Perceptual History Biases Are Predicted by Early Visual-Evoked Activity.

What we see in the present is affected by what we saw in the recent past. Serial dependence, a bias making a current stimulus appear more similar to a previous one, has been indeed shown to be ubiquitous in vision. At the neural level, serial dependence is accompanied by a signature of stimulus history (i.e., past stimulus information) emerging from early visual-evoked activity. However, whether this neural signature effectively reflects the behavioral bias is unclear. Here we address this question by assessing the neural (electrophysiological) and behavioral signature of stimulus history in human subjects (both male and female), in the context of numerosity, duration, and size perception. First, our results show that while the behavioral effect is task-dependent, its neural signature also reflects task-irrelevant dimensions of a past stimulus, suggesting a partial dissociation between the mechanisms mediating the encoding of stimulus history and the behavioral bias itself. Second, we show that performing a task is not a necessary condition to observe the neural signature of stimulus history, but that in the presence of an active task such a signature is significantly amplified. Finally, and more importantly, we show that the pattern of brain activity in a relatively early latency window (starting at ∼35-65 ms after stimulus onset) significantly predicts the behavioral effect. Overall, our results thus demonstrate that the encoding of past stimulus information in neural signals does indeed reflect serial dependence, and that serial dependence occurs at a relatively early level of visual processing.SIGNIFICANCE STATEMENT What we perceive is determined not only by the information reaching our sensory organs, but also by the context in which the information is embedded. What we saw in the recent past (perceptual history) can indeed modulate the perception of a current stimulus in an attractive way, a bias that is ubiquitous in vision. Here we show that this bias can be predicted by the pattern of brain activity reflecting the encoding of past stimulus information, very early after the onset of a stimulus. This in turn suggests that the integration of past and present sensory information mediating the attractive bias occurs early in the visual processing stream, and likely involves early visual cortices.

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct.

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Frontoparietal and salience network synchronizations during nonsymbolic magnitude processing predict brain age and mathematical performance in youth.

The development and refinement of functional brain circuits crucial to human cognition is a continuous process that spans from childhood to adulthood. Research increasingly focuses on mapping these evolving configurations, with the aim to identify markers for functional impairments and atypical development. Among human cognitive systems, nonsymbolic magnitude representations serve as a foundational building block for future success in mathematical learning and achievement for individuals. Using task-based frontoparietal (FPN) and salience network (SN) features during nonsymbolic magnitude processing alongside machine learning algorithms, we developed a framework to construct brain age prediction models for participants aged 7-30. Our study revealed differential developmental profiles in the synchronization within and between FPN and SN networks. Specifically, we observed a linear increase in FPN connectivity, concomitant with a decline in SN connectivity across the age span. A nonlinear U-shaped trajectory in the connectivity between the FPN and SN was discerned, revealing reduced FPN-SN synchronization among adolescents compared to both pediatric and adult cohorts. Leveraging the Gradient Boosting machine learning algorithm and nested fivefold stratified cross-validation with independent training datasets, we demonstrated that functional connectivity measures of the FPN and SN nodes predict chronological age, with a correlation coefficient of .727 and a mean absolute error of 2.944 between actual and predicted ages. Notably, connectivity within the FPN emerged as the most contributing feature for age prediction. Critically, a more matured brain age estimate is associated with better arithmetic performance. Our findings shed light on the intricate developmental changes occurring in the neural networks supporting magnitude representations. We emphasize brain age estimation as a potent tool for understanding cognitive development and its relationship to mathematical abilities across the critical developmental period of youth. PRACTITIONER POINTS: This study investigated the prolonged changes in the brain's architecture across childhood, adolescence, and adulthood, with a focus on task-state frontoparietal and salience networks. Distinct developmental pathways were identified: frontoparietal synchronization strengthens consistently throughout development, while salience network connectivity diminishes with age. Furthermore, adolescents show a unique dip in connectivity between these networks. Leveraging advanced machine learning methods, we accurately predicted individuals' ages based on these brain circuits, with a more mature estimated brain age correlating with better math skills.

Impact of Electric Field Magnitude in the Left Dorsolateral Prefrontal Cortex on Changes in Intrinsic Functional Connectivity Using Transcranial Direct Current Stimulation: A Randomized Crossover Study.

This study investigated whether the electric field magnitude (E-field) delivered to the left dorsolateral prefrontal cortex (L-DLPFC) changes resting-state brain activity and the L-DLPFC resting-state functional connectivity (rsFC), given the variability in tDCS response and lack of understanding of how rsFC changes. Twenty-one healthy participants received either 2 mA anodal or sham tDCS targeting the L-DLPFC for 10 min. Brain imaging was conducted before and after stimulation. The fractional amplitude of low-frequency fluctuation (fALFF), reflecting resting brain activity, and the L-DLPFC rsFC were analyzed to investigate the main effect of tDCS, main effect of time, and interaction effects. The E-field was estimated by modeling tDCS-induced individual electric fields and correlated with fALFF and L-DLPFC rsFC. Anodal tDCS increased fALFF in the left rostral middle frontal area and decreased fALFF in the midline frontal area (FWE p < 0.050), whereas sham induced no changes. Overall rsFC decreased after sham (positive and negative connectivity, p = 0.001 and 0.020, respectively), with modest and nonsignificant changes after anodal tDCS (p = 0.063 and 0.069, respectively). No significant differences in local rsFC were observed among the conditions. Correlations were observed between the E-field and rsFC changes in the L-DLPFC (r = 0.385, p = 0.115), left inferior parietal area (r = 0.495, p = 0.037), and right lateral visual area (r = 0.683, p = 0.002). Single-session tDCS induced resting brain activity changes and may help maintain overall rsFC. The E-field in the L-DLPFC is associated with rsFC changes in both proximal and distally connected brain regions to the L-DLPFC.

Enhancing fluid signal in driven-equilibrium short-TI inversion-recovery imaging with short TR times: A feasibility study.

PURPOSE: Fluid-sensitive turbo spin echo (TSE) MRI with short-TI inversion-recovery preparation for fat suppression (STIR) plays a critical role in the diagnostics of the musculoskeletal system (e.g., close to metal implants). Potential advantages of 3D acquisitions, however, are difficult to exploit due to long acquisition times. Shortening the TR incurs a signal loss, and a driven-equilibrium (DE) extension reduces fluid signal even further. METHODS: The phase of the flip-back pulse was changed by 180° relative to the conventional implementation (i.e., 90° along the positive x-axis (90°x) instead of -90°x). After signal modeling and numerical simulations, the modification was implemented in STIR-TSE sequences and tested on a clinical 3T system. Imaging was performed in the lumbar spine, and long-TR images without DE were acquired as reference. CSF SNR and fluid-muscle contrast were measured and compared between the sequences. Imaging was repeated in a metal implant phantom. RESULTS: A shortening of TR by 43%-57% reduced the CSF SNR by 39%-59%. A conventional DE module further reduced SNR to 26%-40%, whereas the modified DE recovered SNR to 59%-108% compared with the long-TR acquisitions. Fluid-tissue contrast was increased by about 340% with the modified DE module compared with the conventional extension. Similar results were obtained in implant measurements. CONCLUSIONS: The proposed DE element for TSE-STIR sequences has the potential to accelerate the acquisition of fluid-sensitive images. DE-STIR may work most efficiently for 3D acquisitions, in which no temporo-spatial interleaving of inversion and imaging pulses is possible.

An improved method to measure transfer functions using MRI.

PURPOSE: A previously published method for MRI-based transfer function assessment makes use of the so-called transceive phase assumption (TPA). This limits its applicability to shorter leads and/or lower field strengths. A new method is presented where the background electric field is determined from both B 1 + $$ {\mathrm{B}}_1^{+} $$ - and B 1 - $$ {\mathrm{B}}_1^{-} $$ -field distributions, avoiding the TPA and making it more generally applicable. THEORY AND METHODS: These B 1 $$ {\mathrm{B}}_1 $$ -distributions are determined from a spoiled gradient echo multiflip angle acquisition. From the separated B 1 $$ {\mathrm{B}}_1 $$ -components the background electrical field and the induced current are computed. Further improvement is achieved by recasting the B 1 $$ {\mathrm{B}}_1 $$ -field model as a "magnitude squared least squares" problem. The proposed reconstruction method is used to determine transfer functions of various copper wire lengths up to 40 cm inside an elliptical ASTM phantom. The method is first tested on EM-simulated data and subsequently phantom and bench measurements are used to determine transfer functions experimentally. RESULTS: In silica reconstructions demonstrate the validity of the proposed B 1 $$ {\mathrm{B}}_1 $$ -field model resulting in highly accurate reconstructed B 1 $$ {\mathrm{B}}_1 $$ -fields, currents, incident electric fields and transfer functions. The experimental results show slight deviations in the field model, however, resulting transfer functions are accurately determined with high similarity to simulations and comparable to bench measurements. CONCLUSION: A more generally applicable method for MRI-based transfer function assessment is presented. The proposed method circumvents phase assumptions making it applicable for longer objects and/or higher field strengths. Additional improvements are implemented in the B 1 $$ {\mathrm{B}}_1 $$ -mapping method and the solution algorithm.

Ecosystem services at risk from disturbance in Europe's forests.

Global change impacts on disturbances can strongly compromise the capacity of forests to provide ecosystem services to society. In addition, many ecosystem services in Europe are simultaneously provided by forests, emphasizing the importance of multifunctionality in forest ecosystem assessments. To address disturbances in forest ecosystem policies and management, spatially explicit risk analyses that consider multiple disturbances and ecosystem services are needed. However, we do not yet know which ecosystem services are most at risk from disturbances in Europe, where the respective risk hotspots are, nor which of the main disturbance agents are most detrimental to the provisioning of multiple ecosystem services from Europe's forests. Here, we quantify the risk of losing important ecosystem services (timber supply, carbon storage, soil erosion control and outdoor recreation) to forest disturbances (windthrows, bark beetle outbreaks and wildfires) in Europe on a continental scale. We find that up to 12% of Europe's ecosystem service supply is at risk from current disturbances. Soil erosion control is the ecosystem service at the highest risk, and windthrow is the disturbance agent posing the highest risk. Disturbances challenge forest multifunctionality by threatening multiple ecosystem services simultaneously on 19.8 Mha (9.7%) of Europe's forests. Our results highlight priority areas for risk management aiming to safeguard the sustainable provisioning of forest ecosystem services.

Recruitment of magnitude representations to understand graded words.

Language understanding and mathematics understanding are two fundamental forms of human thinking. Prior research has largely focused on the question of how language shapes mathematical thinking. The current study considers the converse question. Specifically, it investigates whether the magnitude representations that are thought to anchor understanding of number are also recruited to understand the meanings of graded words. These are words that come in scales (e.g., Anger) whose members can be ordered by the degree to which they possess the defining property (e.g., calm, annoyed, angry, furious). Experiment 1 uses the comparison paradigm to find evidence that the distance, ratio, and boundary effects that are taken as evidence of the recruitment of magnitude representations extend from numbers to words. Experiment 2 uses a similarity rating paradigm and multi-dimensional scaling to find converging evidence for these effects in graded word understanding. Experiment 3 evaluates an alternative hypothesis - that these effects for graded words simply reflect the statistical structure of the linguistic environment - by using machine learning models of distributional word semantics: LSA, word2vec, GloVe, counterfitted word vectors, BERT, RoBERTa, and GPT-2. These models fail to show the full pattern of effects observed of humans in Experiment 2, suggesting that more is needed than mere statistics. This research paves the way for further investigations of the role of magnitude representations in sentence and text comprehension, and of the question of whether language understanding and number understanding draw on shared or independent magnitude representations. It also informs the role of machine learning models in cognitive psychology research.

Are maximum magnitudes of induced earthquakes controlled by pressure diffusion?

There is an ongoing discussion about how to forecast the maximum magnitudes of induced earthquakes based on operational parameters, subsurface conditions and physical process understanding. Although the occurrence of damage caused by induced earthquakes is rare, some cases have caused significant economic loss, injuries and even loss of life. We analysed a global compilation of earthquakes induced by hydraulic fracturing, geothermal reservoir stimulation, water disposal, gas storage and reservoir impoundment. Our analysis showed that maximum magnitudes scale with the characteristic length of pressure diffusion in the brittle Earth's crust. We observed an increase in the nucleation potential of larger-magnitude earthquakes with time and explained it by diffusion-controlled growth of the pressure-perturbed part of faults. Numerical and analytical fault size modelling supported our findings. Finally, we derived magnitude scaling laws to manage induced seismic hazard of upcoming energy projects prior to operation. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

Inferring maximum magnitudes from the ordered sequence of large earthquakes.

The largest magnitude earthquake in a sequence is often used as a proxy for hazard estimates, as consequences are often predominately from this single event (in small seismic zones). In this article, the concept of order statistics is adapted to infer the maximum magnitude ([Formula: see text]) of an earthquake catalogue. A suite tools developed here can discern [Formula: see text] influences through hypothesis testing, quantify [Formula: see text] through maximum likelihood estimation (MLE) or select the best [Formula: see text] prediction amongst several models. The efficacy of these tools is benchmarked against synthetic and real-data tests, demonstrating their utility. Ultimately, 13 cases of induced seismicity spanning wastewater disposal, hydraulic fracturing and enhanced geothermal systems are tested for volume-based [Formula: see text]. I find that there is no evidence of volume-based processes influencing any of these cases. On the contrary, all these cases are adequately explained by an unbounded magnitude distribution. This is significant because it suggests that induced earthquake hazards should also be treated as unbounded. On the other hand, if bounded cases exist, then the tools developed here will be able to discern them, potentially changing how an operator mitigates these hazards. Overall, this suite of tools will be important for better-understanding earthquakes and managing their risks. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

Towards unbiased interpretations of interactive effects in ecotoxicological studies.

Ecotoxicological research has increasingly focused on the interactive effects of chemical mixtures on biological models, emphasising additive, synergistic, or antagonistic interactions. However, these combination studies often test chemicals at unique concentrations (e.g. x:y), limiting our understanding of the effects across the full spectrum of possible combinations. Evidence from human toxicology suggests that interactive effects among chemicals can vary significantly with total concentration (e.g. x:y vs. 2x:2y), their ratio (e.g. x:2y vs. 2x:y), and the magnitude of the tested effect (e.g. LC10vs. LC50). Our non-exhaustive review of studies on binary mixtures in bee ecotoxicology reveals that such parameters are frequently neglected. Of the 60 studies we examined, only two utilised multiple total concentrations and ratios, thus exploring a broad range of possible combinations. In contrast, 26 studies tested only a single concentration of each chemical, resulting in incomplete interpretations of the potential interactive effects. Other studies utilised various concentrations and/or ratios but failed to capture a broad spectrum of possible combinations. We also discuss potential discrepancies in interactive effects based on different metrics and exposure designs. We advocate for future ecotoxicological studies to investigate a wider spectrum of chemical combinations, including various concentrations and ratios, and to address different levels of effects.

Depression and its associated factors among adult hypertensive patients attending follow-up in South Gondar zone public hospitals, Ethiopia, 2023.

INTRODUCTION: Depression is the most common public health issue affecting the world's population. Like patients with other chronic medical diseases, hypertensive patients experience many intense emotions which increase their risk for the development of depression. This study aimed to assess the magnitude of depression and its associated factors among hypertensive patients in South Gondar zone governmental hospitals, Northwest Ethiopia, 2023. METHODS: An institutional-based cross-sectional study was used in government hospitals of South Gondar Zone. A total of 311 patients were sampled randomly and included in the study. Statistical Package for Social Sciences (SPSS) version 25 was used for analysis. Data were analyzed mainly by using descriptive statistics and binary logistics regression. RESULTS: A total of 311 patients participated with a 100% response rate. Almost half of the participants were female. The mean age of the respondents was 58.85 years. More than 60% of the respondents had a co-morbid illness. Among participants, 83 (26.7%) of hypertensive patients had depression. Being female, age, uneducated, having poor social support, the presence of co-morbid illness and complications, uncontrolled hypertension, having less than or equal to two dietary regimen and duration of hypertension greater than ten years were significantly associated with depression. CONCLUSION: The magnitude of depression was found to be high. This indicated that depression is a common co-morbid illness among hypertensive patients. Healthcare professionals and other stakeholders should consider and diagnose co-morbid diseases like depression among hypertensive patients. It is also better to give particular emphasis to highly vulnerable groups like females, elders, uneducated and those who have poor social support.

Magnitude of neonatal sepsis and its associated factors among neonates admitted to the neonatal intensive care unit in Hawassa Comprehensive Specialized Hospital, Sidama Regional State, Ethiopia, 2020.

BACKGROUND: Neonatal sepsis is one of the most common causes of disease and death among neonates globally. And it made a great contribution to neonatal admission to intensive care units. To mitigate the ongoing neonatal crisis and accomplish the goal of sustainable development through a decrease in neonatal mortality, information from various regions is needed. Despite the considerable burden of neonatal sepsis in our setting, no prior studies were conducted in the study area. So, this study aimed to assess the magnitude and associated factors of neonatal sepsis among neonates admitted to the neonatal intensive care unit at Hawassa University Comprehensive Specialized Hospital, Sidama Regional State, Ethiopia. METHODS: A hospital-based cross-sectional study was carried out among 287 neonates from March 1, 2020, to April 25, 2020. An interviewer-administered structured questionnaire was used to collect the data. The data were cleaned, coded, and entered into Epi Data 3.1 software and exported to Statistical Package for Social Science (SPSS) software version 23.0 for analysis. Binary logistic regression analyses were performed to identify variables having a significant association with neonatal sepsis. A p-value of ≤ 0.05 was considered statistically significant during multivariable logistic regression. RESULTS: The study found that the magnitude of neonatal sepsis was 56%. The mean age of neonates was 3.2(SD±2.2) days. Around two-fifths (39%) of neonates were in the gestational age of <37 completed weeks. A quarter of mothers(25.8%) were delivered through cesarean section. During labor, 251 (87.5%) mothers had ≤4 digital vaginal examinations. Moreover, the finding revealed that mothers who delivered by cesarean section [AOR = 2.13, 95% CI (1.090-4.163)]. neonates who had been resuscitated at birth [AOR = 4.5, 95% CI (2.083-9.707)], and neonates who had NG tube inserted [AOR = 4.29, 95% CI (2.302-8.004)] were found to be significantly associated with neonatal sepsis. CONCLUSIONS: The current study shows that neonatal sepsis was prevalent among more than half of the neonates admitted to the NICU. Therefore, designing strategies to enhance the aseptic techniques of professionals in the provision of care and actively and collaboratively working with cluster health facilities is highly recommended.

The magnitude and associated factors of immediate postpartum anemia among women who gave birth in Ethiopia: systematic review and meta-analysis, 2023.

BACKGROUND: The immediate postpartum period is a very crucial phase for both the life of the mother and her newborn baby. Anemia is the most indirect leading cause of maternal mortality. However, anemia in the immediate postpartum period is a neglected public health problem in Ethiopia. Therefore, this systematic review and meta-analysis aimed to estimate the pooled magnitude of immediate postpartum anemia and the pooled effect size of associated factors in Ethiopia. METHODS: Searching of published studies done through PubMed, Medline, Cochrane, African index Medicus, List of Reference Index, Hinari, and Google Scholar. This systematic review and meta-analysis follow the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) godliness. The quality of studies was assessed by using a Newcastle- Ottawa Scale (NOS) assessment tool. Analysis was performed using a random effect model by using STATA 17 version software. Egger's weighted regression and I2 test were used to evaluate publication bias and heterogeneity respectively. RESULTS: In this systematic review and meta-analysis, a total of 6 studies were included. The pooled magnitude of immediate postpartum anemia in Ethiopia was 27% (95%CI: 22, 32). Instrumental mode of delivery (OR = 3.14, 95%CI: 2.03, 4.24), mid-upper arm circumference (MUAC) measurement < 23 cm (OR = 3.19, 95%CI: 1.35, 5.03), Antepartum Hemorrhage (OR = 4.75, 95%CI: 2.46, 7.03), postpartum hemorrhage (OR = 4.67, 95%CI: 2.80, 6.55), and no iron/foliate supplementation (OR = 2.72, 95%CI: 1.85, 3.60) were the identified factors associated with developing anemia in the immediate postpartum period. CONCLUSION: The overall pooled magnitude of anemia in the immediate postpartum period among Ethiopian women was still a moderate public health problem. Instrumental mode of delivery, mid upper arm circumference (MUAC) measurement < 23 cm, antepartum hemorrhage, postpartum hemorrhage, and no iron/foliate supplementation were the identified factors associated with higher odds of developing anemia among immediate postpartum women in Ethiopia. Therefore, midwives, and doctors, shall focus on prevention of maternal hemorrhage, nutritional advice and counseling including iron /foliate supplementation, and avoid unnecessary instrumental delivery to prevent and reduce anemia related maternal mortality and morbidity in Ethiopia. PROSPERO REGISTRATION: CRD42023437414 with registration date on 02/08/2023.

Abnormal uterine bleeding and its associated factors among reproductive-age women who visit the gynecology ward in Dilla University General Hospital, Southern Ethiopia, 2022.

BACKGROUND: Abnormal uterine bleeding, a frequent gynecological problem among women of reproductive age, significantly affects their health and quality of life. Despite its problem, research on its extent and contributing factors in Ethiopia is scarce. Hence, this study is designed to determine the magnitude and factors associated with abnormal uterine bleeding among women visiting Dilla University General Hospital, Dilla, Ethiopia. METHODS: A cross-sectional study design was conducted with 380 women of reproductive age at Dilla University General Hospital. A systematic sampling method was employed to select the participants for the study. A structured interview administered questionnaire and checklist were used to collect the data. Stata V.14 software was used for cleaning, coding, ensuring completeness and accuracy, and further analysis. Bivariate and multivariable logistic regression analyses were used. Finally, the variables that have a p-value of < 0.05 were considered statistically significant. RESULTS: In this study, the magnitude of abnormal uterine bleeding was 24.21% (95% CI, 20.14-28.79). History of sexually transmitted disease [AOR = 1.44, 95% CI: (1.33, 4.75)], history of anemia [AOR = 3.92, 95% CI: (1.20, 12.74)]., history of alcohol consumption [AOR = 2.49, 95% CI: (1.22, 5.06)], and perceived stress level [AOR = 1.30, 95% CI: (1.15, 1.69)] were found to be significantly associated with abnormal uterine bleeding. CONCLUSIONS: The magnitude of abnormal uterine bleeding was 24.2% in the study setting. Factors such as a history of sexually transmitted disease, anemia, alcohol consumption, and perceived stress level were identified as significant risk factors for abnormal uterine bleeding. Addressing these factors is crucial for management. Further research and interventions targeting these risks are needed to enhance health outcomes. The study provides valuable insights for future interventions.

Is zero more than nothing? Relations between concepts of zero and integer understanding.

The concept of zero is challenging for many children. This study investigated conceptions of zero in fifth- through seventh-grade children (N = 72) in the United States and examined how children's conceptions of zero related to other aspects of their integer knowledge. At the outset of the study, many participants held a null conception of zero (i.e., zero as "nothing"), and some participants held a conception of zero as the symmetry point between the positive and negative integers. Participants in higher grades were more likely to hold a symmetry conception. We hypothesized that participants' conceptions of zero would be related to other aspects of their integer knowledge. Relative to participants who held a null conception of zero, participants who held a symmetry conception demonstrated greater knowledge of the additive inverse principle (for every number x, there exists an inverse, -x, such that the two numbers sum to zero) and greater integer arithmetic skill. Conceptions of zero were not related to integer magnitude understanding. We also examined whether a brief lesson focusing on zero as the symmetry point would lead to shifts in participants' conceptions of zero and gains in understanding of the additive inverse principle. Participants were randomly assigned to receive a lesson about zero as null or zero as the symmetry point between positive and negative integers. Relative to the lesson about zero as null, the lesson about zero as the symmetry point did not lead to substantial changes in conceptions of zero or additive inverse knowledge.

Building integrated number sense in adults and children: Comparing fractions-only training with cross-notation number line training.

Mounting evidence points to the predictive power of cross-notation rational number understanding (e.g., 2/5 vs. 0.25) relative to within-notation understanding (e.g., 2/5 vs. 1/4) in predicting math outcomes. Although correlational in nature, these studies suggest that number sense training emphasizing integrating across notations may have more positive outcomes than a within-notation focus. However, this idea has not been empirically tested. Thus, across two studies with undergraduate students (N = 183 and N = 181), we investigated the effects of a number line training program using a cross-notation approach (one that focused on connections among fractions, decimals, and percentages) and a within-notation approach (one that focused on fraction magnitude representation only). Both number line approaches produced positive effects, but those of the cross-notation approach were larger for fraction magnitude estimation and cross-notation comparison accuracy. In a third study (N = 63), we adapted the cross-notation number line training for use in place of typical classroom warm-up activities for middle school students. Similar to the results with undergraduate students, the cross-notation training program yielded positive benefits for middle school students over a typical warm-up activity (fraction arithmetic practice). Together, these results suggest the importance of an integrated approach to teaching rational number notations, an approach that appears to be uncommon in current curricula.

The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study.

Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.

Children's estimates of equivalent rational number magnitudes are not equal: Evidence from fractions, decimals, percentages, and whole numbers.

Integration of rational number knowledge with prior whole number knowledge has been theorized as critical for mathematical success. Fractions, decimals, and percentages are generally assumed to differ in difficulty based on the degree to which their structure is perceptually similar to whole numbers. Specifically, percentages are viewed as most similar to whole numbers with their fixed unstated denominator of 100. Decimals are often assumed to be easier than fractions because their place-value structure is an extension of the base-ten system for whole numbers, unlike fractions, which have a bipartite structure (i.e., a/b). However, there has been no comprehensive investigation of how fraction, decimal, and percentage knowledge compares with whole number knowledge. To assess understanding of the four notations, we measured within-participants number line estimation of equivalent fractions and decimals with shorter string lengths (e.g., 8/10 and 0.8) and longer string lengths (e.g., 80/100 and 0.80), percentages (e.g., 80%), and proportionally equivalent whole numbers on a 0-100 scale (e.g., 80.0). Middle school students (N = 65; 33 female) generally underestimated all formats relative to their actual values (whole numbers: 3% below; percentages: 2%; decimals: 17%; fractions: 5%). Shorter string-length decimals and fractions were estimated as smaller than equivalent longer string-length equivalents. Overall, percentages were estimated similarly to corresponding whole numbers, fractions had modest string-length effects, and decimals were the most underestimated, especially for single-digit decimals. These results highlight the strengths and weaknesses of children's understanding of each notation's magnitudes and challenge the assumption that decimals are easier than fractions.

From whole numbers to fractions to word problems: Hierarchical relations in mathematics knowledge for Chinese Grade 6 students.

It is well established in the literature that fraction knowledge is important for learning more advanced mathematics, but the hierarchical relations among whole number arithmetic, fraction knowledge, and mathematics word problem-solving are not well understood. In the current study, Chinese Grade 6 students (N = 1160; 465 girls; Mage = 12.1 years, SD = 0.6) completed whole number arithmetic (addition, subtraction, multiplication, and division), fraction (mapping, equivalence, comparison, and arithmetic), and mathematics word problem-solving assessments. They also completed two control measures: number writing speed and nonverbal intelligence. Structural equation modeling was used to investigate the hierarchical relations among these assessments. Among the four fraction tasks, the correlations were low to moderate, suggesting that each task may tap into a unique aspect of fraction understanding. In the model, whole number arithmetic was directly related to all four fraction tasks, but was only indirectly related to mathematics word problem-solving, through fraction arithmetic. Only fraction arithmetic, the most advanced fraction skill, directly predicted mathematics word problem-solving. These findings are consistent with the view that students need to build these associations into their mathematics hierarchy to advance their mathematical competence.