students’ strategies & mistakes using a map in the real world kim a. kastens mg&g seminar

Students’ Strategies & Students’ Strategies & MistakesMistakes

Using a Map in the Real WorldUsing a Map in the Real World

Kim A. Kastens

MG&G Seminar8 March 2007

MindEarth

Fertile researcharea at interface

MindEarth

Fertile researcharea 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

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



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



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.



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.

A Tool for Understanding and Improving how Children Learn to Use Maps

A Manual for Deeptow Transponder Navigators

“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

“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” GroupThe “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 ErrorCorrect Answer

Category 3b Error: Sticker should have been adjacent to a road or path; placed instead on or

adjacent to a structure

CorrectAnswer

Type 3b Error

Category 4a Error: Sticker should have been on structure; placed on or adjacent to the wrong

structure

Correct AnswerType 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

CorrectAnswers

Category 5b Error: Sticker should be adjacent to a road or path; placed on correct path or road segment, but outside the “correct” ring

CorrectAnswer

5b Errors


Correct location is on a wall.

Student sticker on the grass.

Good student stickers.

Student sticker on trees or shrubs.

Student stickers on the wrong building.


Percentage of stickers in each error category

Error Group Error Number Baseline

1 1.3

2 14.7RepresentationalCorrespondence

3a & 3b 6.3

4a & 4b 11.3ConfigurationalCorrespondence 5a & 5b 13.1

No Error No Error 53.4

All RepresentationalCorrespondence

1, 2, 3a, & 3b 20.9

All ConfigurationalCorrespondence

4a, 4b, 5a, & 5b 22.9

All Errors1, 2, 3a, 3b, 4a,

4b, 5a, & 5b46.6


Result #1: Without instruction, many 4th graders (and some adults) find it difficult to accurately locate a real-world object onto a map.


The “Explaining” Group

Same as “Baseline”:

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…”


Baseline Explaining

Result #2: Children who explained their reasoning did better than those who did not.



Error GroupError

NumberBaseline Reflecting

No Error No Error 53.4 67.1

AllRepresentationalCorrespondence

1, 2, 3a, &3b

20.9 10.7

AllConfigurationalCorrespondence

4a, 4b, 5a,& 5b

22.9 22.1

…..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 & Cauzinille-Marmeche (1997)

Studying worked examples of factoring in algebra

Kintsch (1994) Reading science text

Baseline Explaining

Why?

Self-explaining activates existing spatial competencies.

Students find and self-correct incipient errors.



Insights from clue-answers 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


Veridical Counterfactual(true flag locations)

(white K18) “It was across the tree on a light post.”

(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.”


Veridical

(white K18) “It was across the tree on a light post.”

(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.”


Counterfactual clue-answers are very rare in our data: only 7 out of the 223 Landmark clue-answers.

Counterfactual

If the clue-answer is a veridical description of reality, does the clue-answer contain enough information to pinpoint the flag location?

SufficientAccurate but Insufficient(true flag locations)


SufficientAccurate but Insufficient

(orange H13) “It’s on the mansion.”

(white K03) “I put my white sticker where I put it because I saw it on a tree in the circling road.”

(black H06) “I saw the flag on the statue while I was walking.”


(white H14) “I found the white flag by the big tree close to the mansion.”


SufficientAccurate but Insufficient

(orange H13) “It’s on the mansion.”

(white K03) “I put my white sticker where I put it because I saw it on a tree in the circling road.”

(black H06) “I saw the flag on the statue while I was walking.”


“Accurate but Insufficient” clue-answers are quite common in our data: 136 out of the 223 Landmark clue-answers.

(white H14) “I found the white flag by the big tree close to the mansion.”

Does the clue-answer agree with the sticker placement?

Agree Disagree


Agree Disagree

(yellow H19) “End of the parking lot.”

(yellow K10) “I put it by the side of the road.”


Agree Disagree



(green H19) “The green flag is next to an old house.”


Agree Disagree



(green H19) “The green flag is next to an old house.”

“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.

Difficult Not so difficult

Working hypothesis: the hard part about using a map in the real world lies in gathering the relevant information from the environment.

The “Verbal Description” Group

Same as “Baseline” and “Explaining”:

Same as Baseline and Explaining: Different:

“ 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.”

Verbal description read aloud in the classroom.



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.

Baseline Explaining Verbal Description

Result #4: The children who acquired information about the sticker position from a verbal description placed the stickers very accurately onto the map.


Error GroupError

NumberBaseline Reflecting

VerbalDescription

No Error No Error 53.4 67.1 86.4

AllRepresentationalCorrespondence

1, 2, 3a, &3b

20.9 10.7 4.3

AllConfigurationalCorrespondence

4a, 4b, 5a,& 5b

22.9 22.1 9.3

Difficult Not so difficult

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.

Representational Correspondencemethod

Being able to translate from words to map and vice versa doesn’tmean a child can use a map competently within the represented space.

0 10 20 30 40 50 60 70

Learning About Maps (1985)

Map Skills for Today (1986)

Exploring our world (1988)

Geography Skills (1988)

Beginning Map Skills (1990)

Exploring maps (1992)

Finding your way (1992)

Map Coloring Book (1992)

Mapworks (1992)

Around and about (1993)

Using maps in your community (1993)

Maps and Globes (1994)

Maps and Navigation (1994)

Teach with Topographic Maps (1994)

Map Adventures (1995)

Orienteering and map games (1996)

Great Map Mysteries (1997)

Mapmaking with children (1998)

Mapping Skills (1998)

Mega-fun map skills (1998)

Great Map Games (2000)

Maps,Globes,Graphs (2000)

Amazing Hands-on Map Activities (2001)

Comic-Strip Map Skills (2001

Reading maps (2001)

Reading Topographic Maps (2001)

Neighborhoods and Communities (2002)

Marvelous map activities (2002)

Instant map skills: US (2004)

Instant Map Skills (2004)

Number of student products in category

Production Comprehension Representational Correspondence Meta-Representational

Number of student products in each category:

The majority of activities in elementary school map skills materials are of one type: Representational Correspondence….

Representational correspondence exercises are necessary but not sufficient to learn to use a map…

….. because they lack the crucial connection withreality, 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 map-skills 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: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.

students’ strategies & mistakes using a map in the real world kim a. kastens mg&g seminar

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