The Mechanism of Restructuring in Geometry

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Mn,
onr
0
NThe
Mechanism
of
Restructuring
; -
Geometry
Stellan
Ohisson
The
Learning
Research
and
Development
Center.
University
of
Pittsburgh,
Pittsburgh,
PA
15260
Technical Report
No.
KUL-90-04
May,
1990
LEARNING
RESEARCH
AND
DEVELOPMENT
CENTER
_DTIC
"
ELECTE
University
of
Pittsburgh
D1ISTR:BUrON
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The
Mechanism
of
Restructuring
in
Geometry
Stellan
Ohisson
The
Learning
Research
and
Development
Center,
University
of
Pittsburgh, Pittsburgh,
PA
15260
Technical
Report
No.
KUL-90-04
May,
1990
To
appear
in
the
Proceedings
of
the
Twelfth
Annual
Conference
of
the
Cognitive
Science
Socie
Massachusetts
Institute
of
Technology,
Cambridge,
Massachusetts,
July
25-28, 1990.
DTI
C
SE'
,. -'
JUL
3
0
1990!
Preparation
of
this
manuscript
was
supported,
in
part,
by
ONR
grant
N00014-89-J-1681.
Approved
for
public
release;
distribution
unlimited.
The
opinions
expressed
do
not
necessarily
reflect
the
positions
of
the
sponsoring
agency,
and
no
endorsement
should
be
inferred.
This
report
is
a
substantially
rewritten
version
of
an
earlier
technical
report:
Ohlsson,
S. (1983).
Restructuring
revisited.
Iil.
Re-describing
the
problem
situation
as
a
heuristic
in
geometric
problem
solving
(Technical
Report
No.
353).
Uppsala,
Sweden:
Department
of Psychology,
University
of
Uppsala.

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TITLE
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The
Mechanism
of
Restructuring
in
Geometry
12.
PERSONAL
AUTHOR(S)
Stellan
Ohlsson
13a.
TYPE
OF
REPORT
13b
TIME
COVERED
14
DATE
OF
REPORT
(Year,Month
Day)
"
PAGE
CO
,NT
Technical
FROM
TO
May
1990
Nh
SUPPLEMENTARY.
NOTATIO
is
report
is a
substantially
rewritten version
of an
earlier
technical
report:
Ohlsson,
S.
(1983).
"Restructuring
revisited.
III.
Re-describing
the
problem
situation"
17
COSATI
CODES
18
SUBJECT
TERMS
(Conlnue
on
reverse
if
necessary
and
identify
by
block
numOer)
FIELD
GROUP
SUB-GROUP
Search;
Restructuring;
Function; Mechanism;
Heuristic;
05 02
Operators;
Path; Initial
state;
Goal
state;
Description
space.
19
ABSTRACT
(Continue
on
reverse
if
necessary
and
identify
by
block
number)
Restructuring
consists
of
a
change
in
the
representation
of
the
current
search
state,
a
process
which breaks
an
impasse
during
problem solving
by
opening
up
new
search
paths.
A
corpus
of
52
think-aloud
protocols
from
the
domain
of
geometry
was
scanned
for
evidence
of
restructuring.
The
data
suggest
that
restructuring
is
accomplished
by
re-parsing
the
geometric
diagram.
20
0ISTRIBUT!ONiAVA:LAB!LITY
CF
ABSTRACT
2;
ABSTRAC.
SECURir€
CLASS,
C":-
074
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SAME
AS
RPT -
DTIC
USERS
Unclassified
22a
NAME
OF
RESPONSIBLE
INDIVIDUAL
22J2EL)PH(NE
(Inclucje
Ae,
CcdeI
22(
-( '.
Susan
M.
Chipman
(202
696-4318
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DO
Form
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JUN
86
Previous
editions
are
obsolete
SE_(_.'R IT -
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' ,L__ (
,
-,-
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0102-LF-014-6603
UNCLASSIFIED

O
hisson
2
Restructuring
in
Geometry
Knowledge
and
Understanding
in
Human
Learning
Knowledge
and
Understanding
in
Human
Learning
(KUL)
is
an
umbrella
term
for
a
loosely
connected
set
of
activities
lead
by
Stellan
Ohisson
at
the
Learning
Research
and
Development
Center, University
of
Pittsburgh.
The
aim
of
KUL
is
to
clarify
the
role of
world
knowledge in
human
thinking,
reasoning,
and
problem
solving.
World
knowledge
consists
of concepts
and principles,
and
contrasts
with
facts
(episodic
knowledge)
and
with
cognitive
skills
(procedural
knowledge).
The
long
term
goal
is
to
answer
six
questions:
How
can
the
concepts
and
principles
of
particular
domains
be
identified?
How
are
concepts
and
principles
acquired?
How
can
the
acquisition
of
concepts
and
principles
be
assessed?
How
are
concepts
and principles
encoded
in
the
mind?
How
are
concepts
and
principles
utilized
in
performance
and learning?
How
can
instruction
facilitate
the
acquisition
and
utilization
of
concepts
and
principles
(as
opposed
to
episodic
or
procedural
knowledge)?
Different methodologies
are
used
to
investigate
these
questions:
Psychological
experiments,
protocol
studies,
computer
simulations,
historical
studies,
semantic,
logical,
and
mathematical
analyses,
instructional intervention studies,
and
so
on.
A
list
of
KUL
reports
appear
at
the
back
of
this
report.
Aeoesslon
For
9TI"
TAB
0
Unranomce!
0
Jut
!flcntilcn
o
By
__ __ __
_
__Distri!,ution/
Avn1l.blltty
Codes
Av
tl
rr./;r
Dist
Special
May
KUL-90-04
1990

Ohisson
3
Restructuring
in
Geometry
Table of
Contents
Abstract
4
Introduction
5
Method
6
Results
7
Case
1:
Deliberate
restructuring
7
Case
2:
Goal-driven
restructuring
8
Case
3:
Hint-driven
restructuring
9
Discussion
10
References
11
List
of
KUL
reports
12
May
KUL-90-04
1990

Ohisson
4
Restructuring
in
Geometry
Abstract
Restructuring
consists
of
a
change
in the
representation
of
the
current
search
state,
a
process
which
breaks
an
impasse
during
problem
solving
by
opening
up
new
search
paths.
A
corpus
of
52
think-aloud
protocols
from
the
domain
of
geometry
was
scanned
for
evidence
of
restructuring.
The
data
suggest
that
restructuring
is
accomplished
by
re-parsing
the
geometric
diagram.
May
KUL-90-04
1990

Ohlsson
5
Restructuring
in
Geometry
Introduction
A
wide
variety
of
problem solving
processes
have
been
analyzed in
terms
of
heuristic
search
(Newell
&
Simon,
1972).
For
example,
in
geometry
proofs
the
geometric
theorems (operators)
are
applied
to
the
mental
representation
of
the
diagram
(the
knowledge
state)
until
the
desired
proposition
(the
goal
state)
has
been
attained
(Anderson,
1981).
The stepwise
character
of
heuristic
search
contrasts
with
the
Gestalt
hypothesis
that
problem
solving
proceeds
through
(a)
an
initial,
unsuccessful,
attack
on
the
problem,
(b)
a
more
or
less
protracted
impasse,
and
(c)
a
restructuring
of
the
problem,
which
is
typically,
but
not
necessarily,
followed
by
insight
(Ohlsson,
1984a).
Several
attemptz
have
been made
to
reconcile
the
information
processing
and
Gestalt
hypotheses.
Simon
(1966)
proposed
that
it
helps
to
sleep
on
a
problem,
because
goal
tree information
is
forgotten
faster
than
problem
information.
After
a
pause,
a new
goal
tree
is
built
on
the basis
of more knowledge
about
the
problem.
Langley and
Jones
(1988)
interpret
an
impasse
as
a
failure
to
retrieve
the
relevant
problem solving
operator.
Insight
occurs
when
some
external
stimulus
causes
enough
activation
to
spread
to
that
operator
to
allow
its retrieval.
A
related
hypothesis
claims
that
insight
occurs
when
an
appropriate
analogy
is
retrieved
(Keane,
1988).
Both
the
differential
rate
of
forgetting
hypothesis
and
the spread
of
activation
hypothesis
require
that
the
problem solver
moves
attention
away
from
the
problem,
and
so
cannot explain
insight
during
ongoing
problem
solving.
Greeno
and
Berger
(1987)
have
proposed
that
insights
occur
when
a
problem solver
breaks
an
impasse
by
constructing
new
functional
knowledge,
i.
e.,
new
problem
solving
operators.
A
new
operator
is
constructed
by
inferring
that
an
object
can
fulfill
a
particular
function,
e.
g.,
that
a
screwdriver
can
be
used
to
complete
an electric
circuit. This
follows
from
the
fact
that
the
screwdriver
is made of
metal,
in
conjunction
with
the
general
principle
that
metallic
objects
conduct
electricity.
Several
researchers
have
proposed
that
problem
representations
can
be
improved
by
the
construction
of
macro-operators
(Amarel,
1968;
Korf,
1985).
Koedinger and Anderson
(in
press)
have
proposed
the
related
idea
that
geometry
experts
combine
geometric
theorems into
larger
inference
schemas,
called
diagram
configuration
schemas,
which
allow
them
to
find
a
proof
without
step-by-step
search
of
the
proof
space.
The
macro-operator
and
diagram
configuration hypotheses explain
expert
performance,
but
they
do
not
explain
insights
by
novices.
All
of
these
hypotheses
locate
restructuring
in
the
processes
of
problem
solving.
In
contrast,
I
have
proposed
that
restructuring
involves
a
change
in the
mental
representation
of
the
current
search
state
(Ohlsson,
1984b).
A
change
in
the
representation
implies
that
objects,
relations,
and
properties
which
initially
are
seen
as
instances
of
certain
concepts
are
being
re-encoded
as
instances
of
other
concepts.
May
KUL-90-04
1990

Ohisson
6
Restructuring
in
Geometry
For
example, an
object
which is
initially
encoded
as
a
hammer
might
in
the
course
of
problem
solving
become
re-encoded
as
a
pendulum
weight,
a
line
may
be
re-encoded
as
a
triangle
side,
and
so
on.
Re-encoding
a
search
state
changes
the
set
of
operators
which
are
applicable
in
that
state,
and
thus
breaks
an impasse
by
opening
up
new
search
paths.
A
similar
theory has
been
proposed
by
Kaplan
and
Simon
(in press)
to
explain
restructuring
in
the
Mutilated
Checker
Board
Problem. The
critique
by
Montgomery
(1988)
does
not
touch
those
aspects
of
the
theory
that
are
of
main
concern in
this
paper.
The
purpose
of
the
present
paper
is
to
provide evidence
for
re-encoding
from
the
domain
of
geometry,
and
to
propose
a
mechanism
for
re-encoding
in
that
domain.
Table
1.
Geometric
theorems
acquired
by
the
subjects.
Theorem
1.
Supplementary
angles are
congruent.
Theorem
2.
Vertical
angles
are
congruent.
Theorem
3.
The
supplementary
angle
of
a
right
angle
is
a
right
angle.
I
Theorem
4.
If
two
angles and
their
common
side
in
one
triangle
are
congruent
to
the
corresponding
angles
and
their
common
side
in
another
triangle,
then
the
two
triangles
are
congruent.
Theorem
5.
If
two
sides
in a
triangle
are congruent,
then
their
opposite
angles
are
congruent;
and
vice
versa.
Method
Three
undergraduate
psychology
students
participated
in
an
experimental
course
in
elementary
geometry.
The
experimenter
saw each
subject
individually
in
sessions
that
lasted
approximately
one
hour
each.
The subjects
learned
basic
theorems
of
plane
geometry,
the
first
five
of
which
are
shown
in
Table
1.
A
typical
session
began
with
free
recall of
previously
learned
theorems,
continued
with
the
introduction
of
new
theorems,
and
ended
with
problem
solving practice.
The
subjects
had the
theorems
available
during
problem solving, and
they
were
instructed
to
think
aloud.
The
data
consist
of
52
think-aloud
protocols,
representing
a
total
of
approximately nine
hours
of
problem
solving
effort.
May
KUL-90-04
1990

Ohisson
7
Restructuring
in
Geometry
Results
The
protocols
were
scanned
for
the
occurrence
of
restructuring
events.
Ten
such
events
were
found.
The
three
most
informative
events
will
be
analyzed
below.
They
illustrate
deliberate
restructuring,
goal
driven
restructuring,
and
restructuring
in
response
to
a
hint.
Case
1:
Deliberate
restructuring.
Subject
S3
was
given
the
problem
in
Figure
1
after
she
had
studied
Theorems
1-5
(see
Table
1).
She
began
by
proving
that
triangles
AED
and
BEC
are
congruent,
and
then
entered
an
impasse.
In
fragments
F65-F67
(see
Table
2)
she
deliberately
sets
out
to
see
the
problem
from
many
viewpoints.
The
process
of
restructuring
proceeds
through
three
steps.
First,
she
mentally
cuts
the
figure
along
the diagonal
CA,
forming
the
triangles
CDA
and
CBA
(F68-F70). She
then
mentally
cuts
the
figure
along
the
other
diagonal, forming
the
triangles
DCB
and
DBA
(F71-F74).
Finally,
she
keeps
one
triangle
from
each
pair,
as
it
were,
and
sets
herself
the
task
of
proving
them
congruent
(F75-F77).
Figure
2
gives
a
diagrammatic analysis
of
the
process. The
geometric
objects
perceived
by
the
subject
are
drawn
in
bold
lines,
while
the
rest
of
the
diagram
is
drawn
in
broken
lines.
Restructuring
was
not
followed
by
insight
in
this
case.
The
subject
worked
on
the
problem
for
twelve
minutes
without
solving
it.
.....................................................................................................................
Table
2.
Protocol
excerpt
from
Subject
S3.
F65.
but
perhaps
one
can
see
this
in
some
other
way
also
F66.
one
can
perhaps
see
this
from
many
viewpoints
here
F67.
now
we
shall
see
F68.
one
can
see
it
as
F69.
CDA
and
CBA
F70.
triangles
F71. one
can
see
it
on
F72.
DCB
and
DBA
instead
F73.
yes
exactly
yes
F74.
those
two
F75.
well
F76.
now
I
can
see
this
in
another
way
F77.
CDB
and
CAD
ought
to be
congruent
here
in
some
way
May
KUL-90-04
1990

Ohisson
8
Restructuring
in
Geometry
Case
2:
Goal-driven
restructuring.
S1
was given
the
problem
in
Figure
1
as
his
first
problem
after studying
Theorems
1-5
(see
Table
1).
S1
misunderstood
the
goal
of
the
problem
to
be
to
prove
that
angle
ADC
is
congruent
to
angle
BCD.
When
the
protocol
excerpt
in
Table
3
begins,
he
has
proved
that
angles
EDA
and
ECB
are
congruent
by
proving
them
corresponding
parts
of
the
congruent
triangles
EDA
and
ECB.
He
then
sets himself
the
goal
of
proving
that
the
remaining
parts,
i.
e.,
angles
EDC
and
ECD,
are
equal
(F43).
His
plan
is
to
prove
that
they
are
equal
by
proving
that
the
sides
of
the
triangle
EDC
are equal
(F42-F45).
Table
3.
Protocol
excerpt
from
Subject
S1.
F42.
yes
now
I
am
thinking
about
whether
one
can
prove
that
these
two
sides
[DE,
EC]
are
equally
long
F43.
because
if
they
are
then
those
two
angles
[EDC,
ECD]
which
are
just
the
remaining
parts
of
those
angles
which
I
want
to
get
[ADE,
BCD]
must
be
equally
long
F44.
so
then
this
and
that
angle
[ADE,
BCD]
must
be
equally
big
F45.
and
then
the
problem is
solved
F46.
so
it
is
now
a
question
of
proving
that
it
is
isosceles
F47.
that
triangle
[EDC]
F48.
and
that
I
cannot
F49.
but
perhaps
one
can
do
it
in
some
other
way
(What
are
you
thinking?)
F50.
well now
I
am
thinking
F51.
well
it
is
the
same
problem
F52.
but
from
another
angle
F53.
yes
if this
one
F54.
is those
two
lines
[ED,
EC]
are
equally
long
F55.
I
am
thinking
F56.
yes
but
they
must
be
F57.
since
they
are
parts
of
F58.
it
is
congruent
F59.
these
two
here
are
congruent
[triangles
EDA,
ECB]
F60.
and
it
is
[ED,
EC]
corresponding
sides
in
the
triangles
[EDA, ECB]
F61.
therefore these
two
sides
[ED,
EC]
are
equally
long
This
goal
is
reformulated
as
proving
that
the
triangle
EDC
is
isosceles
(F46-F47).
This
view
of
the
problem
leads
to
an impasse
(F48-F49).
Prompted
by
the
experimenter
to
continue
to
think-aloud,
he
states
that
he
is
thinking
about
the
same
May
KUL-90-04
1990

OhIsson
Restructuring
in
Geometry
D C C
D G
A
B
A
B
Prove angles
ECD
and CDE
congruent.
Prove
line
segments
AG
and
BD
congruent.
Figure
1.
Problem
1.
Figure
4.
Problem
2.
C
C
>E lop / E<
A
B
A
B
Figure
5.
Analysis
of
S2's
re-encoding
process.
Perceived geometric
figures
are
drawn
in
bold
lines,
the
rest
of
the
figures
in
broken
lines.

OhLsson
9
Restructuring
in
Geometry
problem
but
from
another
angle
(F50-F52):
he
has
re-encoded
ED
and
EC
as
lines
(F54).
The
goal
is
still
to
prove
them congruent
(F53-F55).
He
suddenly
realizes
that
ED
and
EC
are corresponding
sides
of
the
two
triangles
EDA
and
ECB,
which
he
has
already
proved
congruent
(F56-F61).
Figure
3
shows
a
diagrammatic
analysis
of
the
process
with
perceived
geometric
objects
in
bold
lines
and
the
rest
of
the
diagram--the
background--in
broken
lines.
The
subject quickly
completed
the
correct
solution.
Case
3:
Hint-driven restructuring.
S2
attempted
Problem
2
(see
Figure
4)
after
having
learned
the
five
theorems
in
Table
1,
plus
four
others.
She
decided
to
prove
triangles
AED
and
BEG
congruent
and
quickly
reached an
impasse.
The
protocol
excerpt
in
Table
4
begins
Table
4.
Protocol
excerpt
from
Subject
S2.
(What
other
triangles
could
be
congruent?)
F109.
what others
Fl10
could
there
be
others
which
are congruent
F1ll.
huh
(That
could
be.
You
have
now
been
working
the
hypothesis
that
the
whole
point
is to
prove
that
those
two
triangles
[AED,
BEG]
are congruent.)
F112.
yes
(And
just
now
you
reached
the
conclusion
that
you
cannot
do
that
with
the
information
you
have.
Can
you
find
two
other
triangles
which
one
can
find
which
one
could
believe
could
be
congruent?)
F113.
congruent
exactly
alike
F114.
no
that
is
impossible
there
are
no
others
F115.
it
cannot
be
F116.
there
are
only
one
other
F117.
also
hypothetically
then
this
line
here
F118.
then
there
are
two
here
F119.
and
those
two
here
can
surely
never
be
congruent
F120.
these
two
here
can
surely
never
be
congruent
F121.
no
I
do
not
understand
that
F122.
but
F123.
now
I
see
it
F124.
I
have
forgotten
this
one
here
[AGB
or
BDA]
May
KUL-90-04
1990

OhIsson
Restructuring
in
Geometry
% %
% IU
%
% %%%4.
I Ir
a4. a I I
* 0

O
hisson
10
Restructuring
in
Geometry
when
the
experimenter
gives
her
the
hint
that
there
are
other
pairs
of
triangles
in
the
figure
that
might
be
congruent.
She
first
rejects
this
suggestion
(F113-F115).
She
then
runs
through
the
triangles
in
the
figure
(F113-F121),
and
concludes
that
there
are
no
other
congruent
triangles
in
the
figure
(F121).
She
then
suddenly
sees
the
triangles
AEG
and
BDA
(F123-F124).
Figure
5
shows
a
diagrammatic analysis
of
the
process
with
perceived
geometric
objects
drawn
in
bold
lines
and
the
rest
of
the
diagram
drawn
in
broken
lines.
In spite
of
this
restructuring,
the
subject
failed
to
solve
the
problem.
Discussion
The
restructuring
process
revealed
in
these
three
protocol
excerpts consists
in
re-encoding
the
given
figure.
The
diagram--the
set
of
lines
on
the
paper--contains
within
it
a
large
number
of
different
geometric
objects
(angles,
sides,
triangles,
etc.).
Only
some
of
those
geometric
objects
are
perceived
at
any
one
time.
The
others
recede
into
the background.
In
particular,
if
a
line
configuration
is
perceived
in
one
way,
then
alternative
encodings of
that
same
line
configuration
recede
into
the
background.
Restructuring
consists
of
switching
to
one
of
the
alternative
encodings.
How
does
the
switching
mechanism
work?
The
data
suggest
that
re-encoding is
done
by
re-parsing
the diagram.
During
initial
problem perception
complex
objects
(e.
g.,
triangles)
are
constructed
out
of
simpler
objects
(e.
g.,
lines).
This
process
is
a
search
through
a
description
space
(Ohlsson,
1984b).
Alternative
interpretations
of
the
perceptual information
are
possible,
so
some
choices
are
made,
resulting
in
a
particular
encoding
of
the
given
diagram.
When
an
impasse
forces
the
problem
solver
to
re-encode
the
problem, he/she
backs
up
in
the
description
space,
dismantles
his/her
previous encoding, and
traverses another
path through
the description
space.
This
process
breaks
an
impasse
by
allowing
other
operators
(geometric
theorems)
to
apply
to
the
current
state.
Restructuring
is
a
rare
event:
There
was
approximately
one
restructuring
event
per
hour
of
problem
solving
effort
in
the
present
study.
Restructuring
does
not
necessarily
lead
to
insight:
In
two
of
the
three
excerpts
presented
above,
the
subject
failed
to
solve
the
problem.
This
study
supports
the
idea
that
diagram
parsing
is
central
in
geometry
(Koedinger
&
Anderson, in
press),
but
the
validity
of
the re-parsing
mechanism
for
other
domains
than
geometry
remains
an
open
question.
For example,
a different mechanism
seems
to
be
responsible
for
re-encoding
of
the
Mutilated
Checker
Board
Problem
(Kaplan
&
Simon, in
press).
May
KUL-90-04
1990

Ohlsson
11
Restructuring
in
Geometry
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1990

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12
Restructuring
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research
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Sense
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1986/18).
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Learning
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University
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1987
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Learning
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KUL-87-02).
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Learning
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Learning
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KUL-87-04).
Pittsburgh,
PA:
Learning
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May
KUL-90-04
1990

Ohlsson
13
Restructuring
in
Geometry
1988
Ohlsson,
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1988).
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KUL-88-01).
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Learning
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University
of
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S.
(March,
1988).
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regrouping:
A
mathematical
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(Technical
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No.
KUL-88-02).
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Learning
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1989).
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KUL-89-02).
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Learning
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of
Pittsburgh.
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S.,
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S.
(August,
1989).
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A
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Learning
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1988).
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cognitive
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KUL-89-04).
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PA:
Learning
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Center, University
of
Pittsburgh.
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G.,
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Ohlsson,
S.
(November,
1989).
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structure
of
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(Technical
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No.
KUL-89-05).
Pittsburgh,
PA:
Learning
Research
and
Development
Center, University
of
Pittsburgh.
May
KUL-90-04
1990

OhIsson
14
Restructuring
in
Geometry
Ernst,
A.,
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OhIsson,
S.
(December,
1989).
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A
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(Technical
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KUL-89-06).
Pittsburgh,
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Ohisson,
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E.
(January,
1990).
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constraint
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(Technical Report
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KUL-90-01).
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N.
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1990).
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KUL-90-02).
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S.,
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Rees,
E.
(March,
1990).
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(Technical
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No. KUL-90-03).
Pittsburgh,
PA:
Learning
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1990).
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(Technical
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KUL-90-04).
Pittsburgh,
PA:
Learning
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Development
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of
Pittsburgh.
May
KUL-90-04
1990

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Dr.
Jeff Boner
Dr.
Jere
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Guidance
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Inc.
Cornell
University
Dr.
Thomas
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Anderson
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of
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for
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Study
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Reading
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Center for
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Lynn
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Dr.
Stephen
J.
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Chairman
National
Bureau
of
Standarde Columbia University
Department of
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System
Gaithersburg,
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York,
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System.
Engineering
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University
Dr.
Lyle E.
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Universt
of
Warwick
Faculty,
of
Law
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of
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University
of Limburg
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of
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ysteim
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Boiling
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of
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2520
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Deparmn
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Univerasity
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University
of
Rocheater
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of
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Toronto
ONT
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Pad
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Southern
Illinois
University
--
er
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pey
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logu--e
Dienet
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J.
Stur
Dom,
School
of
Medicine
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Scinc
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"versity
of
Coilorado
Univeraity
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Colorado
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International
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Of
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Kne
Dr.
Sberi* Gott
Dr.
Freda%*k
HayesRoth
University
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Minnesota
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Deparmn of
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Brooks
AFB.
TX
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P.O.
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aid
S*-ms
Engieering
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of Maryland
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Purt.
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Universit
of
Delaware
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Straet
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Dr.
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A
Dep
Amut
CiS.
Inamictional
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Science
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Milto
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Kaui
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University
of
Toronto
European
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Sandford
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Building
Office
Quantico.
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of
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Frank
Keil
Queens
Road
University
of
Delaware Departmenit
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Teddington
Newark.
DE
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University
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Kalbh
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Ithaca
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Department
of Paycholog
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of
Georgia
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Physics
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Athens
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cdo
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Orlando.
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for
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Mkbie
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Technology
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The
Turing
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Oolf
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of
Education.
EMS!'
George
House
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Harvard
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St.
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Corporation
Carnege
Mellon
Univmusty
Code
52
Central Engineering
Labs
Pittsburgh, PA
15213-3890
Navy
persone
R&D
Center
1205
Coleman
Avenue
San
Diego.
CA
92152-6800
Box
580
Dr.
Ji
Levin
Santa
Olars.
CA
95002
Department
01
Dr.
Douglas
L
Media
Educational
Psyholog
Department
01
Psychology
Cair.
Department
01
Weapons
and
210
Edacton Bilding
Universty o
Mthign
Systems
Engieering
1310
South
Sixth
Stre Amn
Arbor,
MI
48109
US
Naval
Acoamy
Caep@igt
IL
6182049Mr90il
emk
Annapolis,
MD
21402
Dr.
John
Le9vMn
Foravarees
Canter
for
Ledertlab
Dr.
T.
NWbet
Leaning
R&D
Canter
chruiuhavns
Voape
6
The
Turing
Institute,
Uniest
041"o Ptzabusar 1424
Kobanhavn
K
George
House
Ploasbtagl
PA
1520
DENMAR
36
North
Hanover
Street
Glosgow
G1
2AD
Matu Loam
Dr.
Arthur
Melmed
UNITED
KINGDOM
Deparmn
01
Psychology
Computer
Arts
and
CaWrgie-Melon
Univert&y
Edutcatio
Laboratory
Library.
NPRDC
Pleatgsl
PA
15213
New
York
University
Code
10291L.
719
Broadway.
12Lb
floor
Sen
Diego,
CA
921524800
Or.
Doria
K.
Luke
New
York.
NY
O00
Sothwae
Productvity
Consortium Librarian
ISI Campu
Commoe,
Drive
North
Dr.
Jone
Mestre
Naval
Center
for
Applied Research
Resin.
VA
2209
Department
o1
Plyioca
in
Atificial
Intelligence
Hashrouck
Laboratr
Naval
Research
Laboratory
University,
01
Massachusetts Code
5510
Amherst.
MA
01003
Washingon
DC
20754M00

Univrity
of
Pinurimotbisson
05/29/"0
Dr.
Herold
F.
O?4ed
Jr.
Dept.
of
Administrative
Sciences
Dr. Linda
0.
Roberts
School
of
Education
-
WPH
801 Code 54
Science.
Education,
and
Depatment
of
Educational
Naval
Postgraduate
School
Transportation
Program
Psycholog
A
Technology
Mon"ey
CA
"0943-5026
Office
of
Technology
Assessment
University
of
Southern
California
Congress
of
the
United
States
Loo
Angeles.
CA
9008W.00I
Dr.
Peter
Pitchi
Washington.
DC
M010
School
of
Education
Dr.
Paul
Oltorke
University
of
California
Dr.
Ernst
Z.
Rothkopf
Infenintion
&
computer
Science
Berkeley,
CA
94720
AT&T
Bell
Laboratories
University
of
Caliornia.
Irvine,
Room
ZD-456
Irvine,
CA
92717
Prot
Tomiaso Poggio
600
Mountain
Avenue
Massachusetts
Instiute
Murray
Hill.
NJ
0394
Dr.
Stati
Ohission
of
Techology
E25-201
Learnig
Rt
A
D
Center
Center
for
Biological
Dr.
Alan
H.
Schoenfeld
Uniiversity
of
Pittsburgh
Information
Processing
University
of
California
Pitiasbiargl,
PA
15260
Cambridge
MA
02139
Department
of
Education
Berkeley,
CA
94720
Dr.
James, B.
Olaw
Dr.
Pete
Poison
WICAT
Systsa
University
of
Colorado,
Losell
Schoer
1875
South
Stae
Street
Deprten
of
Psycholog
Pschological
A
Quantitative
Orem
UT
8400
Boulder CO
8030904W
Foundations
College
of
Education
Dr.
Gary
M.
Olson Dr.
Steven
E.
PoltrockL
University
Of
Iowa
Cognitive
Science
and
Boeing
Advanced
Technology Center
Ioas
City
LA 52242
Machine
Intelligenice Lab. PO
Box
24346
rn/a
7L-64
University
of
Michigan
Seattle,
WA
98124
Dr.
Janet
W.
Scho~wld
701
Tappani
Street
816
LRDC
Building
Ann Arbor, MI
491234
Dr.
Joseph
Psocka
University
of
Pittsburgh
ATTN:
PERI-IC
3939
O'Hara
Street
Dr.
Judith
Reitman
Olso
Army
Resarch
Institute
Pittsburgh.
PA
15260
Graduate
School
of
Businesa
5001
Eiaenhower
Ave.
University
of
Michigan
Alendria.
VA
2233-560
Dr.
Key
Schulze
Ann
Arbor.
MI
48109I234
Computer
Science
Dept
Mr.
Paul
SI
Rau
U1.S.
Naval
Academy
Office
of
Naval
Research. Code
U1-33
Annapolis.
MD
21402-5018
Code
1142CS
Naval
Surface
Weapons
Center
S00
N.
Quincy,
Stree
White Oak
Laboratory
Dr.
Miriam
Schissack;
Arlinpton.
VA
221750100
Silver
Spring
MD
20911
Code
52
(6
COPie)
Navy Personnel
R
a
D
Center
Dr.
James
A.
Regga
San
Diego,
CA
92152-6800
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Judith
Oraaao
University
of
Maryland
Basc
Rearch
Office
School
of
Medicine
Dr. Judith
W. Segal
Army ResarchInestitute
Department
of
Neurology
OERJ
5001
Eisenhower
Avenue
22
South
Greene Street
555
New Jersey
Ave,.
NW
Alendria.
VA
2Z333
Baltimore
MD
21201
Washington.,
DC
2M~
Dr.
lese
Orianaky
Dr.
J.
Wesley
Regian
Dr. Robert
J.
Seidel
Institute
for
Defense
Analse
AFHRL41DI
US
Army
Research
Institute
180M N.
Beauregard
St.
Brooks
AFB.
TX
78235 500
Eisenhower Ave.
Almenrdria.
VA
22311
Almandia, VA
22333
Dr.
Fred Reif
Dr.
Everett Palmer
Physica
Deparmet
Dr
Coleen M.
Seifert
Mail
Stop
2.39.3
University
of
California Institute
for
Cognitive
Science
NASA-Amws
Research
Center
Berkeley,
CA
94720
Mail Code
C-01S
Moffett
Field.
CA
94035
Univeraity
of
California.
San
Diego
Dr% Charles
M.
Reigeluth
La
Jolla.
CA
9209
Dr.
Okchoon
Park: 330
Huntington
Hall
Army
Research
Institute
Syracuse
University
Dr.
Michael
G.
Shafto
PERI.2
Syracuse.
NY
13244
NASA
Ames
Research
tr.
5001
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Avenue
Mail
Stop
239-1
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VA
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Dr.
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Moffet
Field
CA
94035
Reed
College
Dr.
Roy
Pea
Deparmet
of
Psychology
Mr.
Cohn Sheppard
Instituto
for
Rinac
Portland,
OR
97202
AXC2
Block:
3
on
Learning
Adwirality
Research
Establishment
2550
Haoe
Street
Dr.
Lauren
Resnick
Min"sr
of
Defence Portadown
Palo
Alto. CA
9430
Learning
R
A
D
Center
Poetsmouth
Hanta
PO64AA
University
of
Piuaburgh
UNITED
KINGDOM
Dr.
David
N.
Patina
3939
O'Haa
Street
Prose
Zero
Pittsburgh,. PA
15213
Dr.
Lee S.
Shulman
Harard
Graduate
School School
of
Llducaonr
of
Educastions
Dr.
J.
Jeffirey
Richardson
507
Ceaw
7
Appian
Way
Center
for
Applied
Al
Stanford University
Cambridge.
MA
02168 College
of
Busineaa
Stanford.
CA
94
-30904
University
of Colorado,
Dr.
C
Perrio.
Chair
Boulder.
CO
80309-0419
Dr.
Randall
Sbutnaker
Dep.
of
Payeholog
Naval
Resac
Laboratory
Morgan
Stats
University
Dr.
Edm
L
Risaland
Code
5510
Cold
Spring
LA-Kitteni
Rd.
Dept.
of
Computer
and
4555
Overlook
Avenue.
S.W.
Baltimora.
MD
21239
Information
Scence
Washington. DC
20375.5000
University
of
Maattea
Dr.
Nancy
N.
Perry
Amherst,
MA
01003
Dr.
Edward
Silver
Naval
Education
ond
Training
LROC
Prnga
Support
Activity
Mr.
William
A. Rizzo
University
of
Pittsburgh
Cod*447
Code
71 3939
O'Hara
Street
Buidng
243
Naval
Training
Systems
Center Pittsburgh.
PA
13260
Painoesioa. FL.
32509500
Orlando,
FL
32813

University
of
Ploaburgbohlaaon
05/29M9
Dr.
Herbert
A
Simori
Dr.
David
E. Suon
Dr.
Keth
T.
Wacout
Depmlen
of
Paydiolog
Computer
Teaching
Corporatio
FMC
Corporation
Carnelle-Mello
Univarit
1713
South
Neil Street
Central
Enginerig
Labe
Schenley
Part
Urbana.
IL
61820
12M
Colem
Ave-.
Box
580
Pilsbsx6
PA
15213
Saita
Clars.
CA
9562
Dr.
Patrick
Supes
Robert
L
Simpson.
Jr.
Stanford University
Dr.
Dougias Wetzel
DARPA/ISTO
Institute
for
Mathematical
code
51
1400
Wilson
Blvd.
Studies
in
the
Social
Sciences
Navy
Personne
R&D
Center
Arlington.
VA
ZZ99-2306 Stanford.
CA
94305-4115
Son
Diego
CA
92152-680
Dr.
Zito
M.
Simutla
Dr.
Perry
W.
Thorrodyke
Dr.
Barbara
White
Chief,
Techniologies
for
Skidl
FMC
Corporation
School
of
Education
Acqluiaition
and
Retention
Central
Ennarinwg
LAWa Tolmanr
Hat.
EMST
ARI
120S
Coleman Avenue.
Box
580
Uniest
of
California
5001
Eiseanhower
Avenue
Sant
Clama
CA
9%02
Berly
CA
947W0
Alexndria.
VA
22333
Dr.
Sharon
Tkaac
Dr.
David
Wilkinsa
Dr.
Derek
Sleean
Alaen
Corporation
University
of
Ilinos
Computing
Scinc
Deparmn
209
Madleon Stroet
Department
at
Comopu'r
Science
The
University
Alexndia,
VA
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West
Springfield
Amnue
Abrde
ABf9
NX3
Urbana,
IL
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Scotland
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Dougas
Toames
UNITED
KINGDOM
Behavioral
Teclinolg
Labs
Dr.
Marsha
R.
Willian.s
University
of
Southern
California
Applic.
ot
Advanced!
Tedinologies
Me.
Gail
KC.
Slestnon 250 N.
Harbor
Dr..
Suite
309
National
Science
Foundation
LOCIICON. Inc. Redondo
Beach.
CA
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SEE/MDR]SE
P.O.
BOX
85158 800
G
Street.
N.W. Room
635-A
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Diego.
CA
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Major
D. D.
Tucker
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DC
20550
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Code
MA
Room
4023
Dr.
Edward
I.
Smth
Waahington,
DC
208
S.
R
Wilson
Depuian ot
Psychlog
Code
5505
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of
Miduigen
Dr.
Paul
T.
TN'ohig
Naval
Research
Laboratory
330
Packard
Road
Army
Research
Institute
Washington.
DC
20375.50000
Ann
Arbor.
MI
48103
ATIN:
PERIjRL
5001
Eienhwr
Avenue
Dr.
Robert
A.
Wisher
Dr. Alfred
F.
Smode
Alexndria.
VA
22333.5W0 U-1%.
Army
Institute
for
the
Code 7A
Behaviors!
and
Social
Sciences
Research
and
Development
Depit.
Dr.
Zita
P.
Tyer
5001
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Avenue
Naval
Training System
Center
Department
ot
Psychololl
Alexndia.
VA
2233-5600
Orlando. FL
32813-7100
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University
4400
University
Drive
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C.
Witrock
Dr.
OF
Soloexy,
Fairfax.
VA
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of
Education
Yale
Unveity"
UCLA
Computer
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Deparmn
Dr.
Harold
P.
Van
Cott
Los
Angeles,
CA
90024
P.O.
BOX
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on
Humn
Factors
New
Haven.
CT
06520
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Academy
of
Sciences
Mr.
Paul
T.
Wohag
2101
Constitution
Avenue
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Research
Institute
Linde
B.
Sorio
Washington.
DC
20418
5001
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Ame
IBM-Los
Angeles
Scientific Center
ATTN:
PERI-RL
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Wilshire
Blvd..
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Kurt
Van Lehn
Almndia
VA
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Los
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CA
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Department
of
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Carnegie-Mellon University
Mr.
Josephi
WobI
N. S.
Seidharan
Seliley
Park
Alphatedi.
Inc.
FMC
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Pktcbuergb,
PA
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Executiv
Center
BOX 580 111
Midlse
Turnpike
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L
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MA
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Personnel
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San
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Wallace
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III
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Room
B.5124
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Menlo
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CA
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Diego.
CA
921526800
Dr.
Masoud
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Dept.
of
Computer
Science
Dr.
Friedric W.
Steep
Dr.
Thomas
A.
Warm
University
of
Entter
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Academy
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a
Wale Road
des
Verteidipio
P.O.
Box
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Exeter EX44PT
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City.
OK
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1
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Young
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Amews
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2050
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Department
of
Educational
Dr.
Uri
Zernik
Dr.
Saul Sternbierg
Development General
Electr
Uniiversity
of
Pesmalkut
University
of
Delaware Research
A
Developonmt Center
Daparasi
of Psycholo
Newark.
DE
19711
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Intelligence
Propam
3815
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St~e
P
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PA
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Shih-surig Wan
Schenectady.
NY
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of
Pvydxltoo
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Jackson
Stae
Universt
Oak
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Ammoc.
Univ.
1400
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Ba
117
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TN
37831-0117