1. From incompatible numerical representations:
When and how infants compare small and large sets
Danielle Brazel*, Tasha Posid, & Sara Cordes
Boston College Department of Psychology
*Contact: brazeld@bc.edu
*tasha.posid@bc.edu
Introduction
Research Questions
Methods
Results
Results
Discussion
References & Acknowledgements
• When during the course of development do infants develop
the ability to discriminate small (<4) from large (>3) sets?
• What factors (e.g., perceptual variability or verbal counting)
may aid infants’ ability to discriminate small and large
quantities?
Manual Search Task 3,4,7
Conditions
2 vs. 3
2 vs. 4
• Data are first to suggest infants can succeed at a 2 vs. 4
discrimination before 3 years of age.
• Perceptual variability (Heterogeneous) and verbal counting
(Language) may promote infants’ abilities to track small and
large sets.
• Future directions:
- Larger sample size
- Study younger infants (around 14 months)
We would like to thank the members of the Boston College Infant and Child Cognition Lab,
especially Annie Plageman and Elizabeth Bayoff, who assisted in data collection and coding, as well
as all of the families who participated in our study. Funding provided by NSF CAREER #1056726 to
S.C.
Methods
Participants: `
Standard Condition Language Condition
“Look at my toys. 1, 2, 3, 4. See, 4!”
Heterogeneous Condition
• Infants precisely track small quantities using the object-file system
of representation (<4) and approximately represent large sets via a
noisy analog magnitude system (>3)1,2
• Infants are able to discriminate between either two small quantities
(e.g., 1 vs. 2) or two large quantities (e.g., 8 vs. 16) e.g., 3,4,5
• 14-mos olds and younger show robust discrimination failures when
comparing small and large sets, 3,4,6,7 yet 3-year-olds successfully
make this distinction 8
• There is no research to date examining when in development
infants successfully discriminate small vs. large sets
• Evidence suggests perceptual variability9,10 or verbal counting 11,12
may enhance numerical understanding in preschool-age children;
however, no research has examined whether this may aid in infants’
ability to discriminate between small and large sets
1 Feigenson, Dehaene, & Spelke, (2004). Trends in Cognitive Sciences, 8(7), 307-314.
2 Cordes & Brannon (2008). Developmental Science, 11, 803-808.
3 Feigenson & Carey (2003). Developmental Science, 6, 568-584.
4 Feigenson & Carey (2005). Cognition, 97, 295-313.
5 Xu & Spelke (2000). Cognition, 74(1), 1-11.
6 Cordes & Brannon (2009). Developmental Psychology, 45(6), 1583-1594.
7 Barner, Thalwitz, Wood, Yang, & Carey (2007). Developmental Science, 10(3), 365-373.
8 Cantlon, Fink, Safford, & Brannon (2007). Developmental Science, 10(4), 431-440.
9 Feigenson (2005). Cognition, 95(3), B-37-B48.
10 Posid, Huguenel, & Cordes (in preparation).
11 Mix, Sandhofer, Moore, & Russell (2012). Early Childhood Research Quarterly, 27, 274-283.
12 Posid & Cordes (submitted).
16-to-23-months-old 24-to-29-months-old 30-to-36-months-old
Standard N=7 N=11 N=10
Heterogeneity N=8 N=6 N=7
Language N=11 N=8 N=9
Expected Full Expected Empty
Expected Empty
Infant removes 2, Experimenter “finds” last 1,
Experimenter “finds” last 2,
Figure 1. Infants generally searched more with age
on the Expected Full trials (age X trial: F(2, 68)=24.7,
p=.002)
Figure 2. The youngest age group searched longer in
the 2 vs. 4 comparison than the 2 vs. 3 comparison p=.
055), with equal searching for the middle and oldest age
groups (p’s > .2)
Children searched longer with age Longer searching in the 2 vs. 4
condition in youngest subjects
All infants succeed on 2 vs. 4, only oldest infants
discriminate 2 vs. 3
Figure 3. While all infants successfully discriminated 2 vs. 4 items
(p<.02 for all), only the oldest infants successfully discriminated 2
vs. 3 items (p<.001).
Standard:
Successful discrimination of small and large sets
across all ages
Heterogeneous:
Figure 4. Infants generally successfully discriminated 2 vs. 3 and 2
vs. 4 in the Heterogeneous condition (p<.05)
Figure 5. Infants generally successfully discriminated 2 vs. 3 and 2
vs. 4 in the Language condition (p<.05)
Successful discrimination of small and large sets
across all agesLanguage:
• Results were analyzed using difference scores (and used in Figures 3, 4, 5)
• Difference Score = Expected Full – Expected Empty (Avg of Expected Empty (2) & Expected Empty (4))
Vs.
Expected Full
Infant removes 2,
Vs.
Expected Empty
Infant removes 2,
Baseline Search
Expected Empty
Infant removes 2,
Baseline Search
10s search period
2 ducks placed in box
4 ducks placed in box
2 ducks placed in box
3 ducks placed in box
10s search period
10s search period 10s search period
10s search period 10s search period
(Replicating Feigenson & Carey, 2003)
0
1
2
3
4
5
18-23 mos 24-29 mos 30-36 mos
SearchTime(sec)
Age groups
2 vs. 3 2 vs. 4
0
1
2
3
4
5
6
18-23 mos 24-29 mos 30-36 mos
SearchTime(sec)
Age groups
Expected Full Expected Empty
** *
*
0
1
2
3
4
5
6
18-23 mos 24-29 mos 30-36 mos
DifferenceScores
Age groups
2 vs. 3
2 vs. 4
*
*
*
*
0
1
2
3
4
5
6
18-23 mos 24-29 mos 30-36 mos
DifferenceScores
Age groups
2 vs. 3
2 vs. 4
*
* ** *
0
1
2
3
4
5
18-23 mos 24-29 mos 30-36 mos
DifferenceScores
Age groups
2 vs. 3
2 vs. 4