Procedimiento utilizado para el estudio de las principales variables de población y empleo

Whilst (in general) the cross-sectional studies show that there is a relationship between performance on symbolic comparison tasks and children’s arithmetic abilities, an important topic that needs investigating is whether this ability predicts later arithmetic achievement. To address this De Smedt, Verschaffel and Ghesquière (2009) used a longitudinal design to examine the effect of distance on children’s symbolic comparison performance and relate it to their mathematical ability one year later. In order to limit the amount of formal mathematics education they had received Time 1 of the study took place when children were beginning their formal schooling, on average 6 years of age. Children completed a symbolic comparison task and the gradient of the regression slope was used to represent the effect of distance on children’s comparison speed. The mathematics measure

used in this study was a curriculum based standardised achievement test (from the Flemish Student Monitoring System) and included arithmetic calculations alongside word based problems and measurement questions. It was found that children with steeper slopes gained lower mathematics achievement scores one year later (r = .40) and that the slope predicted 10% unique variance in children’s scores over and above age, general ability and time taken to read numbers. Their findings extended the concurrent literature to show that early symbolic comparison ability is a unique predictor of later arithmetic ability (when RTs are used). Whilst children’s overall accuracy on the task was related to their second grade maths performance (r = .38) it was not a unique predictor when age, general ability and number reading accuracy were controlled. An important limitation with the study, which the author’s note, is that the autoregressor (children’s early mathematics ability) was not assessed and included in the analysis. Therefore it is not known what influence the size of the distance effect had over and above children’s prior mathematics skills (i.e. whether it predicts growth in mathematics achievement).

However, other studies have not replicated this longitudinal relationship between a measure of the distance effect and later arithmetic and mathematics achievement.

Sasanguie, Van den Bussche & Reynvoet (2012) administered a symbolic comparison task (alongside other number processing measures; nonsymbolic comparison task, priming comparison task and number line estimation tasks) to 72 children who at Time 1 were kindergartners (5.6 years old), first graders (6.7 years), and second graders (7.6 years). Mathematics achievement was assessed at the first time point and one year later (Time 2) by a curriculum based standardised achievement test for mathematics (same test as used by De Smedt et al., 2009). Reaction times on the symbolic comparison task were adjusted to reflect both speed and accuracy (RT/1(1 – error)) and the effect of distance was quantified by a regression slope. While a significant correlation was found between children’s mathematics achievement and mean RT when controlling for grade (r = -.31), no corresponding association was found with the slope (r = .08). Children’s speed at comparing symbolic digits was found to be a significant predictor (Beta = -.61) of individual differences in mathematics achievement scores when entered alongside performance on the other number processing tasks, grade and spelling. This remained significant (Beta = -.43) when prior mathematics achievement was also included in the final step of the regression analysis.

In a similar study, Sasanguie et al. (2013) assessed both mathematics and

used in the previous study, while arithmetic fluency was assessed with a timed test. Similar methods were also used with children assessed at the first time point ranging in age from 6 to 8 years old (first to third grade) and again at a second time one year later. However, this time the metrics used to measure symbolic comparison performance were the median RT and the distance effect (the average of the median RTs on trials with distances of 4 and 5 subtracted from the average of the median RTs on trials with distances of 1 and 2, then divided by the average of the median RTs on trials with distances of 4 and 5). Both grade and spelling ability were controlled for in the correlation analysis. Speed on the comparison task (median RT) was significantly and negatively related to achievement on both of the tests, with the strength of the association almost the same for both an untimed

mathematics test and a measure assessing calculation fluency (mathematics: r = -.37; timed arithmetic: r = -.35). As before, no relationship was found with mathematics or arithmetic achievement with the effect of distance on children’s comparisons. Separate regression analyses were performed for the two achievement measures with symbolic comparison RT and DE entered alongside other number processing tasks (with age and spelling ability controlled).Speed at comparing digits was found to be a significant predictor of variance in scores on both measures (untimed: Beta = -.36; timed: Beta = -.30), whereas the distance effect was not. However, when prior mathematics achievement was controlled its contribution was no longer significant. This is an interesting finding that symbolic

comparison speed was not a predictor of growth in mathematics achievement. It should be noted that this finding could be partly due to a lack of power to detect the relationship; ten variables were entered into the regression analysis with a sample size of only 71.

Nonetheless this finding warrants further investigation.

Using an alternate method (cluster analysis), Reeve et al. (2012) characterised children’s performance on the comparison task at 6 years old as being slow, medium or fast. They found that subgroup membership at 6 years predicted arithmetic ability not only at the same time point (assessed by single digit addition) but also at 9 and a half years old (assessed by two digit addition, subtraction and multiplication) and at 11 years old (assessed by three digit subtraction, multiplication and division). The faster subgroup performed significantly better than both the medium and slow subgroups on all of the arithmetic measures at each time point, and the medium subgroup also significantly outperformed the slow subgroup.

In the majority of studies assessing symbolic comparison ability, the task is presented on a computer and the numbers range from 1 to 9. Desoete, Ceulemans, De

Weerdt and Pieters (2012) administered a different kind of task, a subtest from the TEDI- MATH Battery (Grégoire, Noël & Van Nieuwenhoven, 2004) (which also includes

comparison of nonsymbolic stimuli and verbal number words). Three arithmetic measures were given which assessed untimed simple calculation skill, complex calculation ability (problems often in word problem format) and (timed) fact retrieval. The sample size was very large and included 315 typically developing children, 64 children who were classified as low achieving and 16 who were classified as having mathematical difficulties. Children were assessed in kindergarten (aged 5 to 6 years old), first grade (6 to 7 years) and second grade (7 to 8 years). No associations were found between performance on the comparison task at Time 1 and arithmetic achievement at Time 2, whereas there were significant but weak associations with Time 3 arithmetic achievement (r = .21 to .36 controlling for IQ).

Children’s performance on the symbolic comparison task was also found to be a significant predictor of grade 2 arithmetic achievement when entered alongside performance on the other two comparison tasks (complex: Beta = .36; simple: Beta = .28); however they did not include IQ in the regression analysis. This difference in the contribution of early comparison ability to later arithmetic achievement assessed one and two years later warrants further investigation, it is possible that the relationship changes over time. Therefore more extended longitudinal studies (e.g. Reeve et al., 2012) are needed.