Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements’ size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

A qualitative study into the experience of living with acalculia after stroke or acquired brain injury

Acalculia, an acquired disability following a stroke or brain injury, involves difficulty processing numerical information and/ or calculations. Acalculia is not routinely screened for, and as a result there is a lack of understanding about the nature and prevalence and the impact of the condition. This qualitative study was initiated by stroke survivors with a strong interest in acalculia. Sixteen stroke/brain injury survivors with acalculia and seven carers were interviewed using semi-structured online interviews. Participants ranged in age, gender, time post onset, country of residence and numeracy level prior to brain injury. Data were analysed using thematic analysis. Three main themes were identified: Awareness and Diagnosis; Emotional and Practical Impact (independence); Support, Coping Strategies and Self-training. Participants and carers repeatedly referred to the lack of awareness and treatment for acalculia and the impact acalculia has had on their lives and independence. Practical impacts included managing money, making appointments, using timetables, organising social activities and employment, and managing medication. Our results highlight the urgent need to develop suitable assessments and interventions for acalculia and the scope for this to be PCPI-led. The data also reveal useful strategies and suggestions regarding effective timing, targets and approaches for intervention.

Motivated reasoning, fast and slow

Are people more likely to (mis)interpret information so that it aligns with their ideological identity when relying on feelings compared to when engaging in analytical thinking? Or is it the other way around: Does deliberation increase the propensity to (mis)interpret information to confirm existing political views? In a behavioral experiment, participants (n = 1207, Swedish sample) assessed numerical information concerning the effects of gender quotas and immigration either under time pressure or under no time pressure. To measure trait differences in cognitive sophistication, we also collected data on numeric ability. We found clear evidence of motivated reasoning when assessing both the effects of gender quotas on companies’ financial results and the effect of refugee intake on crime rates. Subjects who prioritized equality over liberty on the labor market were 13 percentage points less likely to correctly assess numerical information depicting that companies that used gender quotas when hiring made less profit. Subjects who classified themselves as ‘Swedes’ rather than ‘World citizens’ were 14 percentage points less likely to correctly assess numerical information depicting that crime rates decreased following immigration. Time pressure did not affect the likelihood to engage in motivated reasoning, while subjects with higher numeric ability were less likely to engage in motivated reasoning when analyzing information concerning refugee intake, but more likely to engage in motivated reasoning when analyzing information regarding the effect of gender quotas. Together these results indicate that motivated reasoning is primarily driven by individual differences in analytical thinking at the trait level and not by situational factors such as time pressure, and that whether motivated reasoning is primarily driven by analysis or feelings depends on the topic at hand.

Experimental modeling of the interaction of hard and aeriform body and the onset of a drag crisis with a significant change in velocity

The paper deals with the possibilities and prospects of experimental modeling of the interaction of a solid and a gaseous body. It is assumed that reliable experimental data have already been obtained and published. The problem of approximating the complex aerodynamic characteristics of air flow around a spherical body is posed and solved. The study was carried out using the «Cut-Glue» method for approximating numerical information about blowing experiments. Generally, this information reflects the dependence of the drag coefficient on the Reynolds number. The choice of the Cut-Glue method for the approximation of complex, multiextremal characteristics that can be obtained in physical experiments is substantiated.

Cross-Format Integration of Auditory Number Words and Visual-Arabic Digits: An ERP Study

Converting visual-Arabic digits to auditory number words and vice versa is seemingly effortless for adults. However, it is still unclear whether this process takes place automatically and whether accessing the underlying magnitude representation is necessary during this process. In two event-related potential (ERP) experiments, adults were presented with identical (e.g., “one” and 1) or non-identical (e.g., “one” and 9) number pairs, either unimodally (two visual-Arabic digits) or cross-format (an auditory number word and a visual-Arabic digit). In Experiment 1 (N=17), active task demands required numerical judgments, whereas this was not the case in Experiment 2 (N=19). We found pronounced early ERP markers of numerical identity unimodally in both experiments. In the cross-format conditions, however, we only observed late neural correlates of identity and only if the task required semantic number processing (Experiment 1). These findings suggest that unimodal pairs of digits are automatically integrated, whereas cross-format integration of numerical information occurs more slowly and involves semantic access.

Automatic integration of numerical formats examined with frequency-tagged EEG

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (< 5) depicted in single (digits, dots, number words) or mixed notation (dots—digits, number words—dots, digits—number words), presented at 10 Hz. Periodically, a deviant stimulus (> 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits—number words and number words—dots, but not for digits—dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.

The Demands of Simple and Complex Arithmetic Word Problems on Language and Cognitive Resources

Solving arithmetic word problems requires constructing a situation model based on the problem text and translating that into a mathematical model. As such, word problem solving makes demands on students’ language comprehension and their domain-general cognitive resources. These demands may decrease when students get more experienced and use strategies that do not require fully understanding the situation presented in the problem. The current study aims to address this hypothesis. Students (N=444) from third to sixth grade solved a paper-and-pencil task with 48 mathematics problems, comprising symbolic arithmetic problems and standard word problems, as well as more complex word problems that involve two arithmetic steps or include irrelevant numerical information. Their performance was analyzed with multilevel logistic regression analyses. Results showed that within each grade, performance on the different problem types did not differ, suggesting that already in third-grade students seem helped nor hindered by presenting arithmetic problems in a story, even if that story contains irrelevant numerical information. Non-verbal reasoning was more important in standard word problems than in arithmetic problems in symbolic format in one-step arithmetic, and reading comprehension was more important in solving two-step arithmetic word problems than in one-step arithmetic word problems.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn astract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence of the spontaneous use of abstract relative numerical information in archerfish for both small and large numbers.

Understanding of Numerical Information during the COVID-19 Pandemic

Media news during the Coronavirus Disease 2019 (COVID-19) pandemic often entail complex numerical concepts such as exponential increase or reproduction number. This study investigated whether people have difficulties in understanding such information and whether these difficulties are related to numerical competence, reflective thinking, and risk proneness. One hundred sixty-three participants provided answers to a numeracy scale focusing on complex numerical concepts relevant to COVID-19 (COV Numeracy Scale). They also provided responses to well-established objective and subjective scales, questions about affective states, and questions about the COVID-19 pandemic. Higher scores on the COV Numeracy Scale correlated with higher scores on the Health Numeracy Scale, in the Cognitive Reflection Test (CRT), and in self-assessments of verbal comprehension, mathematical intelligence, and subjective numeracy. Interestingly, scores on the COV Numeracy Scale also positively correlated with the number of consulted information sources about COVID-19. Accuracy in the CRT emerged as a significant predictor, explaining ca. 14% of variance on the COV Numeracy Scale. The results suggest that people with lower reflective thinking skills and lower subjective and objective numerical competence can be more at disadvantage when confronted with COVID-related numerical information in everyday life. These findings advise caution in the communication of relevant public health information that entails complex numerical concepts.