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Dementia is commonly associated with various cognitive deficits and the pattern of affected domains differs depending on the etiology: In Alzheimer’ dementia (AD), memory is dominant, while executive, visuo-spatial and attentional dysfunction are likely in Parkinson’s dementia (PDD). While AD diagnosis includes acalculia as a possible symptom, PDD diagnosis does not, despite evidence of numerical impairment in PD (Kalbe, 1999; Loenneker, Becker, et al., 2021; Saban et al., 2021; Zamarian et al., 2006). To be able to intervene at a pre-dementia stage, one of the crucial challenges in Parkinson’s disease (PD) research is the development of sensitive and specific diagnostic tools of cognitive impairments in the early phase of the disease. The spectrum of cognitive impairment in PD neurodegeneration includes mild cognitive impairments (PD-MCI, equivalent to mild neurocognitive disorder, DSM-5) up to dementia (equivalent to severe neurocognitive disorder, DSM-5). Presence of PD-MCI is one of the most important risk factors for PDD (Emre et al., 2007), however, so far no specific cognitive profile allows to predict dementia conversion with high accuracy. The main difference between PD-MCI and PDD is the severity of impairment in the activities of daily living (ADL). Recently it could be shown that first signs of more complex instrumental cognitive ADL (IADL) impairment dramatically increase the risk for the development of PDD (Becker et al., 2022). Many activities of daily living require numerical cognition, for example: medication management, orientation to time and space, use of public transport, cooking, shopping, communication, bank affairs, and health numeracy (Delazer et al., 2013; Semenza et al., 2014). Different dementia tests use tasks requiring numerical cognition, some explicitly (e.g., DemTect: transcoding), others use numerical material to assess attention/ executive function/ working memory (e.g., MMSE). To date, knowledge about the association between different domains of numerical cognition and iADL impairment is sparse and will be investigated in this study. Our data have the potential to provide a basis for suggesting numerical tests in PDD diagnosis and to further characterize a potential risk group for PDD.

Texts presenting novel statistics can shift learners attitudes and conceptions about controversial science topics. However, not a lot is known about the mechanisms underlying this conceptual change. The purpose of this study was to investigate two potential mechanisms that underlie learning from novel statistics: numerical estimation skills and epistemic cognition. This research investigated two treatments--a numerical estimation and epistemic cognition intervention--that were expected to enhance people's ability to make sense of key numbers about climate change. Results indicated that undergraduate students (N = 516) who were given instruction on numerical estimation strategies before shown novel climate change statistics had fewer misconceptions when compared with people who did not. Findings provide emerging evidence that supporting mathematical reasoning skills can enhance conceptual change in science. [For the complete proceedings, see ED629884.]

This article is from PLoS ONE , volume 9 . Abstract In this paper we review, and elaborate on, the literature on a regression artifact related to Lord’s paradox in a continuous setting. Specifically, the question is whether a continuous property of individuals predicts improvement from training between a pretest and a posttest. If the pretest score is included as a covariate, regression to the mean will lead to biased results if two critical conditions are satisfied: (1) the property is correlated with pretest scores and (2) pretest scores include random errors. We discuss how these conditions apply to the analysis in a published experimental study, the authors of which concluded that linearity of children’s estimations of numerical magnitudes predicts arithmetic learning from a training program. However, the two critical conditions were clearly met in that study. In a reanalysis we find that the bias in the method can fully account for the effect found in the original study. In other words, data are consistent with the null hypothesis that numerical magnitude estimations are unrelated to arithmetic learning.

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be conceptualized discretely or continuously (i.e., natural versus real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension, because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions. [This paper was published in "Wiley Interdisciplinary Reviews: Cognitive Science" v6 n6 p491-505 2015.]

A prominent theory assumes that the approximate number system (ANS), which is thought to be measured by non-symbolic magnitude comparison tasks, constitutes the basis for development of numerical skills. Recent studies showing influences of inhibition and visual strategies raise the question of what is measured with this task. Elderly people show age-related inhibitory decline, which can be intensified in Parkinson’s disease (PD) where inhibitory and visuo-spatial deficits occur. Therefore, PD-immanent inhibitory and visuo-spatial deficits in some patients allow for a quasi-experiment studying the influence of these cognitive domains on the performance in a typical ANS task. This enables inferring conclusions for the theory of number processing from this clinical population.

This article is from Frontiers in Psychology , volume 5 . Abstract None

Background: Numerical cognition subsumes a wide range of tasks and underlying cognitive representations. The developmental approach on this domain mostly focuses on educational questions and changes up to young adulthood. However, lifespan research on cognition describes distinct patterns of decline, stability or improvement in at least some numerical domains. Therefore, the aim of the planned systematic review and meta-analysis is (1) to identify tasks and areas of numerical cognition showing improved, preserved, or impaired performance when comparing elderly and younger samples. (2) We aim at identifying moderators of development in numerical cognition such as inter-individual differences like global cognition, effects of cohort, gender, or education. (3) We want to find out when deficits occur in aging and whether the extent of impairment increases with age. Methods: A systematic review and meta-analysis will be conducted following PRISMA criteria. Electronic databases of published and unpublished studies will be searched for relevant articles with predefined search terms. Studies are eligible if they report comparisons of an elderly sample with a younger control group regarding an empirical measure of numerical and/ or arithmetic function. Furthermore, studies reporting performance in a standardized test of numerical cognition with available age-specific reference norms will be included. Experimental case-control designs and group studies will be included. Studies not allowing to assess an age effect, only reporting neuro-imaging data and reviews will be excluded. Original study quality will be assessed with the ROBINS-I tool. Depending on the resulting data structure, meta-analyses will be conducted with random effects models or two-level models with nested effect sizes. Subgroups analyses regarding age groups will be conducted using meta-regression. Discussion: Results of the current review cannot only be used to update existing reviews, but also to systematize numerical and arithmetic performance associated to effects of aging in the light of both neurocognitive theories of numerical cognition and lifespan development. It has the potential to estimate changes in numerical cognition across aging up to old age. However, our systematic review and meta-analysis relies on the quality of the original studies and the quality of available risk of bias assessments.

Background: Numerical cognition subsumes a wide range of tasks and underlying cognitive representations. The developmental approach on this domain mostly focuses on educational questions and changes up to young adulthood. However, lifespan research on cognition describes distinct patterns of decline, stability or improvement in at least some numerical domains. Therefore, the aim of the planned systematic review and meta-analysis is (1) to identify tasks and areas of numerical cognition showing improved, preserved, or impaired performance when comparing elderly and younger samples. (2) We aim at identifying moderators of development in numerical cognition such as inter-individual differences like global cognition, effects of cohort, gender, or education. (3) We want to find out when deficits occur in aging and whether the extent of impairment increases with age. Methods: A systematic review and meta-analysis will be conducted following PRISMA criteria. Electronic databases of published and unpublished studies will be searched for relevant articles with predefined search terms. Studies are eligible if they report comparisons of an elderly sample with a younger control group regarding an empirical measure of numerical and/ or arithmetic function. Furthermore, studies reporting performance in a standardized test of numerical cognition with available age-specific reference norms will be included. Experimental case-control designs and group studies will be included. Studies not allowing to assess an age effect, only reporting neuro-imaging data and reviews will be excluded. Original study quality will be assessed with the ROBINS-I tool. Depending on the resulting data structure, meta-analyses will be conducted with random effects models or two-level models with nested effect sizes. Subgroups analyses regarding age groups will be conducted using meta-regression. Discussion: Results of the current review cannot only be used to update existing reviews, but also to systematize numerical and arithmetic performance associated to effects of aging in the light of both neurocognitive theories of numerical cognition and lifespan development. It has the potential to estimate changes in numerical cognition across aging up to old age. However, our systematic review and meta-analysis relies on the quality of the original studies and the quality of available risk of bias assessments.

This article is from Frontiers in Psychology , volume 4 . Abstract Catechol-O-methyltransferase (COMT) is an enzyme that is particularly important for the metabolism of dopamine. Functional polymorphisms of COMT have been implicated in working memory and numerical cognition. This is an exploratory study that aims at investigating associations between COMT polymorphisms, working memory, and numerical cognition. Elementary school children from 2th to 6th grades were divided into two groups according to their COMT val158met polymorphism [homozygous for valine allele (n = 61) vs. heterozygous plus methionine homozygous children or met+ group (n = 94)]. Both groups were matched for age and intelligence. Working memory was assessed through digit span and Corsi blocks. Symbolic numerical processing was assessed through transcoding and single-digit word problem tasks. Non-symbolic magnitude comparison and estimation tasks were used to assess number sense. Between-group differences were found in symbolic and non-symbolic numerical tasks, but not in working memory tasks. Children in the met+ group showed better performance in all numerical tasks while val homozygous children presented slower development of non-symbolic magnitude representations. These results suggest COMT-related dopaminergic modulation may be related not only to working memory, as found in previous studies, but also to the development of magnitude processing and magnitude representations.

The ability to understand and manipulate numerical concepts is fundamental to success in many areas of life, including education, work and everyday activities. However, many people experience difficulties in developing mathematical skills, which can limit their opportunities for personal and professional growth. Studies of numerical cognition show that the development of mathematical skills is grounded in the basic processing of magnitudes. On the other hand, non-invasive brain stimulation has emerged as a promising technique to improve cognitive skills including numerical cognition. This research project aims to analyse the neural basis of magnitude processing and to evaluate the efficacy of non-invasive brain stimulation as an intervention to improve numerical cognition. To achieve this, a randomised double-blind sham-controlled trial will be conducted in which transcranial direct current electrical stimulation will be applied to two brain areas: the dorsolateral prefrontal cortex and the intraparietal sulcus; and the enhancing effect of each of the protocols on three aspects of numerical cognition will be assessed: magnitude processing and integration, and arithmetic. The results of this study will be important both for basic research in the field of numerical cognition and for clinical application. On the one hand, they will help to improve our understanding of the neural basis of numerical processing. On the other hand, they may contribute to the development of new non-invasive interventions to improve numerical ability in people with difficulties in this area.

This article is from PLoS ONE , volume 9 . Abstract The representation and maintenance of serial order information is one of the main functions of verbal short-term memory (STM) but its neural correlates remain poorly understood. We show here that the neural substrates allowing for coding of order information in STM are shared with those supporting ordinal processing in the numerical and alphabetical domains. We designed an fMRI experiment determining the neural substrates sensitive to ordinal distance effects in numerical judgment, alphabetical judgment and serial order STM tasks. Null conjunction analyses for parametric ordinal distance effects showed a common involvement of the horizontal segment of the left intraparietal sulcus over the three tasks; in addition, right intraparietal sulcus involvement was also observed for ordinal distance effects in the STM and numerical judgment tasks. These findings demonstrate that shared neural correlates in the intraparietal cortex support processing of order information in verbal STM, number and alphabetical domains, and suggest the existence of domain general, potentially ordinal, comparison processes supported by the left intraparietal sulcus.