Elise Klein

French number words provide a unique window into the relationship between numerical cognition and language, because numbers above 60 follow a vigesimal (base-20) word structure (e.g., 72 = “60–12”). In a two-digit magnitude comparison task with sixty French native speakers, we replicated the classic unit-decade compatibility effect (UDCE; slower responses when unit and decade comparisons conflict) and within-decade effect (faster responses when decades are identical), reflecting the place-value structure of Arabic numerals. Given the French vigesimal system, we expected not only the classic UDCE and within-decade effect but also their vigesimal counterparts driven by magnitudes of number words: a unit-vigintade compatibility effect (UVCE) and a within-vigintade effect, in which pairs sharing the same decade word (e.g., “soixante” for the 60s and 70s) are processed faster than other between-decade pairs. Linear mixed models revealed both a UDCE for numbers larger than 60 and a UVCE, indicating that number words were accessed during processing. Participants also responded faster to within-vigintade items (86 vs. 95) than to between-vigintade items (76 vs. 85) and as fast as to within-decade items (82 vs. 85), indicating a verbal equivalent of the within-decade effect. This effect is unaffected by decade distance and can only be explained by access to number words so that the decades were identical (“80–6” vs. “80–15”). Overall, our data indicate that verbal representations can shape basic numerical judgments and that number processing may be more closely tied to language than previously assumed.

Arithmetic skills are crucial for mastering everyday life up to old age. However, it is unknown whether the interplay of different task characteristics affects arithmetic performance differently in older and younger adults. The aim of this study was to investigate whether older adults show deficits in arithmetic fact retrieval besides general slowing. Older (≥ 60 years) and younger adults (18 – 34 years) solved single-digit arithmetic problems in a verbal production paradigm. Arithmetic performance and strategy use were assessed for all four basic arithmetic operations (addition, subtraction, multiplication, division), varying in problem size (small vs. large). Older adults were slower than younger adults in all operations except multiplication. Older adults were able to preserve a similar problem size effect, as they used fast retrieval strategies more often than younger adults to solve large single-digit problems (except for division). While older adults can retrieve arithmetic facts equally well as younger adults, they are slower when using procedural strategies. Overall, this study suggests that older adults do not show deficits in arithmetic fact retrieval but their arithmetic fact knowledge is even superior to that of younger adults and therefore can compensate for some of the age-related domain-general cognitive deficits.

Arithmetic fact retrieval deficits in acute stroke patients can arise after the severing ofwhite matter connections within left temporo-parietal areas (Smaczny et al., 2023). Thecurrent study examined white matter disconnections in multiplication, subtraction, andaddition in patients in the chronic stage of stroke. The strongest effects were found inmultiplication, where the disconnection of long-term memory parahippocampal areaswas strongly associated with lower multiplication scores. Lower subtraction scoreswere related to interhemispheric thalamus disconnections and weakly withdisconnections within the left hemisphere language network. The results for additionproblems were equivocal, yet they were in line with the literature, stating that additioncan be solved by either fact retrieval or magnitude processing. The multiplicationresults are in line with the view that the neuroanatomical correlates of arithmetic factretrieval deficits in chronic stroke point at a relearning deficit, the subtraction results arein line with bilateral redundancy of the magnitude processing network, and all resultstogether suggest that number operations are more in line with strategy-dependentprocessing than operation-dependent processing.

UNSTRUCTURED Digital and web-based at-home tests are increasingly important in neuropsychological assessments, providing various advantages (e.g., automated response recording, standardization, time, and cost savings). Extensive comparability between standard paper-based and online testing has been demonstrated, in particular, among adults. Evidence of test-mode effects (i.e., differences between paper-based or online testing) in older adults (> 60 years), who often show minor digital adoption (e.g., affecting visual, perceptual, cognitive, and physical abilities) attributed to typical age-related changes, is limited. The present study compared the test-mode effects between supervised paper-based and web-based at-home testing using an unconscious but systematic neuropsychological phenomenon, the pseudoneglect, in simple (number) line bisection and number line estimation tasks in N = 77 neurologically healthy over (n = 41 males and n = 36 females over 60 years). Results showed that the pseudoneglect was present in both testing environments in all (number) line bisection tasks, while test mode did not affect this systematic perceptual bias or its variance. However, web-based at-home online testing resulted in a larger skew (i.e., more s-shaped curvature) of estimation in all number line estimation tasks. This bias can be explained by the amended response format (pencil vs. computer mouse) and the age-related inexperience with the test mode. In conclusion, we consider only online line bisection tasks in older adults to be directly comparable to paper-pencil testing, with all the advantages of online data acquisition.

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

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.

It is still a matter of scientific debate whether the line bisection bias frequently observed in patients with spatial neglect is due to attentional underawareness of the left end of the line, attentional hyperattention towards the right end, or a logarithmically compressed perception of the line. To address this question, neglect patients who showed a line bisection bias were administered additional tasks involving horizontal lines (e.g., number line estimation tasks). Their performance was compared to neglect patients not showing a line bisection bias, patients with right hemisphere damage without neglect, and healthy controls. Results indicated that patients with a line bisection bias tended to overestimate lefthand segments when they had to dissect lines into three or four equal parts. This is congruent with both the notions of an underawareness of lefthand segments as well as a logarithmic compression of the line. However, when these patients had to imagine the lines as bounded fraction number lines ranging from 0-1, the results were mixed. When the number lines ranged from 0-10, these patients showed rightward overestimation biases for the numbers 4 and 5. Additionally, all patient groups, but not healthy controls, tended to place number 1 too far to the left and number 9 too far to the right, suggesting a general bias towards endpoints. In sum, this seems more congruent with attentional accounts than a perceptual one. Spatial-numerical associations could be ruled out, as all participants showed a verbal number bisection bias towards smaller numbers (i.e., the ‘left’ of the mental number line). Therefore, these findings seem to indicate that the line bisection bias is most likely due to underawareness of the left end rather than hyperattention towards the right or a logarithmic perception of the line.