Students’ Strategies & Mistakes
Using a Map in the Real World
Kim A. Kastens
MG&G Seminar
8 March 2007
Earth
Fertile research
area at interface
Mind
Earth
Mind
Fertile research
area at interface
Kim’s Priority List of Research Topics in ROLE/ GEO
• Complex systems of the Earth & environment
• Geologic time
• Learning in the Field
• Spatial thinking in Geosciences
Earth
Mind
Fertile research
area at interface
Kim’s Priority List of Research Topics in ROLE/ GEO
• Complex systems of the Earth & environment
• Geologic time
• Learning in the Field
• Spatial thinking in Geosciences
versus
Field photo from: http://www.ldeo.columbia.edu/users/menke/slides/EESC2200FIELDTRIP04/fieldtrip_3.html
Lab photo from: www.ldeo.columbia.edu/edu/DLESE/activities/Galileo/index.html
versus
• Large scale, internal spatial
viewpoint
• Small scale, external spatial
viewpoint
• High level of detail and complexity • Everything on table top is relevant
to inquiry
• Rarely can do controlled
experiments
• Focus on controlled experiments
• Begin with raw materials of
Nature
• Begin with inscriptions such as
maps, diagrams, graphs, equations
• Unfamiliar setting can cause
anxiety: fear of getting lost or hurt
• Familiar setting
Field photo from: http://www.ldeo.columbia.edu/users/menke/slides/EESC2200FIELDTRIP04/fieldtrip_3.html
Lab photo from: www.ldeo.columbia.edu/edu/DLESE/activities/Galileo/index.html
versus
• It doesn’t matter where you are:
focus is on that is which is true
everywhere, every time.
Lab Report
Methods: We made our
observations at 40° 47'
N, 73° 58' W, 72 cm
above the floor level, at
the front table, in room
558 Schermerhorn.
Field photo from: http://www.ldeo.columbia.edu/users/menke/slides/EESC2200FIELDTRIP04/fieldtrip_3.html
Lab photo from: www.ldeo.columbia.edu/edu/DLESE/activities/Galileo/index.html
versus
• It matters crucially where you
are.
– Situation 1: Location is an
independent variable when we are
studying variation along a gradient
or between field sites.
– Situation 2: Location is a
confounding factor, because of the
heterogeneity of the Earth &
environment on all scales.
• It doesn’t matter where you are:
focus is on that is which is true
everywhere, every time.
Lab Report
Methods: We made our
observations at 40° 47'
N, 73° 58' W, 72 cm
above the floor level, at
the front table, in room
558 Schermerhorn.
Field photo from: http://www.ldeo.columbia.edu/users/menke/slides/EESC2200FIELDTRIP04/fieldtrip_3.html
Lab photo from: www.ldeo.columbia.edu/edu/DLESE/activities/Galileo/index.html
A Manual for Deeptow
Transponder Navigators
A Tool for Understanding and Improving how
Children Learn to Use Maps
“THE WORLD IN SPATIAL TERMS…
The geographically informed person
knows and understands...
• How to use maps and other
geographic representations, tools, and
technologies to acquire, process, and
report information from a spatial
perspective…
By the end of the fourth grade, the
student knows and understands: …
• How to display spatial information on
maps and other geographic
representations.”
Knowing how to use a map is
important for everyone who
wants to be able to travel to new
places.
Field-based investigations of
children’s map skills:
• Baseline Group
• Self-Explaining Group
• Verbal Description Group
The “Baseline” Group
The “Baseline” Group
SK
A
T
PLACE ("
CHILD
REPRESE
(ma
The “Baseline” Group
SK
A
T
PLACE ("
CHILD
REPRESE
(ma
The “Baseline” Group
“Put the blue sticker on the
map to show where you think
the blue flag is located….”
The “Baseline” Group
“Put the blue sticker on the
map to show where you think
the blue flag is located….”
2001-2002 and 2002-2003 classes (now 6th & 7th graders):
The “Baseline” Group
The “Baseline” Group
2001-2002 and 2002-2003 classes (now 6th & 7th graders):
The “Baseline” Group
Two scoring methods for
sticker placements:
(1) Quantitative: distance
from center of student
sticker to exact location, in
sticker diameters.
(2) Categorical
Category 1 Error: Sticker is centered on a map object that
resembles sticker in shape and size
Correct Answer
Type 1 Error
Category 2 Error: Sticker is placed on symbol for grass,
trees, or bushes; not on or adjacent to any built object
Type 2 Error
Correct Answer
Category 3b Error: Sticker should have been adjacent to a
road or path; placed instead on or adjacent to a structure
Correct
Answer
Type 3b
Error
Category 4a Error: Sticker should have been on structure;
placed on or adjacent to the wrong structure
Correct Answer
Type 4a Error
Type 4a Error
Category 5a Error: Sticker should be on structure; placed on
correct structure but outside of “correct” ring
Type 5a
Errors
Correct
Answers
Category 5b Error: Sticker should be adjacent to a road or
path; placed on correct path or road segment, but outside the
“correct” ring
Correct
Answer
5b Errors
2001-2002 and 2002-2003 classes (now 6th & 7th graders):
The “Baseline” Group
The “Baseline” Group
Correct location is on a wall.
Student stickers on the wrong building.
Student sticker on the grass.
Student sticker on trees or shrubs.
Good student stickers.
Percentage of stickers in each error category
Error Group
Error Number
Baselin e
1
1.3
Representational
2
14.7
Correspondence
3a & 3b
6.3
4a & 4b
11.3
Configur ational
Correspondence
5a & 5b
13.1
No Error
No Error
53.4
All Representational
Correspondence
All Configur ational
Correspondence
All Errors
1, 2, 3a, & 3b
20.9
4a, 4b, 5a, & 5b
22.9
1, 2, 3a, 3b, 4a,
4b, 5a, & 5b
46.6
2001-2002 and 2002-2003 classes (now 6th & 7th graders):
The “Baseline” Group
The “Baseline” Group
Result #1: Without
instruction, many 4th
graders (and some
adults) find it difficult to
accurately locate a realworld object onto a map.
The “Explaining” Group
Same as “Baseline”:
SK
A
T
PLACE ("reality")
CHILD
REPRESENTATION
(map)
Dependent
Variable
The “Explaining” Group
Same as “Baseline”:
Different:
“After you put one of the
stickers on the map, write
down what clues you used to
decide where to put the
sticker…”
SK
A
T
PLACE ("reality")
CHILD
REPRESENTATION
(map)
Dependent
Variable
The “Explaining” Group
The “Explaining” Group
Result #2:
Children who
explained their
reasoning did
better than
those who did
not.
Baseline
Explaining
Percentage of stickers in each error category
Error
Error Group
Baselin e
Reflecting
Number
No Error
No Error
53.4
67.1
All
1, 2, 3a, &
Representational
20.9
10.7
3b
Correspondence
All
4a, 4b, 5a,
Configur ational
22.9
22.1
& 5b
Correspondence
…..even though:
• the two groups of students were
from the same school
• had the same teachers
• were the same age (end of 4th
grade)
• and were indistinguishable on
standard paper and pencil tests of
mental rotation ability.
The “Self-Explaining Effect”: Eliciting “self-generated
explanations” improves student performance on a wide range of
tasks
Chi et al (1989)
Studying worked examples of physics
problems
Lin & Lehman (1999)
Experimental design using controlled
variables
Chi et al (1994),
Chi (2000)
Studying biology textbook passage
on blood circulation
Aleven & Koedinger
(2002)
Solving geometry problems
Didierjean & CauzinilleMarmeche (1997)
Studying worked examples of
factoring in algebra
Kintsch (1994)
Reading science text
The “Explaining” Group
Why?
Self-explaining
activates existing
spatial
competencies.
Students find and
self-correct
incipient errors.
Baseline
Explaining
The “Explaining” Group
Insights from clueanswers should be
taken as indicative of
students performing
closer to peak capacity.
Coding of Clue-Answers
• Did clue-answer include at least one landmark that exists in the
real world? (landmark/no landmark)
– If so, did the clue-answer accurately describe the real world?
(veridical/ counterfactual)
• If so, was the clue-answer sufficient to pinpoint the flag location
within 15m? (sufficient/ accurate but insufficient)
– If so, did the landmark exist on the map as well as in the real
world? (Viable/ nonviable)
• If so, did the position of the sticker agree with the position
described in the clue-answer? (agree/ disagree)
• Did the clue-answer include topological, projective, or Euclidean
spatial elements?
• Did the clue-answer include at least two elements of spatial
information?
• Did the clue-answer describe process as well as observations?
(kinesthetic, visual)
Coding of Clue-Answers
• Did clue-answer include at least one landmark that exists in the
real world? (landmark/no landmark)
– If so, did the clue-answer accurately describe the real world?
(veridical/ counterfactual)
• If so, was the clue-answer sufficient to pinpoint the flag location
within 15m? (sufficient/ accurate but insufficient)
– If so, did the landmark exist on the map as well as in the real
world? (Viable/ nonviable)
• If so, did the position of the sticker agree with the position
described in the clue-answer? (agree/ disagree)
• Did the clue-answer include topological, projective, or Euclidean
spatial elements?
• Did the clue-answer include at least two elements of spatial
information?
• Did the clue-answer describe process as well as observations?
(kinesthetic, visual)
Did the clue-answer include at least one landmark that exists
in the real world? And if so, did the clue-answer accurately
describe the flag’s position in the real world?
(true flag locations)
Veridical
Counterfactual
Did the clue-answer include at least one landmark that exists
in the real world? And if so, did the clue-answer accurately
describe the flag’s position in the real world?
(light blue K09)
“Well I was
walking along a
road that goes in
a circle, I saw this
flag by cars so I
knew it was near
the parking area.”
(white K18) “It
was across the tree
on a light post.”
(true flag locations)
Veridical
Counterfactual
Did the clue-answer include at least one landmark that exists
in the real world? And if so, did the clue-answer accurately
describe the flag’s position in the real world?
(light blue K09)
“Well I was
walking along a
road that goes in
a circle, I saw this
flag by cars so I
knew it was near
the parking area.”
(white K18) “It
was across the tree
on a light post.”
(true flag locations)
Veridical
Counterfactual
Counterfactual clue-answers are very rare in our data:
only 7 out of the 223 Landmark clue-answers.
If the clue-answer is a veridical description of reality, does
the clue-answer contain enough information to pinpoint the
flag location?
Sufficient
(true flag locations)
Accurate but
Insufficient
If the clue-answer is a veridical description of reality, does
the clue-answer contain enough information to pinpoint the
flag location?
(white K03) “I put my
(white H14) “I found
the white flag by the
big tree close to the
mansion.”
white sticker where I put
it because I saw it on a
tree in the circling road.”
(black H06) “I saw the
(orange H13) “It’s on
the mansion.”
flag on the statue
while I was walking.”
Sufficient
(true flag locations)
Accurate but
Insufficient
If the clue-answer is a veridical description of reality, does
the clue-answer contain enough information to pinpoint the
flag location?
(white K03) “I put my
(white H14) “I found
the white flag by the
big tree close to the
mansion.”
white sticker where I put
it because I saw it on a
tree in the circling road.”
(black H06) “I saw the
(orange H13) “It’s on
the mansion.”
flag on the statue
while I was walking.”
Sufficient
(true flag locations)
Accurate but
Insufficient
“Accurate but Insufficient” clue-answers are quite
common in our data: 136 out of the 223 Landmark
clue-answers.
Does the clue-answer agree with the sticker placement?
Agree
Disagree
Does the clue-answer agree with the sticker placement?
(yellow H19)
“End of the
parking lot.”
(yellow K10)
“I put it by
the side of
the road.”
Agree
Disagree
Does the clue-answer agree with the sticker placement?
(green H19) “The
green flag is next to
an old house.”
(yellow H19)
“End of the
parking lot.”
(yellow K10)
“I put it by
the side of
the road.”
Agree
Disagree
Does the clue-answer agree with the sticker placement?
(green H19) “The
green flag is next to
an old house.”
(yellow H19)
“End of the
parking lot.”
(yellow K10)
“I put it by
the side of
the road.”
Agree
Disagree
“Agree” answer-pairs far outnumber “Disagree” answer-pairs:
139 to 13 (among “Viable” clue-answers)
Result #3:
Among the “explaining”
students, we see:
• the explanation are
accurate descriptions of
reality,
• there are many
explanations that are
insufficient to pinpoint the
sticker,
• there are many sticker
placements that are
wrong, but wrong in a
way that is consistent with
the corresponding
explanation.
Working hypothesis: the hard part about using a map in
the real world lies in gathering the relevant information
from the environment.
Difficult
Not so difficult
The “Verbal Description” Group
Same as “Baseline” and “Explaining”:
The “Verbal Description” Group
Same as Baseline and Explaining:
Different:
Verbal description read aloud in
the classroom.
“ The orange sticker is on the mansion.
It’s on a corner of the mansion.
It’s on the corner closest to the path that
leads to the pond.”
The “Verbal Description” Group
Verbal description:
• The orange sticker is
on the mansion.
• It’s on a corner of the
mansion.
• It’s on the corner
closest to the path that
leads to the pond.
Exactly sufficient information,
No more, no less.
Result #4: The children who acquired information about the sticker
position from a verbal description placed the stickers very accurately onto
the map.
Baseline
Explaining
Verbal Description
Percentage of stickers in each error category
Error
Error Group
Baselin e
Reflecting
Number
No Error
No Error
53.4
67.1
All
1, 2, 3a, &
Representational
20.9
10.7
3b
Correspondence
All
4a, 4b, 5a,
Configur ational
22.9
22.1
& 5b
Correspondence
Verbal
Description
86.4
4.3
9.3
This supports our working hypothesis: the map itself is
not that hard for children to work with; the hard part is
identifying, gathering, and combining the relevant
information from the environment.
Difficult
Not so difficult
Representational
Correspondence
method
Being able to translate
from words to map
and vice versa doesn’t
mean a child can use
a map competently
within the represented
space.
Production
Comprehension
Representational Correspondence
Meta-Representational
Instant Map Skills (2004)
Instant map skills: US (2004)
Number of student
products in each
category:
Marvelous map activities (2002)
Neighborhoods and C ommunities (2002)
Reading Topographic Maps (2001)
Reading maps (2001)
C omic-Strip Map Skills (2001
Amazing Hands-on Map Activities (2001)
Maps,Globes,Graphs (2000)
The majority of
activities in
elementary school
map skills materials
are of one type:
Representational
Correspondence….
Great Map Games (2000)
Mega-fun map skills (1998)
Mapping Skills (1998)
Mapmaking with children (1998)
Great Map Mysteries (1997)
Orienteering and map games (1996)
Map Adventures (1995)
Teach with Topographic Maps (1994)
Maps and Navigation (1994)
Maps and Globes (1994)
Using maps in your community (1993)
Around and about (1993)
Mapworks (1992)
Map C oloring Book (1992)
Finding your way (1992)
Exploring maps (1992)
Beginning Map Skills (1990)
Geography Skills (1988)
Exploring our world (1988)
Map Skills for Today (1986)
Learning About Maps (1985)
0
10
20
30
40
Number of student products in category
50
60
70
Representational correspondence exercises are
necessary but not sufficient to learn to use a
map…
….. because they lack the crucial connection with
reality, the represented space.
Recap
• Many children have difficulty locating themselves or a real world object
on a realistically-complex map.
• Mistakes range from complete failure to grasp the stand-for relationship,
to subtle nuances of configurational correspondence.
• Metacognition improves children’s performance on a real world mapskills task.
• The difficulty in map use lies in gathering task-relevant information from
the represented space, not in positioning information from one’s mental
model onto the map.
• It may help to explicitly model the strategies of (a) seeking landmarks
that exist both on the map and in the real world, and (b) uses two or
more elements of spatial information.
• Ability to translate from a verbal representation to a map does not mean
the child can use a map in the real world.
• Most map-skills curriculum materials under-emphasize making
connections between maps and real world.
Thanks to:
• Co-PI Lynn Liben, Penn State Psychology Dept.
• Data gathering and analysis by Margie Turrin, Linda
Pistolesi, and Jennifer Griffith
• GIS and graphics by Linda Pistolesi
• 4th grade students and teachers of Cottage Lane
School and Valley Cottage Elementary School
• Many LDEO student and staff helpers during 4th
graders’ visits
• NSF Research on Learning & Education (ROLE)
program
• LDEO directors and admin for use of the grounds.