94.11
Frontal versus Parietal Contributions to Elementary School Children’s Number Concepts Edward M. Hubbard and Bruce D. McCandliss Department of Psychology and Human Development, Vanderbilt University, Nashville, TN, USA
Methods
Results
Parietal and frontal regions that respond to quantity in infants1 and young children2 are retrained by education to perform advanced symbolic mathematics in adults.3 Although the neural basis of arithmetic in school children has been extensively studied,4,5 little is known about the basic changes that occur in networks related to the recognition and understanding of number semantics as children learn to recognize and interpret Arabic number symbols.6
• While lying in a 3-Tesla MRI scanner, children played a spaceship game where they passively viewed displays of "stars" ranging in numerosity from 5 to 9. • On each run, one abstract set size of stars (e.g., 6-star-runs, 8-starruns) was repeatedly presented, leading to habituation of neural populations tuned to that number.
All clusters: p < .05 corrected
Children’s number concepts undergo radical changes during early elementary schooling (K-3rd), especially in the small number range (59, the “counting range” between subitizing and two-digit numbers) as children learn to perform exact calculations.7 We therefore examined the development of specific neural links between digits in the counting range (i.e., between 5 and 9) and the quantities that they represent.
L. Mid. IPS: -44 -44 45
L. Ant. IPS: -43 -35 42
4
Grade
Scans
Age
Math Facts (WJC)
Math Speed (WJMF)
Reading (LWID)
K
15
6.28 ± 0.39
103.08 ± 15.87
96.31 ± 11.75
103.67 ± 12.27
1st
16
7.01 ± 0.46
113.38 ± 15.51
108.38 ± 10.59
111.88 ± 12.09
2nd
16
8.33 ± 0.32
105.13 ± 11.06
108.06 ± 13.41
113.81 ± 7.50
3rd
16
9.14 ± 0.44
103.25 ± 10.73
107.56 ± 6.79
111.69 ± 6.85
6
7
8 Age (Years)
F(1,62) = 6.72, p < .05
Digit Response (% signal change)
5Dig
9Dig Deviant Magnitude
L. IPS: -28 -68 24
2 * *
Digits9
* * 1 0.5 0 ‐0.5
Digits5
1.5
* *
* *
3rd
Adults
Digits9
^
^
1 0.5 0 ‐0.5
K
1st
2nd
3rd
Adults
K
1st
2nd
R. BA 19/39: 50 -62 6
2 Digits5
* *
Digits > Baseline
1 0.5 0 ‐0.5 1st
2nd
3rd
* *
Digits9
* *
1 0.5 0
Adults
K
Digits9
^
* *
^
1 0.5 0
2nd
3rd
*
Digits5
1.5
Adults
L. Fus: -40 -50 -18
2 * *
Digits5
*
1st
-42, -52, 42
R. Fus: 35 -47 -21
2
Analysis
Digits5
1.5
‐0.5 K
1.5
L. BA 19/39: -49 -71 6
2
* *
Digits9
*
^
*
* *
Digits9
*
*
* *
1st
2nd
1 0.5 0 ‐0.5
K
-38, -59, -32
0
10
Digits5
1.5
‐0.5
• All data were pre-processed and analyzed using BrainVoyager 2.2. • Data were slice time corrected, motion corrected and temporally filtered prior to coregistration. • Subjects whose movement was less than 3 mm in at least four of the eight runs were considered for inclusion, but were replaced if other subjects with better data quality were run in the same order. • All data were then normalized to the Talairach transformed and smoothed with an 8 mm smoothing kernel. • Data were analyzed using GLM and RFX ANCOVA procedures. • ROI analyses were performed using 10 mm spheres centered on the peaks of the overall group analysis.
9
R. IPS: 29 -68 24
2
1.5
Hab8
-0.5 5
Digit Response (% signal change)
Digit Distance Effect
R = -.293, p < .05
Hab6
Digit Response (% signal change)
• Children were drawn from a larger study of math abilities in 472 children in seven private schools in the Nashville area. • Children whose parents agreed to participate in the second phase (n = 125) were invited for mock scanning. • Children who successfully completed mock scanning (n = 91) were invited back for the fMRI session. • 85 children and 16 adults completed scanning. • 63 children and all 16 adults were included in the final sample, based on low motion during scanning, order, and other factors. • All children were typically developing and achieving, as shown by standardized tests of math and reading abilities (Table 1). • We are currently collecting behavioral and fMRI data on these same children to assess changes over one year.
0 -1
-3
Digit Response (% signal change)
Subjects
1
-2
• Presentation of occasional deviant stimuli permitted us to measure transfer of habituation across several conditions, while controlling for low-level stimulus changes (e.g., dot size, area, luminance). – "Close Nonsymbolic" deviants presented a display of stars that differed from the standard by a single star. – "Far Nonsymbolic" deviants presented a display that differed from the standard by three stars. – "Close Symbolic" deviants presented a digit symbol that differed from the standard set size by one. – "Far Symbolic" deviants presented a digit symbol that differed from the standard set size by three. • Contrasting BOLD responses to Close Nonsymbolic and Far Nonsymbolic deviant stimuli provides an assessment of brain mechanisms engaged in detecting changes in non-symbolic numerosity. • Contrasting BOLD responses to Close Symbolic and Far Symbolic stimuli provides an assessment of the degree to which such brain mechanisms are shared with symbolic processes.
Digit Response (% signal change)
We used a standard method to probe neural systems for number, the fMRI-adaptation paradigm, which shows that neural responses decrease to repeated presentations of a standard numerosity, and dishabituate to different numerosities.8,9 Previous studies with this method have generally been limited to large numerosities, or have used only symbolic notations.10 We measured the developmental course of fMRI responses in regions involved in visual identification and semantic analysis of number symbols, including the fusiform gyrus, and the intraparietal sulcus and prefrontal regions, respectively, to numbers in the counting range.
2
fMRI Response (% signal change)
0.5
3
Digit Response (% signal change)
Introduction
1st
2nd
3rd
Adults
K
3rd
Adults
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Izard, V., Dehaene-Lambertz, G., & Dehaene, S. (2008). Distinct cerebral pathways for object identity and number in human infants. Public Library of Science, Biology, 6(2), e11. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional Imaging of Numerical Processing in Adults and 4-y-Old Children. Public Library of Science, Biology, 4(5), e125. Krueger, F., Spampinato, M. V., Pardini, M., Pajevic, S., Wood, J. N., Weiss, G. H., et al. (2008). Integral calculus problem solving: an fMRI investigation. Neuroreport, 19(11), 1095-1099. Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15(11), 1779-1790. Rosenberg-Lee, M., Barth, M., & Menon, V. (2011). What difference does a year of schooling make? Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving. Neuroimage. In press Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278291. Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Hove, UK: Psychology Press. Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53(2), 293-305. Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A., & Goebel, R. (2007). Notation-dependent and -independent representations of numbers in the parietal lobes. Neuron, 53(2), 307-314. Funded by NSF REESE Grant: 07-595 0816063.
