Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals.

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

Nurturing the reading brain: home literacy practices are associated with children's neural response to printed words through vocabulary skills.

Previous studies indicate that children are exposed to different literacy experiences at home. Although these disparities have been shown to affect children's literacy skills, it remains unclear whether and how home literacy practices influence brain activity underlying word-level reading. In the present study, we asked parents of French children from various socioeconomic backgrounds (n = 66; 8.46 ± 0.36 years, range 7.52-9.22; 20 girls) to report the frequency of home literacy practices. Neural adaptation to the repetition of printed words was then measured using functional magnetic resonance imaging (fMRI) in a subset of these children (n = 44; 8.49 ± 0.33 years, range 8.02-9.14; 13 girls), thereby assessing how sensitive was the brain to the repeated presentation of these words. We found that more frequent home literacy practices were associated with enhanced word adaptation in the left posterior inferior frontal sulcus (r = 0.32). We also found that the frequency of home literacy practices was associated with children's vocabulary skill (r = 0.25), which itself influenced the relation between home literacy practices and neural adaptation to words. Finally, none of these effects were observed in a digit adaptation task, highlighting their specificity to word recognition. These findings are consistent with a model positing that home literacy experiences may improve children's vocabulary skill, which in turn may influence the neural mechanisms supporting word-level reading.

The relation between home numeracy practices and a variety of math skills in elementary school children.

A growing number of studies suggest that the frequency of numeracy experiences that parents provide at home may relate to children's mathematical development. However, the relation between home numeracy practices and children's numerical skills is complex and might depend upon both the type and difficulty of activities, as well as the type of math skills. Studies have also argued that this relation may be driven by factors that are not systematically controlled for in the literature, including socio-economic status (SES), parental math skills and children's IQ. Finally, as most prior studies have focused on preschoolers, it remains unclear to what extent there remains a relation between the home numeracy environment and math skills when children are in elementary school. In the present study, we tested an extensive range of math skills in 66 8-year-olds, including non-symbolic quantity processing, symbolic number understanding, transcoding, counting, and mental arithmetic. We also asked parents to complete a questionnaire about their SES, academic expectations, academic attitudes, and the numeracy practices that they provide at home. Finally, we measured their arithmetic fluency as a proxy for parental math skills. Over and above differences in socio-economic status, parental arithmetic fluency, child's IQ, and time spent with the child, we found a positive relation between the frequency of formal numeracy practices that were at or above grade level and two separate measures of mental arithmetic. We further found that the frequency of these advanced formal numeracy practices was related to parents' academic expectations. Therefore, our study shows that home numeracy experiences predict arithmetic skills in elementary school children, but only when those activities are formal and sufficiently challenging for children.

Effects of Montessori Education on the Academic, Cognitive, and Social Development of Disadvantaged Preschoolers: A Randomized Controlled Study in the French Public-School System.

Previous research on Montessori preschool education is inconsistent and prone to analytic flexibility. In this preregistered study, disadvantaged preschoolers in a French public school were randomly assigned to either conventional or Montessori classrooms, with the latter being adapted to French public education. Adaptations included fewer materials, shorter work periods, and relatively limited Montessori teacher training. Cross-sectional analyses in kindergarten (N = 176; Mage  = 5-6) and longitudinal analyses over the 3 years of preschool (N = 70; Mage  = 3-6) showed that the adapted Montessori curriculum was associated with outcomes comparable to the conventional curriculum on math, executive functions, and social skills. However, disadvantaged kindergarteners from Montessori classrooms outperformed their peers on reading (d = 0.68). This performance was comparable to that of advantaged children from an accredited Montessori preschool.

The ratio processing system and its role in fraction understanding: Evidence from a match-to-sample task in children and adults with and without dyscalculia.

It has been hypothesised that the human neurocognitive architecture may include a perceptual ratio processing system (RPS) that supports symbolic fraction understanding. In the present study, we aimed to provide further evidence for the existence of the RPS by exploring whether individuals with a range of math skills are indeed perceptually sensitive to non-symbolic ratio magnitudes. We also aimed to test to what extent the RPS may underlie symbolic fraction processing in those individuals. In a match-to-sample task, typical adults, elementary school children, and adults with dyscalculia were asked to match a non-symbolic ratio (i.e., target) to one of two non-symbolic ratios (i.e., the match and distractor). We found that all groups of participants were sensitive to the ratio between the match and the distractor, suggesting a common reliance on the RPS. This ratio sensitivity was also observed in another group of typical adults who had to choose which of two symbolic fractions match a non-symbolic ratio, indicating that the RPS may also contribute to symbolic fraction understanding. However, no ratio dependence was observed when participants had to choose which of two symbolic fractions match another symbolic fraction, suggesting that reliance on the RPS in symbolic fraction processing is limited and may not support exact fraction processing.

The neural bases of argumentative reasoning.

Most reasoning tasks used in behavioral and neuroimaging studies are abstract, triggering slow, effortful processes. By contrast, most of everyday life reasoning is fast and effortless, as when we exchange arguments in conversation. Recent behavioral studies have shown that reasoning tasks with the same underlying logic can be solved much more easily if they are embedded in an argumentative context. In the present article, we study the neural bases of this type of everyday, argumentative reasoning. Such reasoning is both a social and a metarepresentational process, suggesting it should share some mechanisms, and thus some neural bases, with other social, metarepresentational process such as pragmatics, metacognition, or theory of mind. To isolate the neural bases of argumentative reasoning, we measured fMRI activity of participants who read the same statement presented either as the conclusion of an argument, or as an assertion. We found that conclusions of arguments, compared to assertions, were associated with greater activity in a region of the medial prefrontal cortex that was identified in quantitative meta-analyses of studies on theory of mind. This study shows that it is possible to use more ecologically valid tasks to study the neural bases of reasoning, and that using such tasks might point to different neural bases than those observed with the more abstract and artificial tasks typically used in the neuroscience of reasoning. Specifically, we speculate that reasoning in an argumentative context might rely on mechanisms supporting metarepresentational processes in the medial prefrontal cortex.

Neural representations of transitive relations predict current and future math calculation skills in children.

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T1), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T1 and again 1.5 years later (T2). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T1 and T2. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

Obstacles to the spread of unintuitive beliefs.

Many socially significant beliefs are unintuitive, from the harmlessness of GMOs to the efficacy of vaccination, and they are acquired via deference toward individuals who are more confident, more competent or a majority. In the two-step flow model of communication, a first group of individuals acquires some beliefs through deference and then spreads these beliefs more broadly. Ideally, these individuals should be able to explain why they deferred to a given source - to provide arguments from expertise - and others should find these arguments convincing. We test these requirements using a perceptual task with participants from the US and Japan. In Experiment 1, participants were provided with first-hand evidence that they should defer to an expert, leading a majority of participants to adopt the expert's answer. However, when attempting to pass on this answer, only a minority of those participants used arguments from expertise. In Experiment 2, participants receive an argument from expertise describing the expert's competence, instead of witnessing it first-hand. This leads to a significant drop in deference compared with Experiment 1. These experiments highlight significant obstacles to the transmission of unintuitive beliefs.

Impaired neural processing of transitive relations in children with math learning difficulty.

Math learning difficulty (i.e., MLD) is common in children and can have far-reaching consequences in personal and professional life. Converging evidence suggests that MLD is associated with impairments in the intraparietal sulcus (IPS). However, the role that these impairments play in MLD remains unclear. Although it is often assumed that IPS deficits affect core numerical abilities, the IPS is also involved in several non-numerical processes that may contribute to math skills. For instance, the IPS supports transitive reasoning (i.e., the ability to integrate relations such as A > B and B > C to infer that A > C), a skill that is central to many aspects of math learning in children. Here we measured fMRI activity of 8- to 12-year-olds with MLD and typically developing (TD) peers while they listened to stories that included transitive relations. Children also answered questions evaluating whether transitive inferences were made during story comprehension. Compared to non-transitive relations (e.g., A > B and C > D), listening to transitive relations (e.g., A > B and B > C) was associated with enhanced activity in the IPS in TD children. In children with MLD, the difference in activity between transitive and non-transitive relations in the IPS was (i) non-reliable and (ii) smaller than in TD children. Finally, children with MLD were less accurate than TD peers when making transitive inferences based on transitive relations. Thus, a deficit in the online processing of transitive relations in the IPS might contribute to math difficulties in children with MLD.

Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children.

Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3rd to 10th grade. We found that the mere perception of a '+' sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving '+' signs - without any operands - elicited enhanced hippocampal activity after around 7th grade (12-13 years old). In these children, hippocampal activity in response to a '+' sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with '×' signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education.

The neural development of conditional reasoning in children: Different mechanisms for assessing the logical validity and likelihood of conclusions.

Scientific and mathematical thinking relies on the ability to evaluate whether conclusions drawn from conditional (if-then) arguments are logically valid. Yet, the neural development of this ability -- termed deductive reasoning -- is largely unknown. Here we aimed to identify the neural mechanisms that underlie the emergence of deductive reasoning with conditional rules in children. We further tested whether these mechanisms have their roots in the neural mechanisms involved in judging the likelihood of conclusions. In a functional Magnetic Resonance Imaging (fMRI) scanner, 8- to 13-year-olds were presented with causal conditional problems such as "If a baby is hungry then he will start crying; The baby is crying; Is the baby hungry?". In Validity trials, children were asked to indicate whether the conclusion followed out of necessity from the premises. In Likelihood trials, they indicated the degree of likelihood of the conclusion. We found that children who made accurate judgments of logical validity (as compared to those who did not) exhibited enhanced activity in left and medial frontal regions. In contrast, differences in likelihood ratings between children were related to differences of activity in right frontal and bilateral parietal regions. There was no overlap between the brain regions underlying validity and likelihood judgments. Therefore, our results suggest that the ability to evaluate the logical validity of conditional arguments emerges from brain mechanisms that qualitatively differ from those involved in evaluating the likelihood of these arguments in children.

Dose mapping using MCNP5 mesh tallies.

Rensselaer Polytechnic Institute has a 69.6 GBq (1.88 Ci) (137)Cs source that is used for research, calibration of various instruments, and teaching. Recently it was calibrated using ion chambers. The source and room were also modeled in Monte Carlo N-Particle transport code (MCNP5) to determine if the use of a new feature called mesh tallies produces a dose map in the entire room that agrees with the measured results. The dose rate in the hallway, while the source is exposed, was also calculated. It was found that the dose rates calculated from the MCNP5 are in reasonable agreement with the measured results and theoretical predictions. It was also confirmed that the dose rates where the user often stays during the measurement are well below the annual limits. This project shows that the MCNP5 mesh tallies are useful tool for dose mapping in many operational radiation protection situations.