Transcript Cognitive Science

Research in the Teaching and
Learning of Physics
Part I: Survey of Cognitive Science
Motivation
• Scientific approaches to science education
– Research-based vs. seat-of-the-pants
• Is teaching an art?
Cognitive “Science”
• Caveat: Why the “science?”
– Context of results
• What is it?
• Why study it?
– Intellectual curiosity (how does the brain work?
What is “genius?”)
– Practical applications (HCI, AI, education)
– Implications for other fields (sociology,
economics, political science…)
History
• Plato, Aristotle (~400 B. C.)
– Empiricism vs. Nativism
• Scientific beginnings of psychology (1879)
– Research by introspection
– Free association experiments
• Behaviorism (1920)
– Consciousness is neither definable nor useful
• Information-processing model (1960)
– Research on human factors
– Rise of computer science, artificial intelligence
– Inadequacy of behaviorism in linguistics
Information processing
• Sternberg (1969)
– Subject given a
string of one to six
digits (e.g., 397)
– Measure time to
determine if a single
digit is in the string
9
Perceive
stimulus
9 = 3?
9 = 9?
9 = 7?
Make
decision
Generate
response
Yes
Features of IP model
• Discussion of what is going on in the brain,
with no reference to physiological processes
• No reference of how symbols are encoded
in brain
• Use of a computational metaphor
• Time measurement important
Domain of analysis
• Cognitive science <==> physiology
• Computer science <==> electrical engineering
• Emerging field: Cognitive neuroscience
Recent controversies
• Ecological approach (situated cognition)
– Structure of the mind, environment, or both
• Connectionism
– How can high-level functions be achieved by
connections of neural-like elements
Some areas of research
• Perception and attention
– How do we recognize what we see and hear?
• Memory
– How do we remember and forget things?
– How does memory work?
• Problem solving
– How do we solve problems we’ve never seen before?
• Development of expertise
– How do we become skilled at cognitive tasks?
• Others: language, knowledge representation, child
development, etc.
What is memory?
• How is it organized?
• How do we get stuff in and out?
• How is stuff stored?
Organization of memory
Sensory store
Attention
Short-term
memory
Rehearsal
Long-term
memory
• Rehearsal was necessary for
getting ideas into long-term
memory
• More rehearsal resulted in
better memory
• Many experiments showed
decrease in accuracy of recall
with time
Memory
• Craik and Lockhart (1972)
–
–
–
–
Subjects given a 4-digit number
They then rehearsed a word for 2, 6, or 18 seconds
They were then asked what word they rehearsed
Subjects recalled 11%, 7%, and 13% of the words
• Rehearsal time is not the key, crucial part is
processing of material
Working memory
• Contents can originate from sensory
memory
• Contains information that one is conscious
of at the moment
• Contents can be acted on and processed, or
maintained by rehearsal
• 7 ± 2 elements
5 0 7 2 3 6 1 2 4 8 2 9
1 7 7 6 1 8 6 5 1 9 4 1
dog
rock
chair
bay
rope
stink
dark
university
aluminum
biographical
constitutional
auditorium
organization
untargetable
Rehearsal and working memory
90
2.2
% correct
80
2
70
1.8
60
1.6
50
# words
readable
40
1.4
# words readable
Items correct (%)
• Has an articulatory loop
• Holds 1.5–2 sec of info
Other evidence (Conrad 1964):
• When subjects asked to recall
a string of letters (HBKLMW)
– Mistakes consisted of
replacing a letter by one
that sounds alike (T with
G), as opposed to looks
alike (Q with G)
– Harder to memorize letters
that rhyme (BCTHVZ) than
ones that don’t
(HBKLMW).
1.2
30
1
2
3
4
5
Number of syllables
(Baddeley 1986)
37
x 28
296
+ 740
1036
374
x 288
Working Memory
• Consists of a visuospatial sketchpad and a
phonological loop, both controlled by a
central executive.
• Physiological evidence--frontal cortex
Central
executive
Visuospatial
sketchpad
Phonological
loop
Area 46
• Test:
– Monkey shown food item that is
hidden in 1 of 2 covered wells
– Monkey is prevented from
looking at wells for 10 seconds
– Monkey allowed to retrieve food
• Monkeys with damage to frontal cortex
unable to perform task
– Neurons in area 46 fire only during delay period
• Human infants unable to perform similar task until 1
year (maturation of frontal cortex)
– Increased blood flow to area 46 when retaining workingmemory information
Memory and meaning
What do we remember?
• We normally remember the meaning of a linguistic
message, rather than its exact wording.
• We tend to remember a meaningful interpretation
of a picture.
• Less meaningful material can be remembered
better by converting it to meaningful material.
• When you score your results, do nothing to correct your
answers but mark carefully those answers which are wrong.
• When you score your results, do nothing to correct your
answers but carefully mark those answers which are wrong.
• When you score your results, do nothing to your correct
answers but mark carefully those answers which are wrong.
• When you score your results, do nothing to your correct
answers but mark carefully those answers which are wrong.
To begin the test, please turn to page 2 of the answer booklet
and judge which of the sentences printed there occurred in the
instructions you just heard.
(Wanner 1968)
(Wanner 1968)
Target picture
(77% recog.)
Type change
(94% reject)
Token change
(60% reject)
Subjects studied 8
pictures for 10 sec each
(Mandler and Ritchey 1977)
• 70% correctly reconstructed when given labels with
which to study the picture
• 51% correctly reconstructed without labels
(Bower, Karlin, Dueck 1975)
Implications of memory for meaning
• Mnemonic techniques can be useful for
learning things that don’t initially have
much meaning
– associating nonsense syllables
– learning a foreign language (carciofi, Atkinson
and Raugh, 1975)
– telephone numbers, names for faces, etc.
• Good memory for material results when it is
processed more elaborately
Processing for memory
• Bobrow and Bower (1969)
– People memorized simple subject-verb-object
sentences
– Condition 1: Sentences provided by
experimenter
– Condition 2: Sentences generated by people
– Task: Given subject, supply object
– Success rate was 29% and 58%
Processing and meaning
• Subjects’ show better memory
for sentences printed upside
down (Kolers 1979).
• Slamecka and Graf (1978):
Generating vs. reading
synonyms or rhymes for words
• Processing need not be focused on meaning of
material.
Processing and intention
• Subjects shown 24 words spaced 3 seconds apart
• Half of the subjects told to check whether word contained
an “e” or “g,” other half told to rate word for pleasantness.
• Half of the subjects told that the purpose of the test was to
check for letters or to rate the words, other half told that
purpose was to memorize the words
incidental
intentional
rate
68%
69%
check e/g
39%
43%
• Whether or not you intend to learn doesn’t matter!
It’s the level of processing in which you engage.
(Hyde and Jenkins 1973)
Implications of processing for memory
• Study strategies (SQ3R, PQ4R)
–
–
–
–
Preview: Survey chapter, identify sections
Questions: Make up questions about each section
Read: Read section with questions in mind
Reflect: Reflect on text, construct examples, relate to
prior knowledge
– Recite: Recall info, answer questions for section
– Review: Review main points, answer questions for
chapter
• Strategies designed to encourage deep processing
Some studies
• Frase (1975)
– Control: Nothing special (50%)
– Group 1: Make up study questions while
reading (70% / 52%)
– Group 2: Answer study questions while reading
(67% / 49%)
• Rothkopf (1966)
– Control: Nothing special (30%)
– Group 1: Interspersed preview Q’s (72% / 29%)
– Group 2: Interspersed review Q’s (72% / 42%)
Application
• Reciprocal teaching
– Student/teacher play both roles inventing
questions
Practice effects
• Time to recognize
sentences vs. number of
days of practice (Pirolli
and Anderson, 1985)
• Power law of learning
y = A xB
Physiological basis
• When a neural pathway is
stimulated with high frequency
current, cells on that pathway
become more sensitive to further
stimulation.
• Measured percent increase in
excitory postsynaptic potential
(decrease in difference of electric
potential between inside and
outside of neuron) due to
stimulating the hippocampus of
rats
Barnes (1979)
Non-practice effects
• Success at word
recognition (from a
learned list) as a
function of delay T
• Power law
y = Ax–B
Physiologically…
Barnes 1979
But forgetting is not just a matter
of time…
Interference effects
Pre-existing knowledge
• Subjects learned 0-4 fantasy
facts about well-known
people (e.g., Napoleon
Bonaparte was from India)
• Subjects then judged three
types of sentences, (a)
fantasy facts, (b) actual facts,
(c) false statements
• The more fantasy facts
learned, the longer the delay
in recalling actual facts (fan
effect).
Lewis and Anderson (1976)
Redundancy
• Subjects learned:
– a single fact (92% immediate recall, 62% recall after one
week)
• Newton became emotionally unstable and insecure as a child
– a single fact + 2 irrelevant facts (80%, 45%)
• Locke was unhappy as a student at Westminister
• Locke felt fruits were unwholesome for children
• Locke had a long history of back trouble
– a single fact + 2 related facts (94%, 73%)
• Mozart made a long journey from Munich to Paris
• Mozart wanted to leave Munich to avoid a romantic entanglement
• Mozart was intrigued by musical developments in Paris.
• Additional knowledge can sometimes be helpful (but
not always…)
Bradshaw and Anderson 1982
Retrieval and inferences
Carol Harris’ Need for Professional Help
Carol Harris was a problem child from birth. She was wild,
stubborn, and violent. By the time Carol turned eight, she was
still unmanageable. Her parents were very concerned about her
mental health. There was no good institution for her problem in
her state. Her parents finally decided to take some action. They
hired a private teacher for Carol.
• “She was deaf, dumb, and blind.”
– Carol Harris: 5%
– Helen Keller: 50%
• Evidence for inference being made at test
Retrieval and plausibility
The heir to a large hamburger chain was in trouble. He
had married a lovely young woman who had seemed to
love him. Now he worried that she had been after his
money after all. He sensed that she was not attracted to
him. Perhaps he consumed too much beer and french
fries. No, he couldn’t give up the fries. Not only were
they delicious, he got them for free.
Retrieval and plausibility
• The heir married a lovely
young woman who seemed
to love him.
• The heir got his french fries
from his family’s hamburger
chain.
• The heir was careful to eat
only healthy food.
• Judged for recognition or plausibility.
• Recognition time increases with # facts. Plausibility
time decreases
Reder 1982
Elaboration and inferences
Nancy went to see the doctor. She arrived at the office and
checked in with the receptionist. She went to see the nurse, who
went through the usual procedures. Then Nancy stepped on the
scale and the nurse recorded her weight. The doctor entered the
room and examined the results. He smiled at Nancy and said,
“Well, it seems my expectations have been confirmed.” When the
examination was finished, Nancy left the office.
Nancy woke up feeling sick again and she wondered if she really
were pregnant. How would she tell the professor she had been
seeing? And the money was another problem.
Elaboration and inferences
• Studied propositions recalled:
– 29.2 for theme condition
– 20.3 for neutral condition
• Inferred propositions:
– 15.2 for theme condition
– 3.7 for neutral condition
• Many in the theme condition reported that
the doctor told Nancy she was pregnant.
Implications for advertising
“Wouldn’t it be great,” asks the mother, “if you could make
him coldproof? Well, you can’t. Nothing can do that.” [Boy
sneezes.] “But there is something that you can do that may
help. Have him gargle with Listerine Anti-septic. Listerine
can’t promise to keep him coldfree, but it may help him fight
off colds. During the cold-catching season, have him gargle
twice a day with full-strength Listerine. Watch his diet, see he
gets plenty of sleep, and there’s a good chance he’ll have fewer
colds, milder colds this year.”
Replaced “Listerine” with “Gargoil.” After hearing this
commercial, all 15 subjects checked “gargling with Gargoil
Anti-septic helps prevent colds” as a true statement.
Schemas
• A representational structure in memory that
includes characteristics of an object.
• House
–
–
–
–
–
–
Isa: building
Parts: rooms
Materials: wood, brick, stone
Function: human dwelling
Shape: rectangular, triangular
Size: 100-10,000 square feet
Schemas and inference
• Thirty subjects brought to room shown and told it
was experimenter’s office. Asked to wait there
while experimenter checked on previous subject.
Left for 35 seconds.
• Subject taken to nearby room, asked to write down
everything they could recall about experimenter’s
office.
• Descriptions influenced by “office schema”
– nearly all recalled desk, chair, walls
– only 8 recalled skull, bulletin board
– 9 recalled books (there weren’t any)
Misc.: Organization and recall
Minerals
Metals
Stones
Rare
Common
Alloys
Precious
Masonry
Platinum
Silver
Gold
Aluminum
Copper
Lead
Iron
Bronze
Steel
Brass
Sapphire
Emerald
Diamond
Ruby
Limestone
Granite
Marble
Slate
Organization and recall
• Subjects studied 4 trees for one minute each
– Words either organized or random
– 4 trials
• Results:
– Organized: 73.0, 106.1, 112 (max), 112
– Random: 20.6, 38.9, 52.8, 70.1
Bower, Clark, Lesgold, and Winzenz 1969
Contextual effects
• Divers learned a list of 40 unrelated words either
while sitting on shore or 20 feet under the water.
• Divers asked to recall words in same environment
or different environment.
Godden and Baddeley 1975
State-dependent learning
• Subjects learned a free recall list after
smoking either a marijuana cigarette or an
ordinary cigarette.
• Subjects tested 4 hours later after smoking
one or the other
Test
Study
Tobacco
Marijuana Average
Tobacco
25%
20%
23%
Marijuana 12%
23%
18%
Summary
• The crucial factor determining how well
new material is learned is how deeply it is
processed by functions such as elaboration,
question posing, comparison with prior
knowledge, organizing hierarchically, etc.
• Prior knowledge has a great effect on what
we think we learn and also on what we infer
about the information we are presented
with.
• Don’t smoke marijuana while studying.
Problem Solving
• What is problem solving?
– When there is a goal you want to accomplish,
you don’t immediately know how to achieve
the goal, and you devise and carry out a set of
steps to meet the goal.
• IP model: Problem solving consists of
moving through a problem space using
operators
Modeling Problem Solving
• IP approach uses production systems
• Production rules for multi-column subtraction
problems
– If the goal is to solve a subtraction problem,
Then make the subgoal to process the rightmost column
– If there is an answer in the current column,
Then make the subgoal to process the column to the left
– If the goal is to process a column and there is no bottom digit,
Then write the top digit as the answer
– If the goals is to process a column and the top digit is not
smaller than the bottom digit,
Then write the difference between the digits as the answer.
Early Research
• Cryptarithmetic puzzles
(Newell and Simon, 1972)
CROSS
+ROADS
DANGER
• Analyze protocols in terms of production rules
• Production rules explain 80 - 90% of protocols
Problem-solving strategies
•
•
•
•
Difference reduction
Means-end analysis
By analogy
Working backwards
Suppose you are a doctor faced with a patient who has a
malignant tumor in his stomach. It is impossible to operate on
the patient, but unless the tumor is destroyed, the patient will
die. There is a kind of ray that can be used to destroy the tumor.
If the rays reach the tumor, all at once at a sufficiently high
intensity, the tumor will be destroyed. Unfortunately, at this
intensity, the healthy tissue that the rays pas through on the way
to the tumor will also be destroyed. At lower intensities the
rays are harmless to healthy tissue, but they will not affect the
tumor either. What type of procedure might be used to destroy
the tumor with the rays, and at the same time avoid destroying
the healthy tissue?
A small country was ruled from a strong fortress by a dictator. The fortress
was situated in the middle of the country, surrounded by farms and villages.
Many roads led to the fortress through the countryside. A rebel general vowed
to capture the fortress. The general knew that an attack by his entire army
would capture the fortress. He gathered his army at the head of one of the
roads, ready to launch a full-scale attack. However, the general then learned
that the dictator had planted mines on each of the roads. The mines were set so
that small bodies of men could pass over them safely, since the dictator needed
to move his troops and workers to and from the fortress. However, any large
force would detonate the mines. Not only would this blow up the road, but it
would also destroy many neighboring villages. It therefore seemed impossible
to capture the fortress. However, the general devised a simple plan. He
divided his army into small groups and dispatched each group to the head of a
different road. When all was ready he gave the signal and each group marched
down a different road. Each group continued down its road to the fortress so
that the entire army arrived together at the fortress at the same time. In this
way, the general captured the fortress and overthrew the dictator.
Analogies
• Similar to learning from examples
• However, subjects often try to use analogies
based on surface similarities
• Implications for solving physics problems
Representation
• Mutilated checkerboard problem
Representation
• Imagine 27 apples packed in a crate 3 x 3 x 3
apples. A worm is in the center apple and its
ambition in life is to eat its way through all the
apples in the crate, but it does not want to
waste time by visiting any apple twice. The
worm can only move from apple to apple by
going directly up, down, or to the side. It
cannot move diagonally. Is such a path
possible? If not, can you prove it?
Representation
• You and an opponent take turns picking a
number 1 through 9. No number can be
picked twice. The winner is the first person
to have a collection of numbers such that
exactly three of them can be combined to
add up to 15.
Set effects
Problem
1
2
3
4
5
6
7
8
9
10
Jug A
21
14
18
9
20
23
15
28
18
14
Jug B
127
163
43
42
59
49
39
76
48
36
Jug C
3
25
10
6
4
3
3
3
4
8
Desired
100
99
5
21
31
20
18
25
22
6
Insight problems
You are given four separate pieces of chain that are each three
links in length. It costs $0.02 to open a link and $0.03 to close a
link. All links are closed at the beginning of the problem. Your
goal is to join all 12 links of chain into a single circle at a cost of
no more than $0.18.
• Control group (given 30 minutes): 55%
• Experiment 1 (half hour break in which they
performed other activities): 64%
• Experiment 2 (4 hour break): 85%
• Interviews showed that subjects did not come back
to problem with finished solutions.
Development of expertise
• Like memory, expertise develops on a power law
• Experiment in training to read inverted text
Expertise
• What differentiates experts from novices in
chess?
QuickTime™ and a
GIF decompressor
are needed to see this picture.
Recall of pieces
Meaningful
Random
Novice
6
5
Intermediate
12
6
Master
22
7
Expert memories
• Untimed chessboard-reproduction task
(move pieces in meaningful chunks)
• No loss in recall after 30-second delay
(better long term memory)
• Estimated that masters have 50,000 chess
patterns stored
• Timing information: Masters recall more
and larger patterns
Transfer
• After 200 hours of practice, subject was
able to remember a string of 81 digits,
repeated 1 per second.
– Transfer to recall of letters = zero
• Brazilian children’s math skills
– Situated context–– 98% accuracy
– Lab context–– 37% accuracy
– Word problems–– 74% accuracy
Expert problem-solving
• Development of useful strategies suited to a
given domain
– Physics and geometry: Working forward vs.
means-end analysis
• Efficient use of working memory–no need to keep
track of goals and subgoals
– Computer programming: Breadth-first vs.
depth-first
• Subgoals of a problem may interact
• Use of more abstract representations wellsuited to problem-solving operations
Summary
• Problem-solving is typically analyzed from
an information-processing point of view
involving a problem space, operators, and
production rules
• Generating an effective representation of a
problem is a key step in its solution
• Transfer of skill is hard!
Implications for instruction
• LISP tutor
– Guides students closely on relatively simple
programming problems
– Monitors student performance on 500
production rules
– Research showing students learn faster using
tutor than ordinary university classroom
instruction.
– Same principle now used in algebra, geometry
tutors
Perception and attention
• What is attention?
“Everyone knows what attention is. It is the taking
possession by the mind, in a clear and vivid form, of one
out of what seem several simultaneously possible objects
or trains of thought. Focalization, concentration of
consciousness are of its essence. It implies withdrawal
from some things in order to deal effectively with others.”
William James (1890)
• Automatic processes
red
orange
blue
orange
purple
black
green
black
blue
purple
green
red
green
blue
orange
purple
red
orange
blue
orange
purple
black
green
black
blue
purple
green
red
green
blue
orange
purple
Stroop effect
750
700
Reaction Time (ms)
• Congruent: Shape has same ink
color as its associated color
• Control: White shapes or
unassociated shapes
• Conflict: Shape has different ink
color than its associated color
Color naming
Shape naming
650
600
550
500
450
Congruent
Control
Conflict
Condition
Color naming
Shape naming
600
Color naming
Interference depends
on use of common
resources (hard to
disprove)
650
550
500
450
McLeod and Dunbar (1988)
Congruent
Control
Condition
Conflict
Representation
A label machine cuts labels and prints a letter on one side (either an
A or a B) and a number on the other (either a 2 or a 3). It has no
other characters and never prints anything but these and on the
proper side. However, on every label that has an “A” it is supposed
to print a “2” on the other side. Sometimes it slips, however, and
makes a mistake on this.
If you are a checker checking labels as they come past you on the
assembly line out of the machine, which of the following labels
flowing past you would you have to turn over to check that they are
done correctly?
A
3
B
2
Representation
In a crackdown against drunken drivers, state police are revoking
liquor licenses left and right if they find out that persons under the
age of 21 are being served alcohol. You are a bouncer in a bar and
it is your job to enforce the law. When a person orders a drink, the
wait-staff writes the drink on one side of a napkin and the person’s
age on the other.
Below are 4 napkins for the people at one table. Which napkins
must you turn over to check if a person is breaking the law?
beer
coke
25
16