This workshop is designed to integrate a wide variety of cognitive science perspectives on the roles diagrams play in cognition, addressing various ways in which people design and use diagrams to spatialize thought and make it public, to work through ideas and clarify thinking, to reduce working memory load, to communicate ideas to others, to promote collaborative work by providing an external representation that can be pointed to and animated by gestures and collectively revised. The morning session (talks by Tversky, Healey, and Kirsh) will focus on creating and diagrams and using them to coordinate various activities, the afternoon (talks by Bechtel, Cheng, and Hegarty) will examine uses of diagrams in science. Both session will also include blitz talks presenting one major idea; scholars who would like to present blitz talks should contact the organizer. http://mechanism.ucsd.edu/diagrammaticcognition.html

1. A cognitive architecture-based model
of expert graph comprehension
David Peebles
University of Huddersfield
July, 2013
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 1 / 11

2. Previous process models of graph use
GOMS-based task-analytic models:
UCIE (Lohse, 1993)
MA-P (Gillan, 1994)
Computational models:
BOZ (Casner, 1991)
CaMerA (Tabachneck-Shijf, Leonardo & Simon, 1997)
ACT-R (Peebles & Cheng, 2003)
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 2 / 11

3. Previous process models of graph use
GOMS-based task-analytic models:
UCIE (Lohse, 1993)
MA-P (Gillan, 1994)
Computational models:
BOZ (Casner, 1991)
CaMerA (Tabachneck-Shijf, Leonardo & Simon, 1997)
ACT-R (Peebles & Cheng, 2003)
Focus of the model:
Question answering (e.g., “When x = 2, what is y?”)
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 2 / 11

4. Previous process models of graph use
GOMS-based task-analytic models:
UCIE (Lohse, 1993)
MA-P (Gillan, 1994)
Computational models:
BOZ (Casner, 1991)
CaMerA (Tabachneck-Shijf, Leonardo & Simon, 1997)
ACT-R (Peebles & Cheng, 2003)
Focus of the model:
Question answering (e.g., “When x = 2, what is y?”)
Automated graph design based on task specification
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 2 / 11

5. Previous process models of graph use
GOMS-based task-analytic models:
UCIE (Lohse, 1993)
MA-P (Gillan, 1994)
Computational models:
BOZ (Casner, 1991)
CaMerA (Tabachneck-Shijf, Leonardo & Simon, 1997)
ACT-R (Peebles & Cheng, 2003)
Focus of the model:
Question answering (e.g., “When x = 2, what is y?”)
Automated graph design based on task specification
Multiple representations in expert problem solving
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 2 / 11

6. Previous process models of graph use
GOMS-based task-analytic models:
UCIE (Lohse, 1993)
MA-P (Gillan, 1994)
Computational models:
BOZ (Casner, 1991)
CaMerA (Tabachneck-Shijf, Leonardo & Simon, 1997)
ACT-R (Peebles & Cheng, 2003)
Focus of the model:
Question answering (e.g., “When x = 2, what is y?”)
Automated graph design based on task specification
Multiple representations in expert problem solving
None of the above address graph comprehension
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 2 / 11

7. Graph comprehension
Initial familiarisation stage prior
to other tasks involving:
Identification & classification
of variables into IV(s) and DV
Association of variables with
axes and representational
features (e.g., colours, shapes,
line styles)
Identification of
relationship(s) depicted
May be an end in itself or a
prerequisite for other tasks
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 3 / 11

8. Interaction graphs
Low High
10
20
30
40
50
60
70
80
90
100
Percent Error as a function of Experience and Time of Day
PercentError
Experience
Time of Day
Day
Night
Students more likely to
misinterpret (Zacks & Tversky,
1999) or inadequately interpret
line graphs (Peebles & Ali,
2009, Ali & Peebles, 2013)
Low High
10
20
30
40
50
60
70
80
90
100
q
q
Percent Error as a function of Experience and Time of Day
PercentError
Experience
Time of Day
Day
Night
Line graphs better at depicting
common relationships for
experts (Kosslyn, 2006)
Interpretation facilitated by
recognition of familiar patterns
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 4 / 11

9. An example expert verbal protocol
High Low
0
25
50
75
100
125
150
175
200
225
250
q
q
q
q
Glucose Uptake as a function of Fasting and Relaxation Training
GlucoseUptake
Fasting
Relaxation Training
Yes
No
1 (Reads) “Glucose uptake as a function
of fasting and relaxation training”
2 Alright, so we have. . . you’re either
fasting or you’re not. . .
3 You have relaxation training or you
don’t. . .
4 And so. . . not fasting. . . er. . .
5 So there’s a big effect of fasting. . .
6 Very little glucose uptake when you’re
not fasting. . .
7 And lots of glucose uptake when you
are fasting. . .
8 And a comparatively small effect of
relaxation training. . .
9 That actually interacts with fasting.
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 5 / 11

10. The ACT-R cognitive architecture
Elements of the architecture:
Hybrid architecture with symbolic and subsymbolic components
Production system model of procedural memory & cognitive control
Semantic network model of declarative memory
Activation-based learning, memory retrieval & forgetting mechanisms
Simulated eyes & hands for interacting with computer-based tasks
Value for diagrammatic reasoning research:
Allows modelling of complex tasks with graphical elements
Imposes valuable cognitive constraints on models
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 6 / 11

11. The ACT-R cognitive architecture
Elements of the graph comprehension model:
Prior graph knowledge (general and specific) required
Information extracted and knowledge structures generated
Sequence of cognitive & perceptual operations involved
Strategic processes that control comprehension
Behavioural output to be compared with human data:
Sequence of propositions to compare with expert verbal protocols
Scan paths to compare with expert eye movements
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 7 / 11

12. Stages of comprehension
Comprehension proceeds in the following order:
1 Read title. Identify variable names and create declarative chunks.
2 Seek variable labels, identify what they are by their location and if
required, associate with label levels
3 Associate variable levels with indicators (position or colour)
4 Look at plot region and attempt to interpret distances. If a highly
salient pattern exists (e.g., cross, large gap) process that first
Individual production rule for each pattern
No production rule then pattern not processed
5 Continue until no more patterns are recognised
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 8 / 11

13. An example model protocol
Artificial Natural
0
5
10
15
20
25
30
35
40
45
50
q
q
q
q
Chick Weight as a function of Diet and Hormone Supplement
ChickWeight
Diet
Hormone Supplement
MPE
GCE
text at top of display. . .
[chickweight] [= variable]
[as] [a] [function] [of] [diet] [= variable]
[and] [hormonesupplement] [= variable]
text at bottom of display. . .
[diet] at [bottom] [= IV]
look to nearest text. . .
[natural] is a level of [diet]
[natural] is [right]
[artificial] is a level of [diet]
[artificial] is [left]
text at far right of display. . .
[hormonesupplement] at [far-right] [= IV]
look to nearest text. . .
[mpe] is a level of [hormonesupplement]
[gce] is a level of [hormonesupplement]
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 9 / 11

14. An example model protocol
Artificial Natural
0
5
10
15
20
25
30
35
40
45
50
q
q
q
q
Chick Weight as a function of Diet and Hormone Supplement
ChickWeight
Diet
Hormone Supplement
MPE
GCE
objects in plot region. . .
a [green] [line]
no memory for [green] look to legend. . .
[green] [rectangle]. look for nearest text. . .
[green] represents [gce]
[blue] [rectangle]. look for nearest text. . .
[blue] represents [mpe]
text at far left of display. . .
[chickweight] at [far-left] [= DV]
look to pattern. . .
substantial difference between legend levels. . .
[0.2] diff [blue] = [small] effect [mpe]
[0.2] diff [green] = [small] effect [gce]
compare [blue] and [green] levels. . .
[moderate] diff: [gce] greater than [mpe]
[moderate] [main] effect [hormonesupplement]
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 10 / 11

15. An example model protocol
Artificial Natural
0
5
10
15
20
25
30
35
40
45
50
q
q
q
q
Chick Weight as a function of Diet and Hormone Supplement
ChickWeight
Diet
Hormone Supplement
MPE
GCE
identify x-axis levels. . .
[0.4] diff [left] = [moderate] effect [artificial]
[0.4] diff [right] = [moderate] effect [natural]
compare [left] and [right] levels. . .
[small] diff [natural] > [artificial]
[small] [main] effect [diet]
compare left and right patterns. . .
[0.0] diff between points. [neither] bigger
[no] diff & [same] order = [no-interaction]
for [artificial], [gce] > [mpe]
for [natural], [gce] > [mpe]
David Peebles (University of Huddersfield) Graph Comprehension CogSci Berlin, 2013 11 / 11