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

Again, a multiple stepwise regression analysis was conducted to evaluate the
differential influences of the variables depicted in Table 2, Panel B on overall addition
performance in third grade. The final model [R = .44, adjusted R 2 = .16, F(4, 90) = 6.99, p <
.001, f 2 = .23] included the three predictors a) number of pure inversion transcoding errors, b)
compatibility effect, and c) (decade) distance effect (see Table 3). Inspection of the beta
weights indicated that children who committed more pure inversion transcoding errors in first
grade also exhibited a higher overall error rate in the third grade addition task. Similarly,
children with a relatively large compatibility effect in the first grade magnitude comparison
task committed more errors in the addition task two years later. This indicated that in both
cases flawed mastery of the place-value concept in first grade was associated with an
increased overall error rate in the addition task in third grade. Finally, in contrast to the
findings of Holloway and Ansari (2009) a larger (decade) distance effect in first grade implied
better overall performance in the third grade arithmetic task.
Table 3: Regression model predicting the overall number of errors in the addition task on the basis of specific
numerical effects
Predictor B 95% CI b
Change in
R 2 t sig. raw partial
Constant .45 .34 – .56 8.19 < .001
Inversion errors (1 st grade) .30 - .13 – .48 .33 .12 3.47 < .001 .35 .34
Compatibility effect (1 st grade) .09 - .003 – .18 .18 .04 1.93 < .05 ( * ) .24 .20
Distance effect (1 st grade) - .18 - .38 – .01 - .18 .03 1.87 < .05 ( * ) - .17 - .19
CI = Confidence interval; ( * ) = tested one-sided
(iii) Effect approach analyses of predictors and criterion variables: Influence of
specific basic numerical competencies on related effects in mental arithmetic
Finally, taking a step beyond Holloway and Ansari (2009) the effect approach was
generalized to both, predictor and criterion variables. That is, we examined in how far mastery
of specific basic numerical competencies, in particular place-value understanding, serves as a
predictor for specific effects in later arithmetic performance. In particular, it was investigated
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