Neural evidence of core foundations and conceptual change in preschool numeracy.

Symbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test competing theories of early number learning by measuring event-related brain potentials during a novel number word-quantity comparison task in 3-4-year-old preschool children (N = 128). We find several qualitative differences in neural processing of number by conceptual stage of development. Specifically, we find differences in early attention-related parietal electrophysiology (N1), suggesting that less conceptually advanced children process arrays as individual objects and more advanced children distribute attention over the entire set. Subsequently, we find that only more conceptually advanced children show later-going frontal (N2) sensitivity to the numerical-distance relationship between the number word and visual quantity. The nature of this response suggested that exact rather than approximate numerical meanings were being associated with number words over frontal sites. No evidence of numerical distance effects was observed over posterior scalp sites. Together these results suggest that children may engage parallel individuation of objects to learn the meanings of the first few number words, but, ultimately, create new exact cardinal value representations for number words that cannot be defined in terms of core, nonverbal number systems. More broadly, these results document an interaction between attentional and general cognitive mechanisms in cognitive development. RESEARCH HIGHLIGHTS: Conceptual development in numeracy is associated with a shift in attention from objects to sets. Children acquire meanings of the first few number words through associations with parallel attentional individuation of objects. Understanding of cardinality is associated with attentional processing of sets rather than individuals. Brain signatures suggest children attribute exact rather than approximate numerical meanings to the first few number words. Number-quantity relationship processing for the first few number words is evident in frontal but not parietal scalp electrophysiology of young children.

On the spore ornamentation of the microsoroid ferns (microsoroideae, polypodiaceae).

Microsoroideae is the third largest of the six subfamilies of Polypodiaceae, containing over 180 species. These ferns are widely distributed in the tropical and subtropical regions of the Old World and Oceania. We documented the spore ornamentation and integrated these data into the latest phylogenetic hypotheses, including a sampling of 100 taxa representing each of 17 major lineages of microsoroid ferns. This enabled us to reconstruct the ancestral states of the spore morphology. The results show verrucate ornamentation as an ancestral state for Goniophlebieae and Lecanoptereae, globular for Microsoreae, and rugulate surface for Lepisoreae. In addition, spore ornamentation can be used to distinguish certain clades of the microsoroid ferns. Among all five tribes, Lecanoptereae show most diversity in spore surface ornamentation.

Exploring phylogeny of the microsoroid ferns (Polypodiaceae) based on six plastid DNA markers.

The microsoroid ferns are one of the largest subfamilies of the Polypodiaceae with over 180 species mainly found in the humid forests of tropical Australasia. The phylogenetic relationships are still unclear, especially the delimitation of the genus Microsorum which has been recognized to be non-monophyletic. We analysed the microsoroid ferns using six chloroplast DNA regions (rbcL, rps4+rps4-trnS, trnL+trnL-trnF, atpA, atpB and matK) in order to present a robust hypothesis of their phylogeny. Our results suggest that they comprise up to 17 genera; of them, 12 agree with a previously accepted generic classification. Five tribes are proposed based on the phylogenetic relationships. Most of the species traditionally included in the genus Microsorum are found in six genera belonging to two tribes. In addition to the commonly used DNA markers, the additional atpA and matK are helpful to provide information about the phylogenetic relationships of the microsoroid ferns.

Default-mode network activation underlies accurate contextual processing of exclusive disjunctions in older but not younger adults.

Young adults proactively engage frontoparietal processing of contextual cues to preempt subsequent events. Rather than being preemptive, older adults engage these brain areas reactively upon event occurrences. Reactive frontoparietal processes in older adults, however, might be insufficient for complex contextual neural computations where utilities of contexts are not straightforward but dependent on a set of stimulus-response rules. Applying non-linear logic (XOR) rules in an fMRI experiment, we found higher default-mode network (DMN) activity critical for correctly responding to such contingency in older but not younger adults. Moreover, older individuals with higher proactive cue processing showed better performances with less DMN activity. Thus, DMN processing provides critical support when older adults are faced with complex contextual contingencies. These findings suggest an age-related change in the neurocomputational role of introspective processes in decision-making from young to older adulthood.

Characterizing exact arithmetic abilities before formal schooling.

Children appear to have some arithmetic abilities before formal instruction in school, but the extent of these abilities as well as the mechanisms underlying them are poorly understood. Over two studies, an initial exploratory study of preschool children in the U.S. (N = 207; Age = 2.89-4.30 years) and a pre-registered replication of preschool children in Italy (N = 130; Age = 3-6.33 years), we documented some basic behavioral signatures of exact arithmetic using a non-symbolic subtraction task. Furthermore, we investigated the underlying mechanisms by analyzing the relationship between individual differences in exact subtraction and assessments of other numerical and non-numerical abilities. Across both studies, children performed above chance on the exact non-symbolic arithmetic task, generally showing better performance on problems involving smaller quantities compared to those involving larger quantities. Furthermore, individual differences in non-verbal approximate numerical abilities and exact cardinal number knowledge were related to different aspects of subtraction performance. Specifically, non-verbal approximate numerical abilities were related to subtraction performance in older but not younger children. Across both studies we found evidence that cardinal number knowledge was related to performance on subtraction problems where the answer was zero (i.e., subtractive negation problems). Moreover, subtractive negation problems were only solved above chance by children who had a basic understanding of cardinality. Together these finding suggest that core non-verbal numerical abilities, as well as emerging knowledge of symbolic numbers provide a basis for some, albeit limited, exact arithmetic abilities before formal schooling.

Culture-related differences in the neural processing of probability during mixed lottery value-based decision-making.

This study evaluated how differences in economic risk-taking in Westerners and East Asians reflect cultural differences in the analytic or holistic processing of probabilistic outcomes during value-based decisions. Twenty-seven Americans (US) and 51 Taiwanese (TW) young adults completed a functional magnetic resonance imaging (fMRI) Lottery Choice Task (LCT) experiment. Participants accepted or rejected stakes with varying probabilities of winning or losing different magnitudes of points. TW participants accepted more stakes when win probabilities were > 0.50, whereas US participants reduced their acceptance rates of winning stakes more discriminately as win probabilities decreased. Both groups rejected losing stakes (win probabilities < 0.50) with similar frequency. Critically, ventromedial prefrontal cortex (VMPFC) responses correspondingly showed greater discrimination between win probability conditions in US than TW groups. Our findings highlight a neurocognitive mechanism in the VMPFC for how cultural differences in distinguishing between probabilistic reward outcomes shape neural computations of risk and prospects.