The influence of the place-value structure of the Arabic number ...

epresentation of two-digit numbers for German-speaking and Italian-speaking children as
assessed in the number line task
100
A
Estimated Value
80
60
40
20
Logarithmic y = 17.15Ln(x) - 3.22
R 2 = 0.93
Linear y = 0.60x + 27.36
R 2 = 0.85
0
0 10 20 30 40 50 60 70 80 90 100
Actual Value
100
Breakpoint
B
80
Logarithmic: y = 17.15Ln(x) - 3.22
R 2 = 0.93
Estimated Value
60
40
20
Two-linear:
y one-digit = 4.16x + 1.45
y two-digit = 0-47x + 36.33
R 2 = 0.97
0
0 10 20 30 40 50 60 70 80 90 100
Actual Value
Figure 4: Regression lines based on the mean estimates of all children per data point showing the differences of
overall logarithmic (dashed line) versus simple linear (solid line, Panel A) and two-linear fitting (solid
line, Panel B) of the 0-to-100 scale. Please note that the data presented here reflects an item analysis and
thus does not directly correspond to the participant-based analyses previously described. These data were
chosen to be given as they allow for a better illustration of differences and similarities of the logarithmic
and the two-linear model. Please also note that an additional two-linear regression in which the optimal
break-point was computed instead of using the theoretically driven breakpoint at 10 revealed an identical
adjusted R 2 of .97 with the optimal break-point at 9.57.
102