scholarly journals Probing the neural basis rational numbers: the role of inhibitory control and magnitude representations

2021 ◽  
Author(s):  
Miriam Rosenberg-Lee

Rational numbers, such as fractions, decimals and percentages, are a persistent challenge in the mathematics curriculum. An underappreciated source of rational number difficulties are whole number properties that apply to some, but not all, rational numbers. I contend that mastery of rational numbers involves refining and expanding whole number representations. Behavioral evidence for the role inhibitory control and magnitude-based processing of rational numbers support this hypothesis, although more attention is needed to task and stimuli selection, especially among fractions. In the brain, there is scant evidence on the role of inhibitory control in rational number processing, but surprisingly good correspondence, in the parietal lobe, between the handful of neuroimaging studies of rational numbers and the accumulated whole number literature. Decimals and discrete nonsymbolic representations are fruitful domains for probing the neural basis role of whole number interference in rational number processing.

2018 ◽  
Author(s):  
Qun Ye ◽  
Futing Zou ◽  
Hakwan Lau ◽  
Yi Hu ◽  
Sze Chai Kwok

AbstractMetacognition is the capacity to introspectively monitor and control one’s own cognitive processes. Previous anatomical and functional neuroimaging findings implicated the important role of precuneus in metacognition processing, especially during mnemonic tasks. However, the issue of whether this medial parietal cortex is a domain-specific region that supports mnemonic metacognition remains controversial. Here, we focally disrupted this parietal area with repetitive transcranial magnetic stimulation in healthy participants of both sexes, seeking to ascertain its functional necessity for metacognition for memory versus perceptual decisions. Perturbing the precuneal activity impaired the metacognitive efficiency selectively in the memory judgment of temporal-order, but not in perceptual discrimination. Moreover, the correlation in individuals’ metacognitive efficiency between the domains disappeared when the precuneus was perturbed. Together with the previous finding that lesion to the anterior prefrontal cortex impairs perceptual but not mnemonic metacognition, we double dissociated the macro-anatomical underpinnings for the two kinds of metacognitive capacity in an interconnected network of brain regions.SIGNIFICANCE STATEMENTTheories on the neural basis of metacognition have thus far largely centered on the role of prefrontal cortex. Here we refined the theoretical framework through characterizing a unique precuneal involvement in mnemonic metacognition with a noninvasive but inferentially powerful method: transcranial magnetic stimulation. By quantifying meta-cognitive efficiency across two distinct domains (memory vs. perception) that are matched for stimulus characteristics, we reveal an instrumental – and highly selective – role of the precuneus in mnemonic metacognition. These causal evidence corroborate ample clinical reports that parietal lobe lesions often produce inaccurate self-reports of confidence in memory recollection and establish that the precuneus as a nexus for the introspective ability to evaluate the success of memory judgment in humans.


1984 ◽  
Vol 31 (6) ◽  
pp. 10-12
Author(s):  
Dora Helen B. Skypek

The characteristics of rational numbers must be considered in a variety of interpretations and coding schemes. It is this variety that, if not sorted and carefully developed in appropriate contexts, results in confusion in teaching and learning about rational numbers. Although a discussion of interpretations necessarily involves the use of coding conventions, the two will be treated separately as special characteristics of the rational numbers. Another important charac-teristic. which is difficult to separate from interpretations and coding conventions. is this: unlike a whole number (or an integer), a rational number has an unlimited number of “behavioral clones.” These clones have different names, but they behave in exactly the same way. Still other Still other characteristics to be considered are the density and order of the rational number.


1967 ◽  
Vol 14 (5) ◽  
pp. 373-376
Author(s):  
Robert D. Bechtel ◽  
Lyle J. Dixon

The elementary school teacher of today needs to have a comprehensive view of eleme ntary mathematics. The present emphasis on the “new” mathematics requires an understanding of number systems such as the natural number system, the whole number system, the rational number system, and the real number system, together with an understanding of some elementary concepts from geometry. This understanding of mathematics can no longer be limited to specific areas covered at one level in graded material, but should encompass the structures of different number systems. One must recognize the role of a specific topic in mathematics in relation to the overall structure of the systems under consideration. Failure to do this often leads to confusion for a student who must relearn or radically alter a previously learned mathematical principle. Such a situation should be avoided.


2003 ◽  
Vol 10 (1) ◽  
pp. 6-7
Author(s):  
Carol A. Powell ◽  
Robert P. Hunting

Watanabe (2001) has argued that the teaching of fractions should be eliminated from the primary mathematics curriculum, based on issues related to curriculum, development, and instructional materials. We disagree, for the following main reasons: First, this approach overlooks young children's developing multiplicative structures, which have their roots in part-whole relationships. Second, although we agree that the teaching of formal symbolism and notation for fractions can be delayed, conversations between teachers and children can establish important ideas from which formal symbols later will flow naturally. Third, sharing situations can help young children develop whole-number knowledge and can lay foundations for the rational-number system.


2020 ◽  
Vol 27 (31) ◽  
pp. 5119-5136 ◽  
Author(s):  
Barbara Carpita ◽  
Donatella Marazziti ◽  
Lionella Palego ◽  
Gino Giannaccini ◽  
Laura Betti ◽  
...  

Background: Autism Spectrum Disorder (ASD) is a condition strongly associated with genetic predisposition and familial aggregation. Among ASD patients, different levels of symptoms severity are detectable, while the presence of intermediate autism phenotypes in close relatives of ASD probands is also known in literature. Recently, increasing attention has been paid to environmental factors that might play a role in modulating the relationship between genomic risk and development and severity of ASD. Within this framework, an increasing body of evidence has stressed a possible role of both gut microbiota and inflammation in the pathophysiology of neurodevelopment. The aim of this paper is to review findings about the link between microbiota dysbiosis, inflammation and ASD. Methods: Articles ranging from 1990 to 2018 were identified on PUBMED and Google Scholar databases, with keyword combinations as: microbiota, immune system, inflammation, ASD, autism, broad autism phenotype, adult. Results: Recent evidence suggests that microbiota alterations, immune system and neurodevelopment may be deeply intertwined, shaping each other during early life. However, results from both animal models and human samples are still heterogeneous, while few studies focused on adult patients and ASD intermediate phenotypes. Conclusion: A better understanding of these pathways, within an integrative framework between central and peripheral systems, might not only shed more light on neural basis of ASD symptoms, clarifying brain pathophysiology, but it may also allow to develop new therapeutic strategies for these disorders, still poorly responsive to available treatments.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiaonan Lin ◽  
Yanmiao Cao ◽  
Linqin Ji ◽  
Wenxin Zhang

AbstractMany efforts have been devoted to investigating the effect of the interaction between the serotonin transporter gene (5-HTTLPR) and environment (G × E) on depression, but they yield mixed results. The inconsistency has suggested that G × E effects may be more complex than originally conceptualized, and further study is warranted. This study explored the association among 5-HTTLPR, peer victimization and depressive symptoms and the underlying mediating role of inhibitory control in this association. A total of 871 Chinese Han adolescents (Mage = 15.32 years, 50.3% girls) participated and provided saliva samples from which the 5-HTTLPR was genotyped. This study found that 5-HTTLPR interacted with peer victimization in predicting depressive symptoms. Adolescents carrying L allele reported more depressive symptoms than SS carriers when exposed to higher level of peer victimization. Furthermore, adolescents’ inhibitory control deficits mediated the association between 5-HTTLPR × peer victimization and depressive symptoms. These findings suggested that one pathway in which G × E may confer vulnerability to depressive symptoms is through disruptions to adolescents’ inhibitory control system.


2017 ◽  
Vol 13 (7) ◽  
pp. P1197
Author(s):  
Suvarna Alladi ◽  
Shailaja Mekala ◽  
Vani K. Kasyap ◽  
Suneel Kumar Bagadi ◽  
Sireesha Jala ◽  
...  

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