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Research on arithmetic uses different experimental paradigms. So far, it is unclear whether these different paradigms lead to the same effects or comparable effect sizes. Therefore, this study explores how different experimental paradigms influence mental arithmetic performance, focusing on understanding the potential differences and similarities in cognitive processes between paradigms. Six paradigms were systematically compared: decision paradigms (verification, forced-choice, delayed forced-choice) and production paradigms (written production, verbal-keyboard production, and simple verbal production). The results show consistent arithmetic effects related to operation (addition vs. subtraction) and task difficulty (with or without carry/borrow) across all paradigms, particularly in reaction time measures. However, accuracy varied between paradigms, with verbal-keyboard production and simple verbal production paradigms showing higher effect sizes for accuracy measures. These findings underscore the importance of considering each paradigm's specific demands and characteristics in arithmetic research, suggesting that paradigm selection can influence the observed outcomes. Our study provides critical methodological insights that can guide future research in the design and interpretation of arithmetic tasks, enhancing the reliability and ecological validity of findings in numerical cognition., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest., (Copyright © 2024. Published by Elsevier B.V.)

Two implicit generalizations are often made from group-level studies in cognitive experimental psychology and their common statistical analysis in the general linear model: (1) Group-level phenomena are assumed to be present in every participant with variations between participants being often treated as random error in data analyses; (2) phenomena are assumed to be stable over time. In this preregistered study, we investigated the validity of these generalizations in the commonly used parity judgment task. In the proposed Ironman paradigm, the intraindividual presence and stability of three popular numerical cognition effects were tested in 10 participants on 30 days: the SNARC (Spatial-Numerical Association of Response Codes, i.e., faster left-/right-sided responses to small/large magnitude numbers, respectively; Dehaene, Bossini, & Giraux, 1993), MARC (Linguistic Markedness of Response Codes; i.e., faster left-/right-sided responses to odd/even numbers, respectively; Nuerk, Iversen, & Willmes, 2004), and Odd (i.e., faster responses to even numbers; Hines, 1990) effects. We replicated the group-level effects; however, they were reliably present in only four to five (SNARC), six (MARC) or five (Odd) of 10 participants. Fluctuations seemed unsystematic, although the SNARC effect decreased over time along with reaction times. No correlation between the SNARC and MARC effects and sleep duration, tiredness, daytime, and consumption of stimulants were detected in most participants. These results challenge the frequent generalizations from group-level phenomena to individual participants and from single sessions to typical behavior. The innovative Ironman paradigm combined with bootstrap analyses permits unique insights into the intraindividual presence and stability of cognitive phenomena., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest with the content of this article., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

Reading/writing direction or number word formation influence performance even in basic numerical tasks such as magnitude comparison. However, so far the interaction of these language properties has not been evaluated systematically. In this study we tested English, German, Hebrew, and Arab participants realizing a natural 2 × 2 design of reading/writing direction (left-to-right vs. right-to-left) and number word formation (non-inverted vs. inverted, i.e., forty-seven vs. seven-and-forty). Symbolic number magnitude comparison was specifically influenced by the interaction of reading/writing direction and number word formation: participants from cultures where reading direction and the order of tens and units in number words are incongruent (i.e., German and Hebrew) exhibited more pronounced unit interference in place-value integration. A within-group comparison indicated that this effect was not due to differences in education. Thus, basic cultural differences in numerical cognition were driven by natural language variables and their specific combination., (Copyright © 2014 Elsevier B.V. All rights reserved.)

In recent years, a strong functional relationship between finger counting and number processing has been suggested. Developmental studies have shown specific effects of the structure of the individual finger counting system on arithmetic abilities. Moreover, the orientation of the mental quantity representation ("number line") seems to be influenced by finger counting habits. However, it is unclear whether the structure of finger counting systems still influences symbolic number processing in educated adults. In the present transcultural study, we pursued this question by examining finger-based sub-base-five effects in an Arabic number comparison task with three different groups of participants (German deaf signers, German and Chinese hearing adults). We observed sub-base-five effects in all groups, but particularly so for both German groups who use an explicit sub-base-five system in their finger counting habits. It is concluded that bodily experiences--namely finger counting--influence the structure of the abstract mental number representations even in adults. Thus, the present findings support the general idea that even seemingly abstract cognition may at least partially be rooted in our bodily experiences., (Copyright (c) 2010 Elsevier B.V. All rights reserved.)

Most models of number recognition agree that among other number representations there is a central semantic magnitude representation which may be conceptualized as a logarithmically compressed mental number line. Whether or not this number line is decomposed into different representations for tens and units is, however, controversial. We investigated this issue in German participants in a magnitude comparison (selection) task in which the larger of two visually presented Arabic two-digit numbers had to be selected. Most importantly, we varied unit-decade-compatibility: a number pair was defined as compatible if the decade magnitude comparison and the unit magnitude comparison of the two numbers would lead to the same response (e.g. 52 and 67) and as incompatible if this was not the case (e.g. 47 and 62). While controlling for overall numerical distance, size and other variables, we consistently found compatibility effects. A control experiment showed that this compatibility effect was not due to perceptual presentation characteristics. We conclude that the idea of one single number line representation that does not additionally assume different magnitude representations for tens and units is not sufficient to account for the data. Finally, we discuss why decade effects were not found in other experimental settings.