Jolien De Brauwer

A longitudinal study of children's performance on simple multiplication and division problems.

The authors investigated the performance on simple multiplication and division problems of 8-year-old children longitudinally to determine the developmental trajectories of both operations. Twice a year, during 2 consecutive school years, children performed a multiplication and division verification task and a number-matching task. All effects that were observed in multiplication performance (problem size, 5, and tie effect and Tie x Size interaction) were also observed in division performance. The developmental trajectories of these effects are described. The authors observed strong developmental parallels between both operations. These results are in line with strongly interconnected memory networks for multiplication and division facts, at least in young children. The results of the number-matching task showed that the interference effect developed differently for multiplication and division, indicating that automatic activation spreading from division operands to division answers is not at work in children of that age.

The development of the SNARC effect: evidence for early verbal coding.

In a recent study, Gevers and colleagues (2010, Journal of Experimental Psychology: General, Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are surrounded by rulers, number lines, and the like in the classroom, it is intuitively appealing to assume that they first use their mental number line to represent numbers and that only later in development a verbal recoding of magnitude information takes place. However, this hypothesis has never been tested. The goal of the current study was to define the developmental pattern of both accounts (spatial and verbal) in explaining the SNARC effect. To this end, 9- and 11-year-olds were tested in a magnitude comparison task. Surprisingly, clear and robust evidence for verbal coding of magnitude information was observed in both age groups. Our results imply that the ability to use verbal coding of magnitude information is robustly present early in formal schooling.

Error adaptation in mental arithmetic

Until now, error and conflict adaptation have been studied extensively using simple laboratory tasks. A common finding is that responses slow down after errors. According to the conflict monitoring theory, performance should also improve after an error. However, this is usually not observed. In this study, we investigated whether the characteristics of the experimental paradigms normally used could explain this absence. More precisely, these paradigms have in common that behavioural adaptation has little room to be expressed. We therefore studied error and conflict adaptation effects in a task that encounters the richness of everyday lifes behavioural adaptation—namely, mental arithmetic, where multiple solution strategies are available. In accordance with our hypothesis, we observed that posterror accuracy increases after errors in mental arithmetic. No support for conflict adaptation in mental arithmetic was found. Implications for current theories of conflict and error monitoring are discussed.

The SNARC effect in the processing of second-language number words : Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.

The representation of multiplication and division facts in memory evidence for cross-operation transfer without mediation

Recently, using a training paradigm, Campbell and Agnew (2009) observed cross-operation response time savings with nonidentical elements (e.g., practice 3 + 2, test 5 - 2) for addition and subtraction, showing that a single memory representation underlies addition and subtraction performance. Evidence for cross-operation savings between multiplication and division have been described frequently (e.g., Campbell, Fuchs-Lacelle, & Phenix, 2006) but they have always been attributed to a mediation strategy (reformulating a division problem as a multiplication problem, e.g., Campbell et al., 2006). Campbell and Agnew (2009) therefore concluded that there exists a fundamental difference between addition and subtraction on the one hand and multiplication and division on the other hand. However, our results suggest that retrieval savings between inverse multiplication and division problems can be observed. Even for small problems (solved by direct retrieval) practicing a division problem facilitated the corresponding multiplication problem and vice versa. These findings indicate that shared memory representations underlie multiplication and division retrieval. Hence, memory and learning processes do not seem to differ fundamentally between addition-subtraction and multiplication-division.