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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

Results

• 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 the abstract semantic category of that number.

* * 1 0.5 0

Digit Response (% signal change)

Digits5

^

• 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.

1st

2nd

3rd

Final

Age

Math Facts (WJC)

Math Speed (WJMF)

Reading (LWID)

K

20

15

6.28 ± 0.39

3.33 ± 2.50

8.07 ± 6.17

19.13 ± 6.24

1st

25

16

7.01 ± 0.46

8.62 ± 3.22

23.63 ± 8.91

31.94 ± 9.49

2nd

20

16

8.33 ± 0.32

11.44 ± 1.83

42.31 ± 11.02

46.63 ± 5.18

3rd

20

16

9.14 ± 0.44

14.38 ± 2.03

57.38 ± 9.51

52.56 ± 4.53

Adult

16

16

25.56 ± 3.46

N/A

N/A

N/A

Adults

0

Adults

* *

K

1st

2nd

Digits > Baseline

Digits9

1 0.5 0

1st

3rd

• 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. -38, -59, -32

* *

1 0.5 0

K

^

* *

2nd

3rd

Adults

L. Fus: -40 -50 -18

2

*

Digits5

Digits9

*

1st

-42, -52, 42 * *

Digits5

^

1 0.5 0

1.5

*

^

*

* *

Digits9

*

*

* *

1st

2nd

1 0.5 0 ‐0.5

1st

Kindergarteners

• 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 provide an assessment of the degree to which such brain mechanisms are shared with symbolic processes.

* *

Digits9

Adults

Digit Response (% signal change)

Digit Response (% signal change)

2nd

R. Fus: 35 -47 -21

2 1.5

Digits5

1.5

‐0.5 K

9

L. BA 19/39: -49 -71 6

2

* *

‐0.5

Analysis Scans

3rd

0.5

R. BA 19/39: 50 -62 6

K

Subjects

* *

^

1

‐0.5

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, the fusiform gyrus and intraparietal sulcus, respectively, to numbers in the counting range.

* *

Digits9

1.5

‐0.5 K

Digits5

5

* *

Digits9

‐0.5

1.5

L. IPS: -28 -68 24

2

Digits5

2

Children’s number concepts undergo radical changes during early elementary schooling (K-3rd), especially in the small number range (59, the “counting range”) as children learn to perform exact calculations.7 We therefore examined the development of neural representations of digits representing quantities in the “counting range” (i.e., between 5 and 9, above the subitizing range, but also below the large number range).

R. IPS: 29 -68 24

2 1.5

Digit Response (% signal change)

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

Digit Response (% signal change)

Methods

Digit Response (% signal change)

Introduction

2nd

3rd

Adults

1st Graders

K

2nd Graders

3rd Graders

3rd

Adults

Adults

Age

WJMF

Age (K&1st only)

WJMF (K&1st)

Age (Planets)

Left IPS

.409 ***

.410 ***

.521 **

.396 *

.152 (ns)

Right IPS

.338 **

.353 **

.564 ***

.428 *

.062 (ns)

Left Fus.

.246 (p = .052)

.243 (p= .055)

.416 *

.367 *

.112 (ns)

Right Fus.

.121 (ns)

.127 (ns)

.458 *

.380 *

.017 (ns)

Left BA 19/39

.347 **

.355 **

.531 **

.408 *

.036 (ns)

Right BA 19/39

.288 *

.287 *

.373 *

.279 (ns)

.055 (ns)

• Multiple regression analyses showed that Math Fluency accounted for more variance than age in the left and right IPS, but only slightly, as age and Math Fluency were highly correlated (R = .887). • While 1st and 2nd graders showed increased IPS responses to 5 but not 9, fMRI responses to 5 and 9 were not differentially correlated with age or WJMF. • The absence of planet-age correlations suggests that these developmental shifts are not due to domain general changes (e.g., in novelty responses or neurovascular coupling).

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

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