QUESTION 2: When students’ “mindsets” do not match Gapminder’s “dataset” (Rosling, TED talk at US State Department, 2005), how do trouble/repair sequences (Schegloff, 1991) drive model refinement?
o We used interaction and conversation analysis (Jordan & Henderson, 1995; Derry et al., 2010; Schegloff, 1991) to explore the sequential organization of trouble and repair as student pairs constructed models using Gapminder. Micro-analysis is complete for the first 10 minutes of the video record for each group.
o Trouble when “mindset”≠“dataset” animates different worlds (Tool, Quantity & Measures, Wealth & Health) o Repair re-aligns these worlds (we conjecture) and refines a model under construction. o Gapminder (dynamic visualization tool) makes contributions in conversation.
QUESTION 1: How do student pairs’ “graph argument paths” compare as a modeling activity? We segmented 70 minutes of video data for each pair using the following rules: o A model is a unique pairing of X- and Y-axis indicators selected from the “dataset” and explicitly mentioned in talk. o Links are transitions from one model (node) to the next. “Playing” that model displays changing indicator values through time. o Numbers in nodes show how often student(s) examined a model.
Turn # Speaker Utterance Trouble/Repair (World)
1 Tara Africa has a lot of murder. Per 100,000 people. ((See Gapminder Display)) Trouble 1 (Health and Wealth)
2 Cara China. ((Looks at Tara's screen)) Are you in lin? Why do ours look different? Trouble 2 (Tool)
2 Tara I'm doing per one hundred thousand. Repair 2 (Quantities and Measures)
4 Cara Oh oh oh oh.
5 Tara I'm studying abroad in South Africa though next semester.
6 Cara Awk-ward.
7 Tara ((Laughs))
8 Cara ((Laughs)) Yep, it's here. ((Looks at Tara))
9 Tara ((Looks at Cara)) What?
10 Cara Are you worried you're going to get murdered? ((Laughs))
11 Tara ((Laughs)) No.
12 Cara ((Laughs))
13 Tara I wonder like where that happens and like.
14 Cara That's so funny::::. Repair 1 (Health and Wealth)
“What in the world?” Trouble and Repair in Multivariable Modeling with Motion Chart Graph Arguments
o Larger design study (Cobb et al., 2003) asked students to interpret, remix, and make-your-own “interesting” motion chart graph arguments using Gapminder
o Setting: Required Mathematics Literacies course for undergraduates and masters students attending an elite university in the South
o Timeline: Activities spanned three 3-hour classes over four weeks of the semester. Data reported come from DIY activity during last 70 minutes of second class meeting
o Focal participants: The course instructor identified two student pairs for selective case study comparison (Flyvbjerg, 2006): Masters students Nathan and Nicole and undergraduates Cara and Tara. We considered all students as non-experts in the creation of graph argument performances (as compared to Gapminder’s designer, Hans Rosling).
o Data Collection: Single HD video record of each student pair working at a table with two computers. Analysis focuses on multi-modal activity of modeling (talk, significant gesture, and interaction with the computer and Gapminder display).
o Motion charts (Al-Aziz, et al., 2010; Rosling et al., 2005) are a new representational form for visualizing multivariate data through time
o This free digital tool, along with public “datasets,” are widely used through Gapminder’s website (gapminder.org)
o This design study treats Gapminder motion charts as Big Data visualizations, producing STEM arguments that increasingly appear in public media
o Modeling the wealth and health of nations invites secondary mathematics licensure students to take a new perspective on mathematical literacy
o How do prospective math teachers make sense of this modeling activity?
Nathan (L) and Nicole (R) Using Single Gapminder Environment
Cara (L) and Tara (R) Using Two Gapminder Environments
Jennifer B Kahn Vanderbilt University Peabody College
FINDINGS LEVEL 1 ANALYSIS o Very different patterns of collaboration
with single vs. two modeling environments; leads to discoordination for C&T whose models are in sync only once (Government Health Spending, Life Expectancy)
o Different use of tool’s dynamic feature: N&N regularly “play” models while C&T mostly treat display as static scatter plot (i.e., conventional school statistical display)
o Both worked serially through a selection of indictors for X- and Y-axes
o N&N show extended periods of progressive model refinement (Collins, Joseph, And Bielaczyc, 2004) (e.g., returning to (Income per person, CO2 Emissions) 7 times. C&T never return to a model.)
o Collaborative refinement in a common modeling environment supports successful graph arguments (e.g., C&T leave the DIY without a graph argument)
FINDINGS LEVEL 2 ANALYSIS o C&T do not consider time, so do not
think developmentally about health and wealth of nations
o N&N build models in order to show developmental influence over time
o C&T reach model path impasses, and abandon models in the face of trouble
o N&N pursue trouble by considering related indicators, contrasts between countries, and research outside Gapminder
o The worlds animated in trouble and repair remain puzzling to us—we need to go deeper on what constitutes a “world” in the dynamic visualization of the health and wealth of nations
Turn # Speaker Utterance Trouble/Repair (World)
1 Gapminder Graph plays from 1981 to 2007. China, India, Mauritius, and Spain are selected with trails. ((See Gapminder Display))
2 Nicole Ok so.
2 Nathan Hmmm.
4 Nicole So. What- ((L hand turns over toward screen)) WHAT in the world? Trouble 1 (Health and Wealth)
5 Nathan ((Points to screen, up and down gesture mimics path of Mauritius)) That was, okay, that was like over the course of like ten years, that it did that.
6 Nicole So it's an African country.
7 Nathan Hmmhmm. Hit the map ((Points to the Map tab)) Repair 1 (Tool)
8 Nicole ((Clicks map tab. Bubbles located on geographic location of nation))
9 Nathan It'sssss ((Points to Mauritius on map))
10 Nicole It's an island! Weird! ((Coughs)) Trouble 2 (Health and Wealth)
11 Nathan That's interesting. I'm tempted to Google that. I want to know what happened. ((Turns towards his computer and pulls up Internet))
12 Nicole You can Google. ((Directs Nathan)) Repair 2 (Health and Wealth)
o Extend micro-analysis across entire DIY modeling effort for each group
o Consider hybridity of animated worlds (Ochs et al., 1996) in analysis of trouble and repair sequences
o Analyze focus group interviews after the design study to relate their very different values regarding “what counts as mathematics” in Gapminder motion chart graph arguments
o Do student’s “mindsets” about mathematical literacy correspond with our (and our programs’) conception of “productive disciplinary engagement” (Engle, 2002)?
“Mindset” (Health and Wealth
of Nations)
“Dataset” (Quantities and Measures)
Gapminder Tool mediates relationship
Turn 1 Speaker 1 Assertion Turn 2 Speaker 2 Trouble Turn 3 Speaker 1 Repair
“Third position repair may be thought of as the last systematically provided
opportunity to catch (among other problems) divergent
understandings that embody trouble in socially
shared cognition of the talk and conduct in interaction.”
Schegloff (1991)
1Murder (total deaths)
Contraceptive use (% of women ages 15-49)
Ratio of girls to boys in primary and secondary
education (%)
Life expectancy (years)
Body Mass Index (BMI), men, Kg/m2
Inco
me
per p
erso
n
(GDP
/cap
ita, P
PP$
infla
tion-
adju
sted
)M
ean
year
s in
sch
ool
(men
25
to 3
4 ye
ars)
Aver
age
age
of d
olla
r
billio
naire
s (y
ears
)Ag
e at
1st
mar
riage
(wom
en)
Brea
st C
ance
r, nu
mbe
r
of n
ew fe
mal
e ca
ses
Brea
st C
ance
r, nu
mbe
r
of fe
mal
e de
aths
Gov
ernm
ent h
ealth
spe
ndin
g
of to
tal g
ov. s
pend
ing
(%)
Smok
ing
adul
ts (%
of
popu
latio
n ov
er a
ge 1
5)Al
coho
l con
sum
ptio
n
per a
dult
15+
(litre
s)
Income per person (GDP/capita, PPP$ inflation-adjusted)
1 1
1
1
1 1
1 1 1
1
2 3
4
5
6
7
8
9 10
11
Series of Indicator Choices for X Axis
Serie
s of
Indi
cato
r Cho
ices
for Y
Axi
s
Played GraphDidn’t Played GraphUnknown
Legend
1
CARA’S ARGUMENT PATH
1Murder (per 100,000 people)
Bad Teeth per child (12 yr)
Life expectancy (years)
Inco
me
per p
erso
n (G
DP/
capi
ta, P
PP$
infla
tion-
adju
sted
)
Ratio
of g
irls
to b
oys
in p
rimar
y
and
seco
ndar
y ed
ucat
ion
(%)
Pove
rty (%
peo
ple
belo
w $2
a da
y)In
equa
lity in
dex
(Gin
i)
High
sch
ool g
radu
ate
(%)
Child
mor
tality
(0-5
yea
r-old
s
dyin
g pe
r 1,0
00 b
orn)
Gov
ernm
ent h
ealth
spe
ndin
g
of to
tal g
ov. s
pend
ing
(%)
Tota
l GDP
(US$
,
infla
tion-
adju
sted
)
Suga
r per
per
son
(g p
er d
ay)
Body Mass Index (BMI), men, Kg/m2
1 1 1 1 1
1
1
11 1
2 3 4 5 6
Series of Indicator Choices for X Axis
Serie
s of
Indi
cato
r Cho
ices
fo
r Y A
xis
1
7
8
9
10
11
Done in Gapminder
USA*
* All other arguments were completed in Gapminder World.
TARA’S ARGUMENTS PATH
1
1 2
1
1
1
1
2
1
1 1 17 2 1 1 1
1
1
6
2
3
45 7
15
17
9
16
18
1011
12
13
1423
1924
27
20
21
22
CO2 emissions (tonnes per person)
Math Achievement -- 8th grade
25 26
Ratio of girls to boys in primary and
secondary education (%)
Economic growth over the past 10 years
Data quality - Income per person
Cumulative CO2 emissions (tonnes)
Yearly CO2 emissions (1000 tonnes)
Pump price for gasoline (US$ per
liter)
Cars
, tru
cks
& bu
ses
per 1
,000
per
sons
Bad
Teet
h pe
r
child
(12
yr)
Inco
me
per p
erso
n
(GDP
/cap
ita, P
PP$
infla
tion-
adju
sted
)Po
pula
tion,
Tot
al
Expo
rts (%
of G
DP)
Indu
stry
(% o
f GDP
)
Tota
l GDP
(US$
,
infla
tion-
adju
sted
)In
dust
ry w
orke
rs
(% o
f lab
our f
orce
)Ro
ads,
pav
ed (%
of to
tal r
oads
)G
DP/c
apita
(US$
,
infla
tion-
adju
sted
)
Literacy rate, adult total (% of people
ages 15 and above)
1
28
8
Series of Indicator Choices for X Axis
Serie
s of
Indi
cato
r Cho
ices
for Y
Axi
s
NATHAN AND NICOLE’S ARGUMENT PATHCara’s Argument Path Tara’s Argument Path Nathan and Nicole’s Argument Path
