momentum toward a new pattern.
Figure 5: Growth
Stages: From Loose Band to Hierarchical Civilization
Table 5:
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Foraging Bands ~ 1.5 million BC 100,000
BCC --Hominid groups began as loose
bands of individuals who foraged to survive. Few in number, these early groups would
have developed shared meanings easily, in the course of constant contact (even
though they did not yet have speech per se).
Organized Hunting Bands~ 75,000 BC - 20,000
BC -- From Neanderthal through Cro-
Magnon, speech, cooperative behaviors and tools all began evolving rapidly. Human
groups developed more complicated interactions, the most notable being the organized
hunting bands. Like wolf packs., human beings began to work together to capture their
prey. Unlike wolves, humans made increasingly elaborate plans such as herding animals
over cliffs or into traps.
Agrarian Villages ~ 18,000 BC 4,000 BC --By
18,000 BC, human groups in Old
Europe, the Indus valley, and the Near East began to settle down in one spot and grow
their own food. This "agricultural revolution" produced the first villages and the first
domesticated animals. Staying in one place also allowed crafts -- pottery, weaving,
metallurgy, etc., -- to emerge along with such new technologies as boats and the wheel.
New social specialties from policeman to priest emerged along with governance handled
by councils.
Anthropologist Riane Eisler (1988) describes these as partnership
societies. She lists
their main characteristics as:
War-centered Hierarchical Civilization~3,000 BC to 2000 AD--Somewhere
around 4,000 BC, partnership culture was subsumed by the hierarchical system we
use today. Early city-states like Sumer, which had one operated on partnership
principles, also became increasingly devoted to war as a means of empire-
building. The entire structure of society changed in suit. Historian Christopher
Brinton describes the result as follows:
"Each of the great
valley states was ruled by a despot: a king who was also
a priest, if not actually considered a God. He ruled through a privileged class
of nobles and priests who commanded a professional army. His subjects
had no appeal from his decisions. They obeyed orders and turned over much
of their crops as taxes to support the bureaucracy. Bureaucrats included
such experts as engineers, clerks who kept tax records, lawyers to argue
disputes, and judges to settle them. After these very great innovations of
urban civilization, these societies apparently changed very slowly." (1964, p.
8)
Eisler calls this dominator culture. She lists
its main characteristics as:
The worship of violent, vengeful Gods, usually through
a bureaucratic priesthood
directed by an autocratic head, often the king himself.
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The pattern of
growing apart and then finding new ways to stay coherent and in sync has also
played a major role in the evolution of human social systems. Since human social systems are a
type of society of mind, the kind of culture also evolves in step. Economic patterns, political
systems, religious systems and general culture all evolve in conjunction with the main
organizational structure.
The rise of integral
civilization, therefore, is not just another small S-curve; it represents the
beginning of a major new stage of development. It will include major new cultural patterns,
economic systems and organizational structures. Even the briefest of examinations suggest that
the next system of civilization must be:
Some of the needed infrastructure is already in place. Computer networks, of
course,
allow grassroots citizenry across the globe to connect and self-organize like at no other
time in history. There is also another side to this same trend. Information-age economics is
creating huge pressures for a new kind of worker and with it a new kind of citizen. Former
Secretary of Labor Robert Reich (1991), for example, points out that the digital age is
part of a larger economic switch from what he calls “high- volume” to “high- value”
economics. The greatest profits are no longer made in the mass-production of uniform
goods (high- volume industrialism), but in the high-quality customization of goods and
services (high-value economics). The highest profits in software, for instance, come from
customizing products to particular business needs and the fastest-growing truck, rail, and
air freight businesses meet specialized needs for pickups and deliveries worldwide.
Whether the industry is old or high-tech, service or manufacturing, the pattern is the same.
The hidden significance
of a high-value economy is that it requires citizen-workers who, like the
new society, must be more collaborative, creative, flexible and equitable (less self-centered). In
19th-century industrial days, companies needed factory workers whose chief characteristics
were the ability to read and follow directions. The schools of the time served these needs well.
They stuffed facts into young brains and taught the discipline, independence and competition
that was thought to make all things good. Customization, on the other hand, requires people
who can rapidly envision and build new things. Teamwork is essential as is the ability to think
“outside the box” and to make connections across fields. Commitment to one another is often
the saving virtue of a team and the saving virtue of a high-value leader is the knack of helping
others be successful. Today, therefore, the irresistible needs of the high-value world are
meeting the immovable object of modern education with an audible crash.
Educational
Movements Already Aimed at the Integral Age
Obviously, K-12
education will play a pivotal role in the success of the new society. Four
existing reform movements are already heading in the right direction: cooperative learning,
service learning, community integration, and brain-based learning.
We all face the challenge of building an integral civilization because we will
all pay the
price[i]
if we fail. There is a great deal to learn and even more to be worked out in the
process of trial-and-error attempts. The sweet knowledge that gives wings to our feet,
however, is that what integral society needs to become has much in common with the
original tough-minded, free-but- compassionate, egalitarian, committed, creative,
hardworking, democratic enlightenment dream that Americans in particular call their own. In
short, pressure is building to become the kind of society that generations huddled masses
have sought. Now we have a better light to see our way through the maze and more
pressure to push our cause.
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AUTHOR J. Shrager and T. Hogg and B. A. Huberman
A Graph-Dynamic Model of the Power Law of Practice and the Problem-Solving Fan-Effect
Numerous human learning phenomena have been observed
and captured by individual laws, but no unified
theory of learning has succeeded in accounting for these observations. A theory and model are proposed
that account for two of these phenomena: the power law of practice and the problem-solving fan-effect.
The
power law of practice states that the speed of performance of a task will improve as a power of the
number
of times that the task is performed. The power law resulting from two sorts of problem-solving changes,
addition of operators to the problem-space graph and alterations in the decision procedure used to decide
which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic
account for both of these sources of the power law. The model also predicts a problem-solving fan-effect,
slowdown during practice caused by an increase in the difficulty of making useful decisions between
possible paths, which is also found empirically.
Chunking-Based Learning Mechanism
Chunking is the single
learning mechanism
supported directly by the Soar architecture. It is
based on the psychological phenomena of chunking: the association of chunks (expressions or
symbols) into a new, single chunk. In Soar, chunking collapses the results of an
impasse
into a
production which can then be fired if the same, or similar situation occurs again, thus avoiding the
impasse. This leads directly to Soar's ability to move from
problematic to routine behavior
. Since
the learning mechanism creates new knowledge in the same form as the rest of the system's
knowledge (i.e.
productions
), the
uniformity of the representation
is maintained by the learning
mechanism.
Because chunking
is based on the results of a resolved impasse, it is an experience-based
learning
technique. The action of the production that is created by chunking simply reflects the
results of the resolved subgoal. The production conditions are based on the working memory
elements that existed prior to the impasse and led to the resolution of the impasse.
Dependency
analysis
is used to determine which working memory elements allowed the achievement of the
subgoal. Since this dependency analysis uses only those working memory elements that were
used in impasse resolution, chunking
generalizes implicitly
. The situation that leads to a chunk
does not need to be reproduced exactly for the chunk to fire later; only those elements which led
directly to the chunk are necessary.
The architecture
directs the creation of a chunk whenever an impasse is resolved. Thus,
chunking is both a universal
and
reflexive
process. Additionally, the chunking mechanism is
fixed and
impenetrable
and can not be improved by learning.
Finally, chunking
can be viewed as a caching mechanism. The actitivity of the problem solver
under an impasse is placed in a chunked production and, when a similar situation is recognized
via the associative
production match, the results of the previous problem solving activity are
made available via the actions of the chunk. Thus, the steps of the problem solving process were
cached into a single step. This view points out the fact that chunks are active processes (
productions
), not static declarative data.
Real-Time Constraint on Cognition
Human cognition
has been shown to occur within well-defined time frames that are
arithmetically related to the number of serial decisions needed to perform the task. The power
law of learning
is a phenomenological measure of this observation. When a task is first presented
to an agent, the agent must deliberate over every move resulting in slow performance. As the
agent
learns
, fewer and fewer serial decisions need to be made and the agent performs faster.
Strict limits have been found in humans that limit the ability to make small numbers of serial
decisions.
This data illustrates
the real-time constraint on cognition: "There are available only ~100
operation times (two minimum system levels) to attain cognitive behavior out of neural-circuit
technology." This constraint shows that the interaction between distinct computational units
(whether in a parallel or serial organization) is minimal.
The data also provides
some insight on the decomposition of perception, delivery of symbols to
memory, deliberation, and action. This decomposition is not discussed here, but can be found
in Newell's Unified
Theory of Cognition
. It also suggests that the hierarchy (or heterarchy) of
deliberation consists of
serial
and
parallel
processes that are configured such that these limits
emerge.
Cognitive Architecture: A Definition
An architecture
can be defined simply as the portion of a system that provides and manages
the primitive resources of an agent. For many cognitive architectures, these resources define the
substrate upon which a physical symbol system
is realized. Addressing the many
issues
surrounding the choice, definition, extent, and limits of these resources and their management
is
one of the purposes of this document. This analysis attempts to assist in determining the
necessary, sufficient and optimal distribution of resources for the development of
agents
exhibiting general intelligence
.
However, many researchers
purposely ignore the constraints posed by human cognition. Often
this is because they are interested in developing agents which populate and behave effectively in
some environment; studying the interactions between the architecture and the environment
(which could be a static, problem-solving situation or a highly dynamic, reactive environment) is
of primary concern. In this sense, the term cognitive architecture is a little misleading.
Although it is used throughout the document, a better term might be agent architecture which
would include both those systems that made a explicit attempt to model human psychology (i.e.
cognitive architectures) and those which simply explored some aspects of general intelligent
behavior.
The Fan Effect
The Fan Effect
is Anderson's
explanation for the brain's ability to optimize memory retrieval by
keeping better access to memories that are more likely to be relevant. The effect is a natural
extension of the propositional
network
(see the definition of
symbolic representation
) Anderson
uses to represent concepts in the brain.
Concepts
with greater probabilistic relevance are
connected via conceptual links to other concepts, and the more connections (that is, the greater
the fan), the more likely the central concept will be activated.
This effect was
proposed with Anderson's ACT* methodology for concept classification as a
model for the human brain, and was based on the assumption that the brain uses a spreading
activation of concepts in order to do classification. His conclusion is that the associativity
of the
brain is based on the
probabilistic nature of the environment
it is exposed to, and that the ability to
classify is an extension of this; the fan of the network is not the critical factor in classification.
This is one of his arguments for the notion that to understand the workings of a
cognitive
architecture
(namely, the human brain), one must look not within the architecture, but at the
environment the architecture acts in. This is known as
rational analysis
.
Assumptions
Simon strongly discounts this point-of-view
in his article titled "Cognitive Architectures:
Comment". His argument is essentially one of
bounded rationality
.
Optimality
Evolution did not
give rise to optimal agents, but to agents which are in some senses locally
optimal at best, locally satisfactory in norm, and becoming extinct at worst. Thus, a theory
based upon optimal behaviors is tenuous at best.
Optimization
implies that the goals of the agent are known explicitly. When synthesizing or
tasking
an agent one can know or determine the goals of the agent, but when analyzing the
behavior of an arbitrary agent, one does not know the goals. In fact, the range of rational goals
can lead to such variant behavior that assumptions about the goals cannot be made with
confidence. The example cited in depth by Simon is that of economic predictions.
Another implicit
assumption underlying optimization is that the utility functions are known (see
recipe
item 3
). In fact, real agents must often act with insufficient knowledge by estimating
these. Estimates will range from accurate to wrong, from simple to sophisticated. Since rational
analysis- a variant of which lead to the economic theories plagued with these problems- does not
account for these phenomena, it cannot be taken as a panacea paradigm for analysis.
Assumptions
Anderson criticizes
mechanism-focused cognitive modelers with making unnecessary
assumptions about how an agent performs architectural functions such as memory management
and computations. However in his analyses, he is forced to make similar assumptions. Examine
the assumptions made by Anderson in his analyses:
Rationality versus behavior
While rational
analysis can yield some information about cognition such as that a solution can
be found, the particular solution found by particular subjects cannot necessarily be found.
Anderson argues that by defining the environment to which the subject has adapted, the optimal
solution will be the solution determined by the subject and that these constraints uniquely define
the optimum. Simon argues that these constraints are not sufficient to determine uniqueness.
Without a uniquely defined solution, subject-specific strategies cannot be determined nor
studied.
Bounded Rationality
In 1957, Simon
proposed the notion of
Bounded Rationality:
that property of an agent that behaves in a manner that is nearly optimal
with respect to its goals as its resources will allow.
Bounded rationality
better describes agent behaviors than Anderson's optimal rationality
approach for the following reasons:
-
agents are not
optimal
- the methods by which architectural tasks
are performed significantly affect the agents
behaviors
- the representations of information and
the strategies for solving problems must all be
discovered by the agent
- agents' behaviors across isomorphic task
domains are not constant
In considering
bounded rationality, Simon suggests that researchers not limit their focus to
signature data but look for all the data they can in order to uncover the underlying processes.
He concludes by providing a lower bound of relevance to cognitive analysis:
The exact ways in which
neurons accomplish their functions is not important- only their
functional capabilities and the organization of these.
Symbols and Representation
A natural question
to ask about symbols and representation is what is a symbol? Allen Newell
considered this question in
Unified Theories of Cognition
. He differentiated between symbols
(the phenomena in the abstract) and tokens (their physical instantiations). Tokens "stood
for"
some larger concept. They could be manipulated locally until the information in the larger concept
was needed, when local processing would have to stop and access the distal site where the
information was stored. The distal information may itself be symbolically encoded, potentially
leading to a graph of distal accesses for information.
Newell defined symbol
systems according to their characteristics. Firstly, they may form a
universal computational system. They have
Finally, Newell
defined symbolic architectures as the fixed structure that realizes a symbol
system. The fixity implies that the behavior of structures on top of it (i.e. "programs")
mainly
depend upon the details of the symbols, operations and interpretations at the symbol system
level, not upon how the symbol system (and its components) are implemented. How well this
ideal hold is a measure of the strength of that level
.
The advantages
of symbolic architectures are:
These advantages
have been considered as one of the fundamental tenets of artificial
intelligence
known as the physical symbol system hypothesis. The hypothesis proposes that a
physical symbol system has the necessary and sufficient means for general intelligence.
Mapping Simulation to the Real World
When designing
a system, one would hope that it would be intended for use in the real world
sooner or later. Yet it is impractical to assume that a first generation system can be adequately
tested and analyzed
in a
dynamic environment
. What these basic conclusions reveal is that
almost every
architecture
which stands the test of time is going to have to make a transition from
a
simulated world
to the real world.
This transition
is no easy task to say the least. A simulation requires that some assumptions be
made about the environment, and these assumptions could be crucial to the generality
of any
system that uses that environment. A classic example of this is a system which assumes that the
necessary elements of the environment are instantly recognizable, and the activators of the
system perform flawlessly. For instance, when designing a robot, we could assume it could
recognize a green box, and we exploit this in the environment by representing it as a logic
predicate GreenBox(P1). Similarly, we could have it execute its movement plan by outputting
commands such as "Turn Left" and "Go Forward 2". If we actually expected to implement
whatever architecture we designed in this system, the dynamic nature of the world and the
difficulties of sensing would set us up for a rude awakening.
Even if the simulation
environment does not have a such fundamentally slanted view of the
world, the manipulation of the system environment could be enough to weaken the value of the
testbed. Consider a system that uses an Explanation- based Learning
algorithm and which
always runs for a set(short) amount of time. Even though it would be likely that an agent could
get really good at using EBL for
goal reconstruction
, opportunistic behavior, etc., this ignores the
fact that if we let it run long enough, the system may slow down significantly because of the
utility problem
. By not addressing the basic problems of EBL, any progress made will be
hampered. In this case it's not the environment per se which is affecting the development of
the
system, but the experimental setting itself.
In the former case,
an author of a cognitive architecture should realize the drawbacks of the
system under development, and yet also realize subverting them will can only harm the
development and refinement of the architecture. The former case is much more tricky; how
detailed can a model be and still be a model? There are no easy answers to this question. It
helps to have a specific domain in mind for a system when testing, and emulating that domain as
best as possible. But for a system which truly displays general intelligence, there is no one
testbed which is wholly sufficient.
THE INTEGRATED
LAW OF HUMAN PERFORMANCE
The Power Law
of Human Performance or of Practice (PLP) states that the time (T) it takes an
individual to perform a given task decreases as the number of times (N) the individual practiced
the task increases. In mathematical terminology, the law is: (Education Vol. 115, No. 1, 31,
1994)
T = A + B (N
+ E)-p or T = A + B/(N + E)p
where A, B, E and
p are constants that vary (a) with the task at hand and (b) with the individual
performing the task. A represents a physiological limit. B and E partly denote prior experiences
before the beginning of the practice sessions, and p is the learning rate. In other words, the law
states that “practice renders perfect.” This law applies to the performance of sensory-motor
(or
athletic), creative (or artistic), and cognitive (or intellectual) tasks.
The shorter the
time T to perform the task - completely and correctly - the higher the level of
proficiency. Hence, as the number of practices increases, so does the proficiency of the
individual. The two figures below graphically show the plot of the above expression for text
editing and problem solving tasks.
The dramatic impact
of this law becomes apparent when one considers its application over
several tasks and several days, months, and years. Then it becomes clear that genius is mostly
the result of sustained, quality practice. The same way adequate practice, at an adequate scope
and depth, is needed for the making of Olympic, National Basketball Association, National
Football Association, and Major League Soccer champions and for the making of musicians
and artists, the same way it is needed for the making of science, engineering, and mathematics
scholars, including scholars in the social and behavioral sciences and any other discipline.
Further, this law
is implacable. It applies whether one likes it or not! It applies to the refinement
of the enhancement of the teaching, mentoring, research, and writing skills of a faculty member
or of a mentee! These points are discussed further by Bagayoko and Kelley (1994) and Moore
and Bagayoko (1994) in connection with the explanation of the creation of educational value
added from K through graduate school and beyond.
The integrated
or compound law of human performance (ILP, Bagayoko and Kelley,
Education, Vol. 115, No. 1, pp. 31-39 1994), is the convolution of the power law of
performance as simultaneously applied to several tasks over a long period of time. The main
difference between the power law and the integrated law is that the former follows a simple
equation that involves an exponent or power (i.e., p) while the mathematical form of the latter is
yet to be determined. The quintessential point here, however, stems from the fact that
according to the integrated law of human performance, the abilities, skills, and attributes of
students that are meaningfully engaged and challenged in and outside the classroom (as by
mentoring activities) — from K through graduate school and beyond — are the ones that will
develop! The integrated law of human performance provides the scientific basis for high
expectations for all students! This point is rigorously established by Bagayoko and Kelley
(1994). Professional mentoring, as defined elsewhere by Bagayoko, provides an almost fail-
safe strategy for promoting the academic excellence of all students (female or male, minority or
non-minority, young or mature). Student retention, on-time graduation, and their success in
graduate school are partly by-product of the quest for proficiency and excellence- - through
quality teaching, mentoring, and learning. It is critical to note that the same way the ILP applies
to the cognitive domain, the same way it applies to non- cognitive (i.e., behavioral) variables.
Character is molded through practice. Also see Education, Vol. 115, No. 1, pp. 11-18 &
pp.19-25, 1994.
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Development of Expertise
Cognitive Psychology and Its Implications: Chapter 9
Overview
§ General Characteristics of Skill Acquisition
§ The Nature of Expertise
§ Transfer of Skill
§ Educational Implications
§ “Through extensive practice, one develops high levels of expertise which help
most when faced
with demanding problems.”
• No pain, no gain.
• When the going gets tough, the tough get going.
General Characteristics of Skill Acquisition
§ Three Stages of Skill Acquisition
• Cognitive stage (declarative encoding)
• Associative stage
– Errors in understanding are detected and eliminated
– The connections among the various elements required for successful performance
are
strengthened
– Declarative and procedural knowledge may both remain
• Autonomous stage (automated and rapid)
§ Power-Law Learning
• “Performance of a cognitive skill improves as a power function of practice
and only shows modest
declines over long retention intervals.”
The Nature of Expertise
§ Proceduralization
§ Tactical Learning
§ Strategic Learning
§ Problem Representation
§ Pattern Learning and Memory
§ Long-Term Memory and Expertise
Proceduralization
§ “Proceduralization refers to the process by which people switch from explicit
use of declarative
knowledge to direct application of procedural knowledge.”
Tactical Learning
§ Learning a method that accomplishes a particular goal (e.g, the sequence of actions
required to
solve a problem).
§ “Tactical learning refers to a process by which people learn specific rules
for solving specific
problems.”
Strategic Learning
§ How one organizes a solution to the overall problem.
§ Larkin (1981)
• Physics problems
– Novices use the method of reasoning backward (means-ends analysis)
– Expert reason forward
Problem Representation
§ Chi, Feltovich, and Glaser (1981)
• Classify physics problems
– Novices classify problems based on surface features
– Experts classify problems based on deeper principles
§ Computer programming
• What happens as programmers become more expert?
Pattern Learning and Memory
§ de Groot (1965, 1966)
• What separates master chess players from others?
• Main difference—experts chose better moves
• Chess master considered about the same number of possible moves before selecting
their move.
• Chess masters able to reconstruct configurations of 20 pieces after 5 seconds
of study.
• Novice players could only reconstruct 4 or 5 pieces.
Pattern Learning and Memory
§ Newell and Simon (1972)
• Speculated that, in addition to learning many patterns, masters have also
learned what to do in
the presence of such patterns.
• Thus experts do relatively better at “lightening chess.”
• Allows them to focus problem-solving efforts on more sophisticated aspects
of chess strategy.
§ “Experts can recognize chunks in problems which are patterns of elements that
repeat over
problems.”
Long-Term Memory and Expertise
§ Charness (1976)
• Experts memory for chess positions show no loss in recall over a 30-second
delay.
• Expert chess players have an increased capacity to store information about
the domain.
• Increased long-term memory is only for the domain of expertise.
§ Chase and Simon
• Experts recall larger patterns but also recall more of them.
• Digit span and subject SF (81 random digits)
Transfer of Skill
§ “There is often failure to transfer skills to similar domains and virtually
no transfer to very different
domains.”
§ Theory of Identical Elements
• “There is transfer between skills only when these skills involve the
same abstract knowledge
elements.”
Transfer of Skill
§ The Doctrine of Formal Discipline
• Studying subjects such as Latin and geometry was valuable because it served
to discipline the
mind.
• The mind is composed of general faculties (observation, attention, discrimination,
and reasoning)
which are exercised in the same way as muscles (content not important, only level of exertion).
• Effectively no evidence supporting the doctrine of formal discipline.
Theory of Identical Elements
§ According to Thorndike, the mind is not composed of general faculties but rather
specific habits
and associations.
§ Training in one kind of activity will transfer to another only if the activities
share common situation-
response elements.
§ Thorndike’s position was a bit too narrow—transfer isn’t tied
to the identity of surface elements.
Negative Transfer
§ Learning one skill seldom makes a person worse at learning another skill.
§ Polson, Muncher, and Kieras (1987)
• No negative transfer for text editing.
§ Only Einstellung effect (mechanization of thought)
§ What’s your personal experience?
Educational Implications
§ “Instruction is improved by approaches that identify the underlying knowledge
elements and bring
students to mastery on them all.”
§ Intelligent Tutoring Systems
• “By carefully monitoring individual components of a skill and providing
feedback on learning,
intelligent tutors can bring students to rapid mastery of complex skills.”
Educational Implications
§ Componential analysis
• Approaches to instruction that begin with an analysis of the elements to be
taught.
• Higher achievement is generally obtained in programs that involve such componential
analysis.
§ Mastery learning
• Follow the students on the performance of each of the components underlying
the cognitive skill
and ensure that they are all mastered.
Intelligent Tutoring Systems
§ Private human tutoring is very effective.
§ Intelligent tutoring systems are computer systems that interact with students while
they are
learning and solving problems much as a human tutor would.
§ The LISP tutor at CMU.
• “The success of the LISP tutor is one piece of evidence that these 500
[production] rules are
indeed what underlie coding skill in LISP.” |
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1. Technologies
