Task- and age-dependent effects of visual stimulus properties on children’s explicit numerosity judgments

Highlights

• Children’s numerosity judgments are affected by the visual stimulus manipulations.

• The influence of the visual stimulus manipulations depends on the task at hand.

• Children can be differentially influenced by the visual stimulus manipulations.

• The effect of the visual stimulus manipulations changes throughout development.

• The performance on the tasks is not associated with mathematics achievement.

Abstract

Researchers investigating numerosity processing manipulate the visual stimulus properties (e.g., surface). This is done to control for the confound between numerosity and its visual properties and should allow the examination of pure number processes. Nevertheless, several studies have shown that, despite different visual controls, visual cues remained to exert their influence on numerosity judgments. This study, therefore, investigated whether the impact of the visual stimulus manipulations on numerosity judgments is dependent on the task at hand (comparison task vs. same–different task) and whether this impact changes throughout development. In addition, we examined whether the influence of visual stimulus manipulations on numerosity judgments plays a role in the relation between performance on numerosity tasks and mathematics achievement. Our findings confirmed that the visual stimulus manipulations affect numerosity judgments; more important, we found that these influences changed with increasing age and differed between the comparison and the same–different tasks. Consequently, direct comparisons between numerosity studies using different tasks and age groups are difficult. No meaningful relationship between the performance on the comparison and same–different tasks and mathematics achievement was found in typically developing children, nor did we find consistent differences between children with and without mathematical learning disability (MLD).

Introduction

Numerosity and its continuous visual properties are correlated in everyday life. For instance, when more marbles are added to a collection of marbles, numerosity as well as the size of the collection increases. Therefore, it is common practice that studies investigating numerosity processing manipulate the visual cues of the numerosity stimuli. These manipulations should prevent participants from relying on the visual cues when judging numerosity and, thus, allow researchers to study pure number processes. However, an increasing number of studies show that numerosity judgments are sensitive to the continuous visual properties of the numerosity stimuli. These studies show, for instance, that numerosity judgments are influenced by density (Dakin et al., 2011, Sophian and Chu, 2008, Tibber et al., 2012), the size of the individual elements (Gebuis and Reynvoet, 2011b, Hurewitz et al., 2006, Rousselle and Noël, 2008, Tokita and Ishiguchi, 2010), or patch size (Gebuis and Gevers, 2011, Tokita and Ishiguchi, 2010).

Only a few researchers have investigated whether and how the visual stimulus manipulations they use in their experiments affect the measurements of numerosity processing. Researchers mostly believe that the visual confounds are sufficiently controlled and collapse the data from congruent trials (e.g., the larger numerosity has larger visual cues) and incongruent trials (e.g., the smaller numerosity has larger visual cues) without further examining whether the visual stimulus manipulations in these conditions lead to different findings (e.g., De Smedt and Gilmore, 2011, Piazza et al., 2004). However, investigating the effect of the different visual manipulations in congruent and incongruent trials separately seems to be necessary because some studies have shown that participants respond to the visual properties even when controlling for the visual cues (Gilmore et al., 2011, Inglis et al., 2011). For instance, approximately 30% of the 8-year-olds in a study by Inglis and colleagues (2011) and approximately 40% of the adults in a study by Gilmore and colleagues (2011) were removed. The performance of these participants in the congruent and incongruent conditions differed by more than 50% in accuracy, suggesting that they relied on the visual stimulus properties. Apparently, the performance on numerosity tasks is unavoidably affected by the manipulations of the continuous visual properties.

To allow comparisons across numerosity studies using different designs and including different age groups, it is essential to find out how the visual stimulus manipulations affect numerosity performance throughout development. It is not clear whether children of different ages are influenced differently by the visual stimulus properties. Infant studies have revealed inconsistent results about the effect of the visual stimulus properties on numerosity judgments. There are studies showing that infants might be more sensitive to the continuous visual properties at the expense of numerosity (Clearfield and Mix, 1999, Clearfield and Mix, 2001, Feigenson et al., 2002), that infants are equally sensitive to numerosity and visual cues (Brannon et al., 2006, Cordes and Brannon, 2009, vanMarle and Wynn, 2006), and that infants prefer to attend to numerosity over visual properties (Brannon et al., 2004, Cordes and Brannon, 2008, Cordes and Brannon, 2011, Xu, 2003, Xu and Spelke, 2000, Xu et al., 2005). The few studies using explicit paradigms, which examined the effects of the visual stimulus manipulations, showed a more consistent pattern of findings. These studies point to a reliance on visual cues in young children at the expense of number, which seems to decrease with increasing age (Rousselle and Noël, 2008, Rousselle et al., 2004) but remains visible even in adults (Gebuis and Van der Smagt, 2011, Gilmore et al., 2011, Halberda et al., 2008). However, the age at which children could compare numerosities while the visual cues were manipulated differed. Rousselle and colleagues (Rousselle and Noël, 2008, Rousselle et al., 2004) showed that 3-year-old children were unable to compare numerosities when the stimuli were controlled for surface area, whereas 4- and 5-year-olds performed significantly above chance. In contrast, Soltész, Szucs, and Szucs (2010) observed that 4-year-olds performed at chance level when the visual properties and numerosity were manipulated inconsistently, whereas performance was above chance from 5 years onward.

Research on the impact of the visual stimulus manipulations on numerosity judgments is necessary when considering the important conclusions that are drawn from the results of numerosity studies. It is, for instance, suggested that performance on numerosity tasks is related to mathematics achievement. Typically developing children who performed worse on numerosity discrimination showed less proficiency in mathematics than children who performed better on this task (e.g., Halberda et al., 2008, Inglis et al., 2011, Mazzocco et al., 2011b). Similarly, children with mathematical learning disability (MLD) performed worse than controls on numerosity comparison (Mazzocco et al., 2011a, Mussolin et al., 2010, Piazza et al., 2010). However, there are also several studies that show no correlation between the performance on numerosity tasks and mathematics achievement in typically developing children (e.g., Holloway and Ansari, 2009, Sasanguie et al., 2012, Soltész et al., 2010) or that show no difference between children with and without MLD on numerosity discrimination ability (De Smedt and Gilmore, 2011, Iuculano et al., 2008, Rousselle and Noël, 2007).

The idea has been proposed that the influence of the visual stimulus properties could explain the mixed findings regarding the relationship between numerosity processing and mathematics achievement (Gebuis & Reynvoet, in press). To date, only a few studies investigating the association between numerosity discrimination and mathematics achievement have taken the influence of the visual stimulus properties into account. Mussolin and colleagues (2010) suggested that children with MLD were more sensitive than controls to continuous visual properties, such as density and surface area, during comparison of random stick patterns. Similarly, Mejias, Mussolin, Rousselle, Grégoire, and Noël (2012) showed that, in contrast to control children, children with MLD relied more on the visual cues that correlated with numerosity because they made better estimations in a task with homogeneous-sized dots (where the cumulative area covaried with numerosity) than in a task with heterogeneous-sized dots (where the cumulative area was constant across numerosities). These studies suggest that children with MLD are more influenced by the visual stimulus properties than control participants.

Our goals in this study were twofold. First, we investigated whether the visual cues influence numerosity judgments differently across development and across task designs. Insight into these variables will reveal whether data from different studies can be compared or whether caution is warranted. Second, we investigated whether the visual cues could explain the observed discrepancies between numerosity studies regarding the relationship between numerosity processing and mathematics achievement. To this end, we conducted an experiment in a group of typically developing children from first, second, third, and sixth grades (Experiment 1) and in children with MLD (Experiment 2). The performance of both typically developing children and children with MLD was investigated because difficulties in typically developing children with low math proficiency are not necessarily the same as the difficulties in children with MLD (e.g., Desoete et al., 2012, Mazzocco et al., 2008). We administered both a comparison task and a same–different task in which we manipulated the visual properties of the numerosity stimuli using a more stringent method to control the visual cues than the method used in most previous studies (Gebuis & Reynvoet, 2011a). Similar to previous studies, in the comparison task, in half of the trials the numerically larger numerosity consisted of a larger surface, density, and diameter but a smaller convex hull (congruent condition), and in the other half the numerically larger numerosity consisted of a smaller surface, density, and diameter but a larger convex hull (incongruent condition) (for a similar design, see Condition 4 in Gebuis & Reynvoet, 2011a). The visual cues of the trials with two numerically different stimuli in the same–different task were manipulated in the same way as in the comparison task. The numerically same trials also consisted of a stimulus with larger visual cues and a stimulus with smaller visual cues. Differences in the reliance on the visual cues in a comparison task and a same–different task can be expected. Namely, in the comparison task, where participants need to indicate the numerically larger numerosity, participants might be prone to indicate the stimulus consisting of larger visual properties as numerically larger. In contrast, in the same–different task, where participants need to decide whether the numerosities are numerically the same or different, participants might be prone to judge the numerosities as different because the visual properties of the numerosities always differ (also in the numerically same trials, one of the two stimuli was always larger in visual stimulus properties). To examine the relationship between the performance on the tasks and mathematics achievement in Experiment 1, we administered both a general mathematics achievement test and a timed arithmetic test.