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A comparative interpretation of mammograms has become increasingly important, and it is crucial to develop subtraction processing and registration methods for mammograms. However, nonrigid image registration has seldom been applied to subjects constructed with soft tissue only, such as mammograms. We examined whether subtraction processing for the comparative interpretation of mammograms can be performed using nonrigid image registration. As a preliminary study, we evaluated the results of subtraction processing by applying nonrigid image registration to normal mammograms, assuming a comparative interpretation between the left and right breasts. Mediolateral-oblique-view mammograms were taken from noncancer patients and divided into 1000 cases for training, 100 cases for validation, and 500 cases for testing. Nonrigid image registration was applied to align the horizontally flipped left-breast mammogram with the right one. We compared the sum of absolute differences (SAD) of the difference of bilateral images (Difference Image) with and without the application of nonrigid image registration. Statistically, the average SAD was significantly lower with the application of nonrigid image registration than without it (without: 0.0692; with: 0.0549 (p < 0.001)). In four subgroups using the breast area, breast density, compressed breast thickness, and Difference Image without nonrigid image registration, the average SAD of the Difference Image was also significantly lower with nonrigid image registration than without it (p < 0.001). Nonrigid image registration was found to be sufficiently useful in aligning bilateral mammograms, and it is expected to be an important tool in the development of a support system for the comparative interpretation of mammograms. [ABSTRACT FROM AUTHOR]

Dual tasks (DTs) combining walking with a cognitive task can cause various levels of cognitive–motor interference, depending on which brain resources are recruited in each case. However, the brain activation and functional connectivity underlying cognitive–motor interferences remain to be elucidated. Therefore, this study investigated the neural correlation during different DT conditions in 40 healthy young adults (mean age: 27.53 years, 28 women). The DTs included walking during subtraction or N‐Back tasks. Cognitive–motor interference was calculated, and brain activation and functional connectivity were analysed. Portable functional near‐infrared spectroscopy was utilized to monitor haemodynamics in the prefrontal cortex (PFC), motor cortex and parietal cortex during each task. Walking interference (decrease in walking speed during DT) was greater than cognitive interference (decrease in cognitive performance during DT), regardless of the type of task. Brain activation in the bilateral PFC and parietal cortex was greater for walking during subtraction than for standing subtraction. Furthermore, brain activation was higher in the bilateral motor and parietal and PFCs for walking during subtraction than for walking alone, but only increased in the PFC for walking during N‐Back. Coherence between the bilateral lateral PFC and between the left lateral PFC and left motor cortex was significantly greater for walking during 2‐Back than for walking. The PFC, a critical brain region for organizing cognitive and motor functions, played a crucial role in integrating information coming from multiple brain networks required for completing DTs. Therefore, the PFC could be a potential target for the modulation and improvement of cognitive–motor functions during neurorehabilitation. [ABSTRACT FROM AUTHOR]

The mechanisms regulating the content ratio of unsaturated fatty acid in sesame oil need to be clarified in order to breed novel varieties with high contents of unsaturated fatty acids. Full‐length cDNA libraries prepared from sesame seeds 1 to 3 weeks after flowering were subtracted with cDNAs from plantlets of 4 weeks after germination. A total of 1545 cDNA clones was sequenced. The functions of novel genes expressed specifically during the early maturation of sesame seeds were investigated by the transformation of Arabidopsis thaliana. Thirteen genes for a transcription factor were identified, four of which were involved in ethylene signaling. Fifty‐nine genes, including those for the aquaporin‐like protein and ethylene response factor, were analyzed by overexpression in A. thaliana. The overexpression of novel genes and the aquaporin‐like protein gene in A. thaliana increased the content of unsaturated fatty acids. The localization of these products was investigated by the induction of the expression vectors for the GFP fusion protein into onion epidermal cells and sesame root cells with a particle gun. As a result, two cDNA clones were identified as good candidate genes to clarify the regulation in the yield and the ratio of unsaturated fatty acids in sesame seeds. Sein60414 (Accession No. LC603128), an intrinsic membrane protein, may be involved in the increase of unsaturated fatty acids, and Sein61074 (Accession No. LC709278) MAP3K δ‐1 protein kinase in the regulation of the total ratio of unsaturated fatty acids in sesame seeds. [ABSTRACT FROM AUTHOR]

The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical aspects and their relations of the object of learning. In this paper, we focus on what number relations students see in a three-digit subtraction task, and how they see them. We analyzed interview data from 55 second-grade students who used decomposition strategies to solve 204 − 193 =. The variation theory of learning was used to analyze what number relations the students experienced and how they experienced them, aiming to explain why they made errors even though they used presumably powerful strategies in their problem-solving. The findings show that students who simultaneously experienced within-number relations and between-number relations when solving the task succeeded in solving it, whereas those who did not do this failed. These findings have importance for understanding what students need to discern in order to be able to solve subtraction tasks in a proficient way. [ABSTRACT FROM AUTHOR]

This replication study aims to investigate a potential bias toward addition in the German language, building upon previous findings of Winter and colleagues who identified a similar bias in English. Our results confirm a bias in word frequencies and binomial expressions, aligning with these previous findings. However, the analysis of distributional semantics based on word vectors did not yield consistent results for German. Furthermore, our study emphasizes the crucial role of selecting appropriate translational equivalents, highlighting the significance of considering language‐specific factors when testing for such biases for languages other than English. [ABSTRACT FROM AUTHOR]

We have evolved to become who we are, at least in part, due to our general drive to create new things and ideas. When seeking to improve our creations, ideas, or situations, we systematically overlook opportunities to perform subtractive changes. For example, when tasked with giving feedback on an academic paper, reviewers will tend to suggest additional explanations and analyses rather than delete existing ones. Here, we show that this addition bias is systematically reflected in English language statistics along several distinct dimensions. First, we show that words associated with an increase in quantity or number (e.g., add, addition, more, most) are more frequent than words associated with a decrease in quantity or number (e.g., subtract, subtraction, less, least). Second, we show that in binomial expressions, addition‐related words are mentioned first, that is, add and subtract rather than subtract and add. Third, we show that the distributional semantics of verbs of change, such as to improve and to transform, overlap more with the distributional semantics of add/increase than subtract/decrease, which suggests that change verbs are implicitly biased toward addition. Fourth, addition‐related words have more positive connotations than subtraction‐related words. Fifth, we demonstrate that state‐of‐the‐art large language models, such as the Generative Pre‐trained Transformer (GPT‐3), are also biased toward addition. We discuss the implications of our results for research on cognitive biases and decision‐making. [ABSTRACT FROM AUTHOR]

Children with intellectual disabilities experience well-documented challenges in the development of problem-solving, particularly related to mathematical word-problem solving. Such challenges are related to both linguistic and conceptual skills. While interventions to assist children in developing conceptual skills are well reported, linguistic interventions within the mathematical field are limited. This study aimed to determine the effect of an augmented-input intervention, on subtraction word-problem solving for children with intellectual disabilities. A multiple baseline across behaviours design was used and replicated across the seven participants. Intervention was provided in three tiers (one week each) for change, combine, and compare subtraction word-problems. Intervention was withdrawn for a four week period and followed by a maintenance phase. Results suggested that for older participants with higher receptive language and numerical operation scores, the augmented-input intervention provided significant gains across all three types of word-problems. Overall, four of the seven participants showed improvement in subtraction word-problem solving. Augmented input may provide language supports for subtraction word-problem solving for some children with mild intellectual disability. [ABSTRACT FROM AUTHOR]

This study investigates three facets of teacher mediation: a) The sensitivity to the needs of the student with difficulty (perceived difficulty), b) The way to organize activities and experiences that encourage learning and c) The ability to institute tasks with diverse levels of complexity (instituted difficulty). The Test for Assessment of Instituted Difficulty in Situations of Addition and Subtraction (DISAS) (Santana & Herrera, 2017) was applied to 20 Peruvian and 20 Colombian teachers from 1st to 5th grade of elementary school, who described their way of orienting students with difficulty to add and subtract. The results obtained suggest that the cultural environment is important in the organization of the teacher's activity when teaching these operations. [ABSTRACT FROM AUTHOR]

Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade classes. One goal was that by the end of first grade, students would be able to solve tasks such as subtracting 8 from 15 by using part-whole number relations. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after, and one year after the intervention, in order to investigate long-term effects and whether students used a structural approach when solving tasks in a higher number range in the second grade. In comparison to controls, students in the intervention group showed higher increases in their learning outcomes. Moreover, the intervention group used a structural approach to a larger extent when solving tasks in higher number ranges, whereas students in the control group more commonly used single-unit counting to solve such tasks. These findings have implications both for teaching and for research on students’ development of arithmetic skills. [ABSTRACT FROM AUTHOR]

Study Design: Fourteen cadaveric specimens were separated into two groups: (1) L3 pedicle subtraction osteotomy (PSO) with transforaminal lumbar interbody fusion (TLIF) or (2) lateral lumbar interbody fusion (LLIF). A 2-rod configuration (2R) was compared with two supplemental rod configurations: 4-rod (4R) with accessory rods (ARs) using connectors or 4R with satellite rods (SRs) without connectors.Objective: Compare PSO constructs with different rod configurations and adjacent-level interbody support.Summary Of Background Data: Supplemental rods and anterior column support enhance biomechanical performance.Methods: Pure moments were applied in (1) intact, (2) pedicle screws and rods, (3) PSO + 2R, (4) 4R AR, and (5) 4R SR conditions. Primary and supplemental rods had strain gauges across the index level. Sacral screw bending moments and range of motion (ROM) were recorded.Results: For TLIF, AR decreased ROM during flexion (P = 0.02) and extension (P < 0.001) versus 2R. For LLIF, AR and SR decreased motion versus 2R during left (AR: P  = 0.03; SR: P  = 0.04) and right (AR: P  = 0.002; SR: P  = 0.01) axial rotation. For LLIF, sacral screw strain increased with SR compared with AR in compression and right lateral bending (P ≤ 0.03). During lateral bending, rod strain increased with PSO+TLIF+SR versus PSO+LLIF+2R and PSO+LLIF+AR (P ≤ 0.02). For LLIF, SR configuration increased rod strain versus AR during flexion, extension, and lateral bending (P≤ 0.01); for TLIF, rod strain increased with SR versus AR during extension (P = 0.03). For LLIF, AR configuration increased posterior supplemental rod strain versus SR during flexion (P = 0.02) and lateral bending (P < 0.001).Conclusion: Both supplemental rod configurations reduced motion in both groups. Constructs with the SR configuration increased the primary rod strain and the sacral screw bending moment compared with AR constructs, which can share strain. Deep-seated SRs, which have become increasingly popular, may be more vulnerable to failure than ARs. LLIF provided more stability in sagittal plane. Protective effect of supplemental rods on rod strain was more effective with TLIF.Level of Evidence: NA. [ABSTRACT FROM AUTHOR]

In planning randomized clinical trials (RCTs) for diseases such as Alzheimer's disease (AD), researchers frequently rely on the use of existing data obtained from only two time points to estimate sample size via the subtraction of baseline from follow‐up measurements in each subject. However, the inadequacy of this method has not been reported. The aim of this study is to discuss the limitation of sample size estimation based on the subtraction of available data from only two time points for RCTs. Mathematical equations are derived to demonstrate the condition under which the obtained data pairs with variable time intervals could be used to adequately estimate sample size. The MRI‐based hippocampal volume measurements from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Monte Carlo simulations (MCS) were used to illustrate the existing bias and variability of estimates. MCS results support the theoretically derived condition under which the subtraction approach may work. MCS also show the systematically under‐ or over‐estimated sample sizes by up to 32.27% bias. Not used properly, such subtraction approach outputs the same sample size regardless of trial durations partly due to the way measurement errors are handled. Estimating sample size by subtracting two measurements should be treated with caution. Such estimates can be biased, the magnitude of which depends on the planned RCT duration. To estimate sample sizes, we recommend using more than two measurements and more comprehensive approaches such as linear mixed effect models. [ABSTRACT FROM AUTHOR]

In this study, to investigate the influence of numerical surface forms on strategy execution in subtraction and addition, 25 college students were required to perform a mental arithmetic task. Behavioral and electroencephalography responses were recorded to explore the stages of strategy execution. Arithmetic problems were presented within 11–20 by Arabic, Chinese and English numerals, respectively. The results showed that, compared with Arabic and Chinese numerals, participants had longer RTs under the condition of English numerals. English numerals induced stronger N100, P200 and P300 amplitudes, and longer latency in P200 and P300 amplitudes than in other conditions. These findings indicated that numerical surface forms affected the execution of mental arithmetic strategies, with Chinese and English numerals being processed deeper in the brain. Especially, the English digital word form occupied more psychological resources, and it was activated more in the frontal area and the parietal area, which would obviously hinder the processing of arithmetic information. [ABSTRACT FROM AUTHOR]

In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across the entirety of Latin America and South America. Whereas lack of financial resources often predicts low measures, the history of educational practice teaches us that students' poverty need not predict their educational outcomes – creative instructional approaches may turn the tables. Here we report on an innovative, body-based arithmetic technique, the Botetano Method, that has been enabling poverty rural children from remote mountainous regions of Peru to match and even greatly surpass their urban peers on comparable test items. The article explains the method's guiding humanistic and cognitive principles and then reports on findings from explorative action research that implemented and evaluated the method. Using observational methodologies, we argue that the students developed in their conceptual understanding of the content as well as in their attraction to the discipline, their professional identity, their personal pride in their achievement, and their general epistemic capacity for concentration and self-regulation. Throughout, we emphasize the methodological limitations of this grassroots proof-of-concept action research, which threaten the validity of the assertions. We speculate on early extensions of the method to literacy studies. [ABSTRACT FROM AUTHOR]

Children are highly inclined to attend to the properties of numbers, operations and equality when given helpful tools for doing so. Our aim was to investigate early algebraic thinking with the compensation property of equality for subtraction. We provided 22 (9–11-year-old) students with physical blocks for building vertical towers and conducted individual interviews with them as they completed a sequence of 15 tasks involving subtraction as difference using concrete, numeric, and symbolic representations. Relational thinking was evidenced across a range of subtraction calculation skill levels. Those students who could use both indirect addition and take-away strategies flexibly, depending on the size of the numbers involved, were more likely to evidence attention to generality with symbolic equations. The shift to symbolic equations elicited some students' productive attempts to connect subtraction as difference and subtraction as take way but seemed to hinder others by provoking a return to take away calculations rather than relational thinking strategies. • A core route for early algebra learning is generalized arithmetic. • The literature documents children's difficulties with the subtraction-compensation property. • Relational thinking was evidenced with vertical towers of blocks, even by those who only used direct counting strategies. • Children who used both indirect addition and take-away strategies flexibly evidenced relational thinking with symbolic equations. [ABSTRACT FROM AUTHOR]

This article examines analyses from a master's research project in the field of education, aiming to present psychological and didact assumptions regarding mathematical problem solving. The research project, which is theoretical-methodological, discusses the difficulties of students, in the early years of elementary school, in solving mathematical problems. To that end, the researches of Vigotski and Kalmykova have been used for psychological and Saviani didactic matters, respectively. The results appoint that problem solving requires students to transcend from descriptive to explanatory procedures and thus become aware of their actions. Moreover, to better value problem resolution, teachers must propose that students explicit their process besides just providing the correct answers, favoring the mobilization of his ideas and arriving at thinking through concepts. [ABSTRACT FROM AUTHOR]

This research aimed to examine whether the activities related to mental computation strategies had any effect on the development of the second-grade elementary school students' problem-solving (PS) skills. Participants of the study are comprised of 14 children aged 7-8 years and enrolled in the second grade of the elementary school of a village. For the collection of data, the Problem-Solving Task (PST) which is composed of 12 problems linked with addition and subtraction operations was utilized. The identification of problems to be included in PST was based on problem types suggested by Sarama and Clements (2009). In this action research which lasted five weeks and three hours per week, 13 mental addition-subtraction activities (MASAs) were applied to children. Responses given by children to PST were examined in the context of time, accuracy, and strategy variables. At the end of executed activities, it was discerned that mental computation strategies used by children in solving problems got diversified, children's response speed was accelerated and the number of correct answers given by children went up. Before MASAs, it was found that children had difficulty in solving problems through mental computation, gave random answers, or tried to count with their fingers for computation. After MASAs, it was deduced that strategies that were selected by children differed on the basis of problem types. [ABSTRACT FROM AUTHOR]

A purely phonological account of reduplication based on the affixation of empty prosodic nodes predicts the attested typology of multiple reduplication. Languages that can combine more than one reduplication-triggering morpheme in a word differ in (1) whether all reduplicants surface faithfully, (2) whether they systematically avoid adjacent multiple reduplicants, or (3) whether one of the reduplicants is smaller than expected if another reduplicant is adjacent in multiple reduplication contexts. Morphological accounts of reduplication not only violate the modularity between phonology and morphology, they also fail to predict this attested typology. [ABSTRACT FROM AUTHOR]

In the present research. we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3= 8), subtraction (e.g., 5 - 3 = 2). and multiplication (e.g.,5 x 3= 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. [ABSTRACT FROM AUTHOR]

One of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform‐based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized in the Essential Understanding Series (EU) presented by NCTM against the backdrop of mathematics education reform. In particular, we analyzed the features of the lessons for teaching addition and subtraction word problem solving. In some aspects, the results indicated that in terms of teaching problem comprehension and algebra readiness, the two textbook series showed improvement compared to formerly used textbooks. However, both textbook series may fall short of reflecting some important EU big ideas (e.g., teaching the underlying structure and part‐part‐whole relation of addition and subtraction word problems; providing students with chances to deal with exhaustive problem types and situations). In particular, our findings highlight the need for teaching word problem solving through building abstract level conceptual understanding. Implications for future textbook developing and limits are discussed. [ABSTRACT FROM AUTHOR]

In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: proportional equivalence and unit equivalence. These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a) the distinction of equivalence gives a unified framework of equal fractions that has not previously been described in the literature; (b) a conceptual understanding of both fraction equivalences is integral to understanding rational numbers; and (c) knowledge of both conceptions of equivalence is important for developing a conceptual understanding of fraction arithmetic. Past research has largely overlooked the distinction between the two types of equivalence. However, this may provide an important foundation for central topics that build on equivalence, and a better understanding of these two types of equivalence may support a more flexible understanding of fractions. Last, we propose future directions for teaching equivalence in mathematics. [ABSTRACT FROM AUTHOR]

Background and Purpose: To evaluate the performance of multiparametric MR images in differentiation of different regions of the gross tumor area and for assessment of glioma grade.Methods: Forty-six glioma subjects (18 grade II, 11 grade III, and 17 grade IV) underwent a comprehensive MR and spectroscopic imaging procedure. Maps were generated by subtraction of T1-weighted images from contrast-enhanced T1-weighted images (ΔT1 map) and T1-weighted images from T2-weighted images (ΔT2 map). Regions of interest (ROIs) were positioned in normal-appearing white matter (NAWM), enhancing tumor, hyperintense T2, necrotic region, and immediate and distal peritumoral regions (IPR and DPR). Relative signal contrast was estimated as difference between mean intensities in ROIs and NAWM. Classification using support vector machines was applied to all image series to determine the efficacy of regional contrast measures for differentiation of low- and high-grade lesions and grade III and IV lesions.Results: ΔT1 and ΔT2 maps offered higher contrast as compared to other parametric maps in differentiating enhancing tumor and edematous regions, respectively, and provided the highest classification accuracy for differentiating low- and high-grade tumors, of 91% and 90.4%. Choline/N-acetylaspartate maps provided significant contrast for delineating IPR and DPR. For differentiating high-grade gliomas, ΔT2 and ΔT1 maps provided a mean accuracy of 90.9% and 88.2%, which was lower than that obtained using cerebral blood volume (93.7%) and choline/creatine (93.3%) maps.Conclusion: This study showed that subtraction maps provided significant contrast in differentiating several regions of the gross tumor area and are of benefit for accurate tumor grading. [ABSTRACT FROM AUTHOR]

Learning to solve subtraction problems that require borrowing (e.g., 83–57=) is challenging, and these problems often cause 'bridging' errors, such as the smaller-from-larger error. This study explores how bridging errors in subtraction are related to students' mathematical ability. The study involved 694 third-grade students and 35 teachers from 25 Dutch schools. Multilevel regression analyses showed that the number of bridging errors was positively related to the students' mathematical ability, after controlling for the total number of errors in subtraction. Thus, the students who had a high proportion of bridging errors within the total number of errors had a relatively higher mathematical ability compared to the students who had a low proportion of bridging errors. This result implies that diagnosing bridging errors may help to identify where students' stand within their mathematical development. The practical implications of this result for the design of diagnostic instruments are addressed in the discussion section. [ABSTRACT FROM AUTHOR]

Several teaching moves have been suggested to support young children's simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, Big Fish Story, with dyads of 3 to 4-year-old students. As part of the implementation, the teacher-researchers used these teaching moves to support young children's in-the-moment answers to simple addition and subtraction problems. We use session-level data (n = 94 sessions) nested in dyads to examine and compare the frequency with which the use of these teaching moves are associated with two types of student responses, in order to preliminarily identify teaching moves that may support young children's performance on simple arithmetic tasks. We conclude with implications for the field and early childhood practitioners. [ABSTRACT FROM AUTHOR]

Medical confidentiality is an essential duty in the medical profession. In this paper, we introduce a novel robust blind watermarking method for securing the medical report in a DICOM (Digital Imaging and Communications in Medicine) imaging. The insertion of each bit is done in the subtraction of adjacent DC coefficients of the FFT (fast Fourier transformation) using a key kw. Each bit of the watermark is eXORed with a bit generated by a proposed system which generates a bit sequence in function of the key kw. The proposed method has the features of having better security, invisibility, and robustness. Experimental results show that it is robust to single, double, and triple attacks and that it has better robustness than recently proposed watermarking schemes. Graphical abstract The proposed security system. [ABSTRACT FROM AUTHOR]

Background: The addition of 3D CT scans for observers evaluating tibial plateau fractures decreases agreement and diagnostic accuracy, possibly due to obstruction of the view by unfractured bones (i.e., patella, fibula, and femur) in 3D reconstructions.Questions/purposes: This study compared (1) the interobserver agreement between (subgroups of) observers classifying 3DCT reconstructions of tibial plateau fractures according to Schatzker, Luo, and AO/OTA, (2) recognition of different fracture characteristics, and (3) the level of confidence on a scale from 0 to 10 with and without subtraction of the unfractured bones.Methods: We selected twenty consecutive 3DCT reconstructions of tibial plateau fractures treated in a level I trauma center between 2013 and 2014. Members of the Science of Variation Group were randomized (1:1) to evaluate reconstructions with or without subtraction of the unfractured bone. Forty-nine surgeons completed the survey. The interobserver agreement was determined using Fleiss' kappa, and bootstrapping (resamples = 1000) was used to calculate the standard error, z statistic, and confidence intervals.Results: Overall, subtraction of unfractured bones did not affect interobserver agreement in Schatzker, Luo, and AO/OTA classification systems, agreement on the presence of fracture characteristics, and level of confidence. In subgroup analysis, non-trauma surgeons had significantly higher agreement in the three classification systems with subtraction. For fracture characteristics, some subgroups had higher agreement while others had lower agreement with subtraction.Discussion: The finding that agreement on classification of tibial plateau fractures is limited on 3DCT scan and is not improved by subtraction of unfractured bones suggests that disagreement may be based on variations in understanding and bias. Reliability of these classification systems might benefit from a focus on accounting for these pre-existing conceptualizations rather than further emphasis on imaging detail.Level Of Evidence: Diagnostic, level 1. [ABSTRACT FROM AUTHOR]

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report is based on an analysis of assessments with 103 children (intervention group n = 65 and control group n = 38) before and after the intervention and a follow-up assessment 1 year after the intervention. Our findings show that the learning outcomes of the intervention group were significantly higher compared to those of the control group after the intervention and that differences between the groups remained even 1 year after the intervention. In particular, the results show that children participating in the intervention group learned to recognize and use part-part-whole relations in novel arithmetic tasks. [ABSTRACT FROM AUTHOR]

This article proposes 'biopolitics multiple' as an approach to the heterogeneity of biopolitical technologies deployed to govern migration today. Building on work that has started to develop analytical vocabularies to diagnose biopolitical technologies that work neither by fostering life nor by making people die in a necropolitical sense, it conceptualises 'extraction' and 'subtraction' as two such technologies that take 'hold' of migrants' lives today. Extraction, explored in the article through a focus on borderzones in Greece, captures the imbrication of biopolitics and value through the 'outside' creation of the economic conditions of data circulation. Subtraction, which is analysed in this article through a focus on Calais, captures the practices of (partial) non-governing by taking material and legal terrain away from migrants and reconfiguring convoluted geographies of (forced) hyper-mobility. This move allows us to understand the governmentality of migration beyond binary oppositions such as 'making live/letting die', biopolitics/necropolitics and inclusion/exclusion. Biopolítica múltiple: migración, extracción, sustracción [ABSTRACT FROM AUTHOR]

The purpose of this study was to assess the effectiveness of explicit instruction, compared to constructivist instruction, in teaching subtraction in schools with a high concentration of students from a disadvantaged social background: eighty-seven second graders (mean age in months = 90.95, SD = 5.30). Two groups received explicit versus constructivist instruction during 5 weeks. Pre- and posttest analyses were conducted to compare the effects of the instruction type on subtraction skills taught through the partitioning subtraction method. Results showed that although all students progressed between both evaluations, those who received explicit instruction performed better. The findings from this study suggest that explicit instruction teaching is a promising approach in supporting the learning of mathematical knowledge for low-achieving students from disadvantaged social background. A larger scale study comparing the outcomes of children from different socioeconomic backgrounds would be needed to extend the applicability of the positive effects of this study. [ABSTRACT FROM AUTHOR]

In order to visualize restricted diffusion, the present study developed a novel method called 'apparent diffusion coefficient (ADC) subtraction method (ASM)' and compared it with diffusion kurtosis imaging (DKI). The diffusion-weighted images of physiological saline, in addtion to bio-phatoms of low cell density and the highest cell density were obtained using two sequences with different effective diffusion times. Then, the calculated ADC values were subtracted. The mean values and standard deviations (SD) of the ADC values of physiological saline, low cell density and the highest cell density phantoms were 2.95±0.08×10−3, 1.90±0.35×10−3 and 0.79±0.05×10−3 mm2/sec, respectively. The mean kurtosis values and SD of DKI were 0.04±0.01, 0.44±0.13 and 1.27±0.03, respectively. The ASM and SD values were 0.25±0.20×104, 0.51±0.41×104 and 4.80±4.51×104 (sec/mm2)2, respectively. Using bio-phantoms, the present study demonstrated that DKI exhibits restricted diffusion in the extracellular space. Similarly, ASM may reflect the extent of restricted diffusion in the extracellular space. [ABSTRACT FROM AUTHOR]

The question of teaching a standard written algorithm for the four arithmetical operations in the first years of elementary school is increasingly raised as a consequence of the possibility of using calculators, tablets, and computers. This article first presents arguments both against and for maintaining this teaching in the first school years. Then, it presents an analysis of the procedure—whether it implies the standard algorithm or not—used by second grade students to solve a subtraction verbal problem. The 4720 students involved in the research were divided in a control group (n = 2101) and an experimental group (n = 2619) in which the standard written algorithm (SWA) was taught, or not taught, respectively. The effectiveness of algorithm use was analyzed not only in terms of accuracy of the answers, but also for its influence on the choice of the correct arithmetical operation and for its choice by the students as a function of their ability. The SWA was strongly associated with the use of the false arithmetical operation (effect size ϕ = 0.79)—addition instead of subtraction—but was chosen by students of all levels of ability. The latter result suggests that the SWA is well suited for the most advanced students but far less for the others who use it mechanically and without reflection. [ABSTRACT FROM AUTHOR]

We present a computationally efficient method for the calculation of impedance (Z-) matrices for a large class of standing- and traveling-wave structures used in klystrons, traveling-wave tubes, and other RF vacuum electronic devices. We apply joining formulas by which the Z-matrix of a structure can be constructed from the Z-matrices of its component parts without a full-scale finite-element (FE) electromagnetic (EM) simulation of the whole structure. For the inverse operation, we apply subtraction formulas that define the Z-matrix of a structure from which a selected section has been removed. New Z-matrix modification equations are derived which determine the Z-matrix of a modified structure, without recomputing the entire structure Z-matrix. The approach and examples are extended to multibeam RF structures. The obtained Z-matrices are suitable for the large-signal 1-D and 2-D beam-wave interaction codes CHRISTINE-CC and TESLA-Z. Application of the techniques described here greatly facilitates the accurate calculation of Z-matrices and optimization of large, complex circuits that are difficult to model whole in a single FE simulation. [ABSTRACT FROM AUTHOR]

Abstract Background We previously showed that CT perfusion (CTP) and arterial spin labelled (ASL) MRI can localize the seizure onset zone in humans via postictal perfusion patterns. As a step towards improving the feasibility/ease of collecting postictal CBF data, we determined whether EEG electrodes need to be removed for CTP data collection and whether a cross-modality comparison between baseline ASL and postictal CTP data is possible. New method Five patients with epilepsy underwent postictal CTP scanning. Three patients had an interictal ASL scan; one patient had both an ASL and CTP interictal scan. Postictal CTP maps were quantitatively compared to 1) ASL maps averaged from 100 healthy controls, 2) each patient's baseline ASL map and 3) each patient's baseline CTP map. To assess for electrode artifacts, a phantom and one patient underwent CTP scanning with EEG electrodes in place. The acquired scans were assessed for artifacts and for postictal hypoperfusion. Results Focal postictal hypoperfusion was observable only in intra-modality comparisons (CTP to CTP) and not in cross-modality comparisons (CTP to ASL). EEG electrodes produced streaking artifact that decreased image quality and precluded quantitative analysis. Comparison with existing methods(s) An intra-modality comparison of baseline CTP to postictal CTP was the only comparison method that showed localized hypoperfusion. Conclusions Quantitative comparison between postictal CTP and baseline ASL scans is not feasible. Postictal hypoperfusion can be detected by CTP only when two CTP scans are collected and when metallic EEG electrodes are removed. [ABSTRACT FROM AUTHOR]

Abstract Arithmetic reasoning activates the occipital cortex of congenitally blind people (CB). This activation of visual areas may highlight the functional flexibility of occipital regions deprived of their dominant inputs or relate to the intrinsic computational role of specific occipital regions. We contrasted these competing hypotheses by characterizing the brain activity of CB and sighted participants while performing subtraction, multiplication and a control letter task. In both groups, subtraction selectively activated a bilateral dorsal network commonly activated during spatial processing. Multiplication triggered activity in temporal regions thought to participate in memory retrieval. No between-group difference was observed for the multiplication task whereas subtraction induced enhanced activity in the right dorsal occipital cortex of the blind individuals only. As this area overlaps with regions showing selective tuning to auditory spatial processing and exhibits increased functional connectivity with a dorsal "spatial" network, our results suggest that the recruitment of occipital regions during high-level cognition in the blind actually relates to the intrinsic computational role of the activated regions. [ABSTRACT FROM AUTHOR]

In recent years honeybees have demonstrated intriguing numerical capacities, leading to the recent discovery of their ability to perform simple arithmetic by learning to add or subtract 'one' using symbolic representations of operators. When training an insect with a miniature brain containing less than one million neurons to understand a conceptual rule, the procedure is of vital importance. We explain in detail the controls and process of designing an experiment to test for complex behaviors in a relatively simple brained animal. Furthermore, we will discuss the finding that individual honeybees do not demonstrate a consistent learning scenario when trained to perform the same tasks, rather they appear to acquire arithmetic rules through individual processes. [ABSTRACT FROM AUTHOR]

Abstract Phonological and articulatory programming impairments may co-occur in aphasic patients and previous research does not offer a clear-cut picture of their anatomical counterparts. Hickok and Poeppel (2007) put forward a seminal model of speech processes. The ventral stream (mostly bilateral) would be involved in speech recognition and phonological-lexical processing, whereas the dorsal stream (largely lateralized to the left hemisphere) would map phonological representations onto articulatory motor patterns. In this study we analyzed repetition errors for single words and spontaneous speech ratings on the Italian version of the Aachen Aphasia Test. Through a VLSM procedure we aimed at discriminating the neuroanatomical substrates of the phonological and articulatory impairment (and of their normal functional processing). We also estimated functional connectivity networks related to articulation and phonology using seed-to-voxel connectivity analysis with resting state fMRI data. Results indicate that repetition deficit of single words is associated with lesions in a network of left perisylvian areas including the central operculum, the Heschl's gyrus, the angular gyrus, and the supramarginal gyrus (posterior part). Articulatory impairment is associated with lesions in a number of areas in the left dorsal stream, such as the insula (anterior portion), the pars opercularis of the inferior frontal gyrus, the central operculum and the precentral gyrus. On the contrary, phonological impairment is underpinned by lesions of the Heschl's gyrus, and of the posterior portion of the superior temporal and supramarginal gyri. Anatomo-clinical correlative results partly support Hickok and Poeppel's functional model of phonological and articulatory processing. Highlights • We used an anatomo-correlative procedure to disentangle the neuroanatomical foundation of phonological and articulatory damage in aphasia. • We analyzed repetition errors for single words and spontaneous speech samples using VLSM. • VLSM results partly support Hickok and Poeppel's functional model of phonological and articulatory processing [ABSTRACT FROM AUTHOR]

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction opcn-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis of the WoRs also led to the identification of 3 problem types: change-positive, all-negatives, and counterintuitive. We found that problem type influenced student performance and tended to evoke a different way of reasoning. We showed dial those with more experience with negative numbers use WoRs more flexibly than those with less experience and that flexibility is correlated with accuracy. We provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory' of learning about integers. [ABSTRACT FROM AUTHOR]

A large body of research has identified cognitive skills associated with overall mathematics achievement, focusing primarily on identifying associates of procedural skills. Conceptual understanding, however, has received less attention, despite its importance for the development of mathematics proficiency. Consequently, we know little about the quantitative and domain-general skills associated with conceptual understanding. Here we investigated 8–10-year-old children’s conceptual understanding of arithmetic, as well as a wide range of basic quantitative skills, numerical representations and domain-general skills. We found that conceptual understanding was most strongly associated with performance on a number line task. This relationship was not explained by the use of particular strategies on the number line task, and may instead reflect children’s knowledge of the structure of the number system. Understanding the skills involved in conceptual learning is important to support efforts by educators to improve children’s conceptual understanding of mathematics. [ABSTRACT FROM AUTHOR]

Objective To explore the feasibility of a modified two breath-hold method with radiation dose reduction technique using lower voltage of 100 kV in subtraction coronary CT angiography (CCTA) for patients with limited breath-hold (<15 s).Methods A total of 17 patients with Agatston score >400,and body mass index less than 25 kg/m2 were enrolled in this study.The pre-contrast and post-contrast volume data was acquired during two breath-holds with the same time window period in 65%-80% of the R-R interval. A 4-point scale was used for the evaluation of subjective image quality.Results A total of 53 calcified coronary segments were evaluated.There was an improvement in the image quality from 2.51±0.95 with conventional CCTA to 3.36±0.92 with subtraction CCTA (P<0.01).The non-diagnostic segments significantly reduced from 23(43.4%) to 6 (11.3%) using subtraction CCTA (P=0.02). The average total effective radiation dose was (2.80±0.64) mSv.Conclusions This preliminary study has shown that our modified method in subtraction CCTA could significantly reduce the non-assessable segments and improve the accessibility of severe calcified segments by reducing or eliminating artifacts.Using 100 kV tube voltage,the total radiation dose was distinctly reduced with maintained image quality in BMI＜25 kg/m2 patients. [ABSTRACT FROM AUTHOR]

The purpose of this article was to propose a work with sums and subtractions, starting from an educational game, as a teaching strategy. We believe that this type of approach needs more discussion, reflection and debating. As a methodology, we chose the qualitative approach. We consider our interest in sum and subtraction justified because in Brazil (2017) we see a recurring concern in working with this knowledge, from the first year of elementary school to the third year, so we held game sessions with classes from those years to observe his reactions to this type of strategy, in a public school on the outskirts of the city of São Paulo. We believe that this activity had as its strengths the interest, socialization and engagement of the students, while allowing the learners to perform accounts using predominantly strategies such as counting in the fingers. Another relevant point was the children's interest in the game, which was superior to their enthusiasm for traditional teaching activities. When asked about the amount of time each of the three groups was interested in activities, it was possible to establish a relationship with the class teachers that, through educational games, it is possible to keep children interested in activities for a greater amount of time. Another relevant point was that the students could train techniques, ask questions and assign meaning to sums and subtractions. [ABSTRACT FROM AUTHOR]

Background: During visual exploration or free-view, gaze positioning is largely determined by the tendency to maximize visual saliency: more salient locations are more likely to be fixated. However, when visual input is completely irrelevant for performance, such as with non-visual tasks, this saliency maximization strategy may be less advantageous and potentially even disruptive for task-performance. Here, we examined whether visual saliency remains a strong driving force in determining gaze positions even in non-visual tasks. We tested three alternative hypotheses: a) That saliency is disadvantageous for non-visual tasks and therefore gaze would tend to shift away from it and towards non-salient locations; b) That saliency is irrelevant during non-visual tasks and therefore gaze would not be directed towards it but also not away-from it; c) That saliency maximization is a strong behavioral drive that would prevail even during non-visual tasks. Methods: Gaze position was monitored as participants performed visual or non-visual tasks while they were presented with complex or simple images. The effect of attentional demands was examined by comparing an easy non-visual task with a more difficult one. Results: Exploratory behavior was evident, regardless of task difficulty, even when the task was non-visual and the visual input was entirely irrelevant. The observed exploratory behaviors included a strong tendency to fixate salient locations, central fixation bias and a gradual reduction in saliency for later fixations. These exploratory behaviors were spatially similar to those of an explicit visual exploration task but they were, nevertheless, attenuated. Temporal differences were also found: in the non-visual task there were longer fixations and later first fixations than in the visual task, reflecting slower visual sampling in this task. Conclusion: We conclude that in the presence of a rich visual environment, visual exploration is evident even when there is no explicit instruction to explore. Compared to visually motivated tasks, exploration in non-visual tasks follows similar selection mechanisms, but occurs at a lower rate. This is consistent with the view that the non-visual task is the equivalent of a dual-task: it combines the instructed task with an uninstructed, perhaps even mandatory, exploratory behavior. [ABSTRACT FROM AUTHOR]

Separate lines of research suggest that people who are better at estimating numerical quantities using the approximate number system (ANS) have better math performance, and that people with high levels of math anxiety have worse math performance. Only a handful of studies have examined both ANS acuity and math anxiety in the same participants and those studies report contradictory results. To address these inconsistencies, in the current study 87 undergraduate students completed assessments of ANS acuity, math anxiety, and three different measures of math. We considered moderation models to examine the interplay of ANS acuity and math anxiety on different aspects of math performance. Math anxiety and ANS acuity were both unique significant predictors of the ability to automatically recall basic number facts. ANS acuity was also a unique significant predictor of the ability to solve applied math problems, and this relation was further qualified by a significant interaction with math anxiety: the positive association between ANS acuity and applied problem solving was only present in students with high math anxiety. Our findings suggest that ANS acuity and math anxiety are differentially related to various aspects of math and should be considered together when examining their respective influences on math ability. Our findings also raise the possibility that good ANS acuity serves as a protective factor for highly math-anxious students on certain types of math assessments. [ABSTRACT FROM AUTHOR]

Most research on children’s arithmetic concepts is based on (a) additive concepts and (b) a single concept leading to possible limitations in current understanding about how children’s knowledge of arithmetic concepts develops. In this study, both additive and multiplicative versions of six arithmetic concepts (identity, negation, commutativity, equivalence, inversion, and associativity) were investigated in Grades 5, 6, and 7. The multiplicative versions of the concepts were more weakly understood. No grade-related differences were found in conceptual knowledge, but older children were more accurate problem solvers. Individual differences were examined through cluster analyses. All children had a solid understanding of identity and negation. Some children had a strong understanding of all the concepts, both additive and multiplicative; some had a good understanding of equivalence or commutativity; and others had a weak understanding of commutativity, equivalence, inversion, and associativity. Associativity was the most difficult concept for all clusters. Grade did not predict cluster membership. Overall, these results demonstrate the breadth of individual variability in conceptual knowledge of arithmetic as well as the complexity in how children’s understanding of arithmetic concepts develops. [ABSTRACT FROM AUTHOR]

This study aims to investigate primary school students' addition and subtraction based mathematical word problem solving levels and to identify the types of questions asked to students in mathematics course books. A form with problem types was administered to 158 third year students. Also, 6 mathematics course books and students' books were analyzed through document analysis. The results showed students had difficulties in initial unknown addition and subtraction problems and compare problems. In addition, it was found out that result unknown addition and subtraction based word problems were mostly used in the mathematics course books and students' books prepared by the Ministry of National Education. It was also observed that compare problems were very scarcely used. [ABSTRACT FROM AUTHOR]

Investigating infants’ numerical ability is crucial to identifying the developmental origins of numeracy. Wynn (1992) claimed that 5-month-old infants understand addition and subtraction as indicated by longer looking at outcomes that violate numerical operations (i.e., 1 + 1 = 1 and 2 − 1 = 2). However, Wynn’s claim was contentious, with others suggesting that her results might reflect a familiarity preference for the initial array or that they could be explained in terms of object tracking. To cast light on this controversy, Wynn’s conditions were replicated with conventional looking time supplemented with eye-tracker data. In the incorrect outcome of 2 in a subtraction event (2 − 1 = 2), infants looked selectively at the incorrectly present object, a finding that is not predicted by an initial array preference account or a symbolic numerical account but that is consistent with a perceptual object tracking account. It appears that young infants can track at least one object over occlusion, and this may form the precursor of numerical ability. [ABSTRACT FROM AUTHOR]

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate children's neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9- to 10-year-olds), who, in a behavioral session, were asked to verbally report on a trial-by-trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event-related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the children's verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657-4670, 2017. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed findings. The present meta-analysis aimed to systematically compile and synthesize all of the primary replications and extensions of Wynn (1992) that have been conducted to date. The synthesis included 12 studies consisting of 26 independent samples and 550 unique infants. The summary effect, computed using a random-effects model, was statistically significant, d = +0.34, p < .001, suggesting that the phenomenon Wynn originally reported is reliable. Five different tests of publication bias yielded mixed results, suggesting that while a moderate level of publication bias is probable, the summary effect would be positive even after accounting for this issue. Out of the 10 metamoderators tested, none were found to be significant, but most of the moderator subgroups were significantly different from a null effect. Although this meta-analysis provides support for Wynn's original findings, further research is warranted to understand the underlying mechanisms responsible for infants''visual preferences for "mathematically incorrect" test stimuli. [ABSTRACT FROM AUTHOR]

This cross-sectional study investigated the age-related differences in dual-task performance both in mobility and cognitive tasks and the additive dual-task costs in a sample of older, middle-aged and young adults. 74 older adults (M = 72.63±5.57 years), 58 middle-aged adults (M = 46.69±4.68 years) and 63 young adults (M = 25.34±3.00 years) participated in the study. Participants performed different mobility and subtraction tasks under both single- and dual-task conditions. Linear regressions, repeated-measures and one-way analyses of covariance were used, The results showed: significant effects of the age on the dual and mobility tasks (p<0.05) and differences among the age-groups in the combined dual-task costs (p<0.05); significant decreases in mobility performance under dual-task conditions in all groups (p<0.05) and a decrease in cognitive performance in the older group (p<0.05). Dual-task activity affected mobility and cognitive performance, especially in older adults who showed a higher dual-task cost, suggesting that dual-tasks activities are affected by the age and consequently also mobility and cognitive tasks are negatively influenced. [ABSTRACT FROM AUTHOR]

Background A major model of the cerebral circuits that underpin arithmetic calculation is the triple-code model of numerical processing. This model proposes that the lateralization of mathematical operations is organized across three circuits: a left-hemispheric dominant verbal code; a bilateral magnitude representation of numbers and a bilateral Arabic number code. New method This study simultaneously measured the blood flow of both middle cerebral arteries using functional transcranial Doppler ultrasonography to assess hemispheric specialization during the performance of both language and arithmetic tasks. The propositions of the triple-code model were assessed in a non-clinical adult group by measuring cerebral blood flow during the performance of multiplication and subtraction problems. Participants were 17 adults aged between 18–27 years. We obtained laterality indices for each type of mathematical operation and compared these in participants with left-hemispheric language dominance. It was hypothesized that blood flow would lateralize to the left hemisphere during the performance of multiplication operations, but would not lateralize during the performance of subtraction operations. Results Hemispheric blood flow was significantly left lateralized during the multiplication task, but was not lateralized during the subtraction task. Comparison with existing method(s) Compared to high spatial resolution neuroimaging techniques previously used to measure cerebral lateralization, functional transcranial Doppler ultrasonography is a cost-effective measure that provides a superior temporal representation of arithmetic cognition. Conclusions These results provide support for the triple-code model of arithmetic processing and offer complementary evidence that multiplication operations are processed differently in the adult brain compared to subtraction operations. [ABSTRACT FROM AUTHOR]

Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills. [ABSTRACT FROM AUTHOR]