Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.

Effects of Presentation Type and Visual Control in Numerosity Discrimination: Implications for Number Processing?

Performance in a non-symbolic comparison task in which participants are asked to indicate the larger numerosity of two dot arrays, is assumed to be supported by the Approximate Number System (ANS). This system allows participants to judge numerosity independently from other visual cues. Supporting this idea, previous studies indicated that numerosity can be processed when visual cues are controlled for. Consequently, distinct types of visual cue control are assumed to be interchangeable. However, a previous study showed that the type of visual cue control affected performance using a simultaneous presentation of the stimuli in numerosity comparison. In the current study, we explored whether the influence of the type of visual cue control on performance disappeared when sequentially presenting each stimulus in numerosity comparison. While the influence of the applied type of visual cue control was significantly more evident in the simultaneous condition, sequentially presenting the stimuli did not completely exclude the influence of distinct types of visual cue control. Altogether, these results indicate that the implicit assumption that it is possible to compare performances across studies with a differential visual cue control is unwarranted and that the influence of the type of visual cue control partly depends on the presentation format of the stimuli.

The power of emotion versus the power of suggestion: memory for emotional events in the misinformation paradigm.

Research has shown that emotional events are remembered better than neutral events, but might also elicit an increase in false memories. The present study was designed to disentangle the influences of valence and arousal on event memory in the misinformation paradigm. Participants were shown six types of photographs (positive with high/low arousal, negative with high/low arousal, ambiguous, neutral), after which half of them were exposed to misleading information. A recognition test assessed memory for both correct and false central and peripheral details. Negative and ambiguous events elicited fewer correct and more false memories for peripheral details than positive and neutral events, regardless of previous exposure to misinformation. Arousal improved memory for correct central details, and both negative valence and arousal inhibited control participants' tendency to endorse false central details. The power of emotion was overruled by the power of suggestion, however, as the latter effect disappeared with previous exposure to misinformation. Results are discussed in the light of earlier research on emotion and cognition, recent motivational theories, and implications for forensic practice.

Concurrent validity of approximate number sense tasks in adults and children.

Reasoning with non-symbolic numerosities is suggested to be rooted in the Approximate Number System (ANS) and evidence pointing to a relationship between the acuity of this system and mathematics is available. In order to use the acuity of this ANS as a screening instrument to detect future math problems, it is important to model ANS acuity over development. However, whether ANS acuity and its development have been described accurately can be questioned. Namely, different tasks were used to examine the developmental trajectory of ANS acuity and studies comparing performances on these different tasks are scarce. In the present study, we examined whether different tasks designed to measure the acuity of the ANS are comparable and lead to related ANS acuity measures (i.e., the concurrent validity of these tasks). We contrasted the change detection task, which is used in infants, with tasks that are more commonly used in older children and adults (i.e., comparison and same-different tasks). Together, our results suggest that ANS acuity measures obtained with different tasks are not related. This poses serious problems for the comparison of ANS acuity measures derived from different tasks and thus for the establishment of the developmental trajectory of ANS acuity.

Comparing the neural distance effect derived from the non-symbolic comparison and the same-different task.

As a result of the representation of numerosities, more accurate and faster discrimination between two numerosities is observed when the distance between them increases. In previous studies, the comparison and same-different task were most frequently used to investigate this distance effect. Recently, it was questioned whether the non-symbolic distance effects derived from these tasks originate at the same level. In the current study, we examined the behavioral and neural distance effects of the comparison and same-different task to assess potential differences between both tasks. Participants were first year university students. Each participant completed both tasks, while their reaction time, accuracy and brain activity on predefined components was measured. The early N1-P2p transition and the P2p component on temporo-occipital (TO) and inferior parietal (IP) electrode groups were considered, as well as the late P3 component on a central (C) electrode group. The results showed that the behavioral distance effects from both tasks were comparable, although participants' performance was worse on the same-different task. The neural results revealed similar effects of distance on the mean amplitudes for the early components for both tasks (all p's < 0.02) and an additional effect of task difficulty on the mean amplitudes of these components. Similar as in previous studies, we found a (marginally) significant increase in mean amplitude of the later P3 component with increasing distance for the comparison (p = 0.07), but not for the same-different task. Apparently, the initial stages of number processing are comparable for both tasks, but an additional later stage is only present for the comparison task. The P3 effect would be indicative of this decisional stage, which was previously proposed to underlie the comparison distance effect (CDE).