The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia.

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Spatial neglect in the digital age: Influence of presentation format on patients' test behavior.

OBJECTIVE: Computerized neglect tests could significantly deepen our disorder-specific knowledge by effortlessly providing additional behavioral markers that are hardly or not extractable from existing paper-and-pencil versions. This study investigated how testing format (paper versus digital), and screen size (small, medium, large) affect the Center of cancelation (CoC) in right-hemispheric stroke patients in the Letters and the Bells cancelation task. Our second objective was to determine whether a machine learning approach could reliably classify patients with and without neglect based on their search speed, search distance, and search strategy. METHOD: We compared the CoC measure of right hemisphere stroke patients with neglect in two cancelation tasks across different formats and display sizes. In addition, we evaluated whether three additional parameters of search behavior that became available through digitization are neglect-specific behavioral markers. RESULTS: Patients' CoC was not affected by test format or screen size. Additional search parameters demonstrated lower search speed, increased search distance, and a more strategic search for neglect patients than for control patients without neglect. CONCLUSION: The CoC seems robust to both test digitization and display size adaptations. Machine learning classification based on the additional variables derived from computerized tests succeeded in distinguishing stroke patients with spatial neglect from those without. The investigated additional variables have the potential to aid in neglect diagnosis, in particular when the CoC cannot be validly assessed (e.g., when the test is not performed to completion).

An exploratory study examining the changes to Australia's social security system during COVID-19 lockdown measures.

During the 2020 COVID-19 wave, the Australian Government made an additional $550 Coronavirus Supplement available for people receiving social security payments, and temporarily suspended mutual obligation requirements. By doing so, the government effectively gave people who had been long stigmatised and subject to punitive conditionality to compel them into the labour market, financial security and their time back. Drawing on survey responses from people who received the $550 Supplement and had their mutual obligation activities suspended or reduced, this research examines how people used their time during this period and whether it differed from pre-pandemic government policy. We find that the increase in payments through the Supplement and the suspension of mutual obligations impacted positively on people's lives including the (1) the ability of respondents to meet basic needs and improve their long-term financial security, (2) improvements to physical and emotional well-being, (3) increased labour market engagement and (4) engagement in other forms of unpaid productive work.

Mode effect: An issue of perspective? Writing mode differences in a spelling assessment in German children with and without developmental dyslexia.

Digital technology has an increasing influence on writing processes. In this context, the question arises whether changes in writing mode (i.e., handwriting vs. computer-keyboard typing) also require changes in writing assessments. However, data directly comparing writing mode influences in children with and without developmental writing deficits are scarce. This study investigated the influence of writing mode in German-speaking, typically developing children and children with developmental dyslexia (DD) from two different levels. Results showed on a general level that writing mode influenced overall spelling accuracy, writing time, and self-corrections comparably in children with and without DD. On a rule-specific level, outcomes for writing time and self-corrections substantiated these findings. However, as regards spelling accuracy, a mode effect was only apparent for capitalization, whereas other spelling rules were resistant to writing mode influences. Present findings suggest that a mode effect is present only for typing specific aspects (e.g., capitalization) rather than reflecting a general influence on orthographic principles (e.g., grapheme-phoneme assignment, morphologic principles). These mode-specific aspects seem to comparably affect the writing performance of typically developing children and children with DD. We recommend writing assessments to consider that different writing modes may influence individual spelling rules differently.

Roadmap to recovery: Reporting on a research taskforce supporting Indigenous responses to COVID-19 in Australia.

In April 2020 a Group of Eight Taskforce was convened, consisting of over 100 researchers, to provide independent, research-based recommendations to the Commonwealth Government on a "Roadmap to Recovery" from COVID-19. The report covered issues ranging from pandemic control and relaxation of social distancing measures, to well-being and special considerations for vulnerable populations. Our work focused on the critical needs of Aboriginal and Torres Strait Islander communities; this paper presents an overview of our recommendations to the Roadmap report. In addressing the global challenges posed by pandemics for citizens around the world, Indigenous people are recognised as highly vulnerable. At the time of writing Australia's First Nations Peoples have been largely spared from COVID-19 in comparison to other Indigenous populations globally. Our recommendations emphasise self-determination and equitable needs-based funding to support Indigenous communities to recover from COVID-19, addressing persistent overcrowded housing, and a focus on workforce, especially for regional and remote communities. These latter two issues have been highlighted as major issues of risk for Indigenous communities in Australia It remains to be seen how governments across Australia take up these recommendations to support Indigenous peoples' health and healing journey through yet another, potentially catastrophic, health crisis.

Anticipation of difficult tasks: neural correlates of negative emotions and emotion regulation.

BACKGROUND: Difficult cognitive tasks are often associated with negative feelings. This can be already the case for the mere anticipation of having to do a difficult task. For the case of difficult math tasks, it was recently suggested that such a negative emotional response may be exclusive to highly math-anxious individuals. However, it is also conceivable that negative emotional responses simply reflect that math is perceived as difficult. Here we investigated whether non-math-anxious individuals also experience negative emotional responses when anticipating to do difficult math tasks. METHODS: We compared brain activation following the presentation of a numerical cue indicating either difficult or easy upcoming proportion magnitude comparison tasks. RESULTS: Comparable to previous results for highly math-anxious individuals we observed a network associated with negative emotions to be activated in non-math-anxious individuals when facing cues indicating a difficult upcoming task. Importantly, however, math anxiety scores did not predict the neural response. Furthermore, we observed activation in areas associated with processes of cognitive control areas such as anterior cingulate cortex, which were suggested to play a key role in emotion regulation. CONCLUSION: Activation in the emotion processing network was observed when anticipating an upcoming difficult (math) task. However, this activation was not predicted by individual' degree of math anxiety. Therefore, we suggest that negative emotional responses to difficult math tasks might be a rather common reaction not specific to math-anxious individuals. Whether or not this initial negative response impairs math performance, however, might depend on the ability to regulate those emotions effectively.

Set size influences the relationship between ANS acuity and math performance: a result of different strategies?

Previous research has proposed that the approximate number system (ANS) constitutes a building block for later mathematical abilities. Therefore, numerous studies investigated the relationship between ANS acuity and mathematical performance, but results are inconsistent. Properties of the experimental design have been discussed as a potential explanation of these inconsistencies. In the present study, we investigated the influence of set size and presentation duration on the association between non-symbolic magnitude comparison and math performance. Moreover, we focused on strategies reported as an explanation for these inconsistencies. In particular, we employed a non-symbolic magnitude comparison task and asked participants how they solved the task. We observed that set size was a significant moderator of the relationship between non-symbolic magnitude comparison and math performance, whereas presentation duration of the stimuli did not moderate this relationship. This supports the notion that specific design characteristics contribute to the inconsistent results. Moreover, participants reported different strategies including numerosity-based, visual, counting, calculation-based, and subitizing strategies. Frequencies of these strategies differed between different set sizes and presentation durations. However, we found no specific strategy, which alone predicted arithmetic performance, but when considering the frequency of all reported strategies, arithmetic performance could be predicted. Visual strategies made the largest contribution to this prediction. To conclude, the present findings suggest that different design characteristics contribute to the inconsistent findings regarding the relationship between non-symbolic magnitude comparison and mathematical performance by inducing different strategies and additional processes.

Neuro-cognitive mechanisms of global Gestalt perception in visual quantification.

Recent neuroimaging studies identified posterior regions in the temporal and parietal lobes as neuro-functional correlates of subitizing and global Gestalt perception. Beyond notable overlap on a neuronal level both mechanisms are remarkably similar on a behavioral level representing both a specific form of visual top-down processing where single elements are integrated into a superordinate entity. In the present study, we investigated whether subitizing draws on principles of global Gestalt perception enabling rapid top-down processes of visual quantification. We designed two functional neuroimaging experiments: a task identifying voxels responding to global Gestalt stimuli in posterior temporo-parietal brain regions and a visual quantification task on dot patterns with magnitudes within and outside the subitizing range. We hypothesized that voxels activated in global Gestalt perception should respond stronger to dot patterns within than those outside the subitizing range. The results confirmed this prediction for left-hemispheric posterior temporo-parietal brain areas. Additionally, we trained a classifier with response patterns from global Gestalt perception to predict neural responses of visual quantification. With this approach we were able to classify from TPJ Gestalt ROIs of both hemispheres whether a trial requiring subitizing was processed. The present study demonstrates that mechanisms of subitizing seem to build on processes of high-level visual perception.

Magnitude processing of symbolic and non-symbolic proportions: an fMRI study.

BACKGROUND: Recent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates. METHODS: We conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated. RESULTS: A conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats. CONCLUSION: Our findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.

Monotonic non-linear transformations as a tool to investigate age-related effects on brain white matter integrity: A Box-Cox investigation.

Non-linear effects of age on white matter integrity are ubiquitous in the brain and indicate that these effects are more pronounced in certain brain regions at specific ages. Box-Cox analysis is a technique to increase the log-likelihood of linear relationships between variables by means of monotonic non-linear transformations. Here we employ Box-Cox transformations to flexibly and parsimoniously determine the degree of non-linearity of age-related effects on white matter integrity by means of model comparisons using a voxel-wise approach. Analysis of white matter integrity in a sample of adults between 20 and 89years of age (n=88) revealed that considerable portions of the white matter in the corpus callosum, cerebellum, pallidum, brainstem, superior occipito-frontal fascicle and optic radiation show non-linear effects of age. Global analyses revealed an increase in the average non-linearity from fractional anisotropy to radial diffusivity, axial diffusivity, and mean diffusivity. These results suggest that Box-Cox transformations are a useful and flexible tool to investigate more complex non-linear effects of age on white matter integrity and extend the functionality of the Box-Cox analysis in neuroimaging.

Fact learning in complex arithmetic-the role of the angular gyrus revisited.

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Patterns of linguistic and numerical performance in aphasia.

BACKGROUND: Empirical research on the relationship between linguistic and numerical processing revealed inconsistent results for different levels of cognitive processing (e.g., lexical, semantic) as well as different stimulus materials (e.g., Arabic digits, number words, letters, non-number words). Information of dissociation patterns in aphasic patients was used in order to investigate the dissociability of linguistic and numerical processes. The aim of the present prospective study was a comprehensive, specific, and systematic investigation of relationships between linguistic and numerical processing, considering the impact of asemantic vs. semantic processing and the type of material employed (numbers compared to letters vs. words). METHODS: A sample of aphasic patients (n = 60) was assessed with a battery of linguistic and numerical tasks directly comparable for their cognitive processing levels (e.g., perceptual, morpho-lexical, semantic). RESULTS AND CONCLUSIONS: Mean performance differences and frequencies of (complementary) dissociations in individual patients revealed the most prominent numerical advantage for asemantic tasks when comparing the processing of numbers vs. letters, whereas the least numerical advantage was found for semantic tasks when comparing the processing of numbers vs. words. Different patient subgroups showing differential dissociation patterns were further analysed and discussed. A comprehensive model of linguistic and numerical processing should take these findings into account.

Embodied markedness of parity? Examining handedness effects on parity judgments.

Parity is important semantic information encoded by numbers. Interestingly, there are hand-based effects in parity judgment tasks: right-hand responses are faster for even and left-hand responses for odd numbers. As this effect was initially explained by the markedness of the words even vs. odd and right vs. left, it was denoted as the linguistic markedness of response codes (MARC) effect. In the present study, we investigated whether the MARC effect differs for right and left handers. We conducted a parity judgment task, in which right- and left-handed participants had to decide whether a presented single or two-digit number was odd or even by pressing a corresponding response key. We found that handedness modulated the MARC effect for unit digits. While we replicated a regular MARC effect for right handers, there was no evidence for a MARC effect for left handers. However, closer inspection revealed that the MARC effect in left handers depended on the degree of left-handedness with a reversed MARC effect for most left-handed participants. Furthermore, although parity of tens digits interfered with the processing of unit digits, the MARC effect for tens digits was not modulated by handedness. Our findings are discussed in the light of three different accounts for the MARC effect: the linguistic markedness account, the polarity correspondence principle, and the body-specificity hypothesis.

Where numbers meet words: a common ventral network for semantic classification.

Recent research has shown that both language and number processing are clear examples of distributed and connected processing in the human brain, emphasizing the importance of white matter connections between the associated cortex sites. Against this background we hypothesized joint cognitive processes and functions in a cross-domain manner to be reflected by the involvement of specific white matter tracts. Therefore, we evaluated white matter connectivity for the specific cognitive process of semantic classification, which is an integral part of tasks commonly employed to investigate the neural correlates of language and number processing. In line with our expectations, fiber tracking results clearly indicated a common ventral network for semantic classification for the domains of language and number processing. Thereby, the present data are hard to reconcile with a localizationalist view on processing characteristics of the human brain, but strongly suggest that white matter connectivity should be considered when investigating the neural underpinnings of human cognition.

Object-based neglect in number processing.

Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and --if so --how object-based neglect influences number processing.To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing.Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system.In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients.

Magnitude representation in sequential comparison of two-digit numbers is not holistic either.

There is accumulating evidence suggesting that two-digit number magnitude is represented in a decomposed fashion into tens and units rather than holistically as one integrated entity. However, recently, it has been claimed that this property does not hold for the case when two to-be-compared numbers are presented sequentially. In the present study, we pursued this issue in two experiments by evaluating perceptual as well as strategic aspects arising for sequential stimulus presentation in a magnitude comparison task. We observed reliable unit-decade compatibility effects indicating decomposed processing of tens and units in a magnitude comparison task with sequential presentation of the to-be-compared numbers. In particular, we found that both confounding low-level perceptual features and stimulus set characteristics determining cue validity of the units influenced the compatibility effect. Taken together, our results clearly indicate that decomposed representations of tens and units seem to be a general characteristic of multi-digit number magnitude processing, rather than an exception occurring under very specific conditions only. Implications of these results for the understanding of number magnitude representations are discussed.

Challenges in Understanding Numerical Learning: Editorial for Brain Sciences Special Issue "Neurocognitive Signatures of Math (Learning) across the Lifespan and Their Interrelation with Other Aspects of Cognition and Emotion".

Living in our information- and technology-driven society at the beginning of the 21st century requires the ability to understand and handle numbers not only for a successful career but also for coping with everyday life tasks [...].

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data.

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

Laterality in simple multiplication: Assessing hemispheric specialization of arithmetic fact retrieval in a visual hemifield paradigm.

The prominent view in numerical cognition is that highly overlearned arithmetic facts are verbally mediated and unilaterally processed in a left-hemispheric network, including language areas. However, this view has recently been challenged. Here, we evaluated the hemispheric specialization of verbal arithmetic fact retrieval and number magnitude processing using two verification tasks (i.e., multiplication and number magnitude comparison) in a divided hemifield paradigm in healthy participants (n = 35). In the number comparison task, we replicated bilateral processing advantages for the unit-decade compatibility effect. Magnitude processing was facilitated after bilateral compared with a unilateral presentation. In the multiplication task, lateralized presentation to the left hemisphere yielded processing advantages in arithmetic fact retrieval when the required interhemispheric transitions from the input, processing, and output stages were considered. Crucially, we observed a systematic processing advantage in left visual hemifield stimuli presentation (i.e., initial right-hemisphere processing). Our findings corroborate the assumption that arithmetic fact retrieval is subserved by left-lateralized verbal/linguistic processing. Thereby, they suggest a distinction between unilateral left-hemispheric linguistic processing of arithmetic fact retrieval and bilateral number magnitude processing. Interestingly, however, our data present right-hemispheric processing advantages in identifying early processed visual symbolic numerical stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data.

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.