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Background: Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'., Aims: The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels., Sample: Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later)., Methods: Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured., Results: Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2., Conclusion: Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2., (© 2024 British Psychological Society.)

Interest in socioeconomic differences in academic motivation has been longstanding. However, previous research has often treated both low- and high-SES students as homogenous groups. This study aims to address this gap by investigating the developmental trajectory profiles of mathematics motivation during early adolescence, with a focus on variations within and across SES groups. Multigroup latent class growth analysis was used on a sample of 3718 early adolescents in China (initial M age was 9.40 ± 0.52 years; 48.0% girls) across 2 years from grades 4 through 6. The analysis identified three distinct self-determined mathematics motivation trajectory profiles within each SES group: a good-quality profile (i.e., initially high autonomous but low controlled), a high-quantity profile (i.e., initially high both autonomous and controlled), and a low-quantity profile (i.e., initially low both autonomous and controlled). A greater proportion of low-SES students were observed within the low-quantity profile than within the good-quality profile. The study found that the failure-is-enhancing view was a protective factor against two relatively maladaptive motivational trajectory profiles (i.e., high-quantity profile and low-quantity profile), irrespective of socioeconomic background. These findings emphasize the importance of implementing motivational interventions for early adolescents that consider both structural factors (e.g., socioeconomic backgrounds) and psychological factors (e.g., failure beliefs), to foster students' academic development., (© 2024. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik [1].

The Abbreviated Math Anxiety Scale (AMAS) is one of the most popular instruments measuring math anxiety (MA). It has been validated across several linguistic and cultural contexts. In this study, we investigated the extent of administration method invariance of the AMAS by comparing results (average scores, reliabilities, factorial structure) obtained online with those from paper-and-pencil. We administered the online version of the AMAS to Polish students. Results indicate that psychometric properties of the AMAS do not differ between online and paper-and-pencil administration. Additionally, average scores of the AMAS did not differ considerably between administration forms, contrary to previous results showing that computerized measurement of MA leads to higher scores. Therefore, our results provide evidence for the usefulness of the AMAS as a reliable and valid MA measurement tool for online research and online screening purposes across cultures and also large similarity between administration forms outside an American-English linguistic and cultural context. Finally, we provide percentile and standard norms for the AMAS for adolescents and adults (in the latter case for both online and paper-and-pencil administration) as well as critical differences for the comparison of both subscales in an individual participant for practical diagnostic purposes.

Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians. [ABSTRACT FROM AUTHOR]

Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in the literature before, but a systematic analysis of these two kinds of proofs and of their relation was lacking. We propose a general proof-theoretic framework for handling both kinds of coinduction arising in Horn clause logic. To this aim, we propose a coinductive extension of Miller et al's framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic.

RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish behavioral properties of cubical functional programs embodying the constructive content of proofs. Notably, RedPRL implements a two-level type theory, allowing an extensional, proof-irrelevant notion of exact equality to coexist with a higher-dimensional proof-relevant notion of paths.

The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings,” Demonstr. Math. 53 (2020), 38–43.

The first sentence in the abstract should be replaced with the sentence "A sequence $(x_{k})$ is called arithmetically convergent if for each $\varepsilon > 0$ there is an integer $n_{0}$ such that $|x_{m} - x_{}| \geq n_{0}$, where the symbol $< m, n >$ denotes the greatest common divisor of the integers $m$ and $n$".

Many researchers have tried to understand why some learners engage in and others disengage from mathematics by exploring learners' mathematical identities. Significant others (i.e., teachers, peers and family members) offer learners' different opportunities for mathematical identity support, but no study has explored their collective role in supporting or constraining learners' identities. In this paper, we explore how relationships between high school learners and different groups of significant others shaped learners' narrated mathematical identities. Fifty Grade 10 learners responded to a mathematical identity questionnaire. After analysing the results of the questionnaire, six learners were purposively selected for a semi-structured interview, and the interview data were analysed thematically. Identities are described as robust-leaning, mixed or fragile-leaning, depending on learners' narrated confidence, persistence, beliefs and sense of belonging to or exclusion from mathematics communities. Relationships with teachers, peers and family members are described as robust-enhancing or fragile-enhancing, depending on the kind of identity encouraged by the relationships. The findings show that many learners narrated fragile-leaning identities, and all the learners showed some robustness and fragility in their identities. The more groups of significant others a learner developed robust-enhancing relationships with, the more likely the learner narrated a robust-leaning identity. We argue that understanding learners' identities requires understanding their relationships with the three different groups of significant others as a collective.

Being able to understand, interpret, and critically evaluate data is necessary for all individuals in our society. Using the PreK-12 Guidelines for Assessment and Instruction in Statistics Education-II (GAISE-II; Bargagliotti et al., 2020) curriculum framework, the current paper outlines five evidence-based recommendations that teachers can use to build understanding of statistical investigation and data analysis for students with mathematics difficulties, including: (1) Explicitly teach important vocabulary related to statistical investigation and data analysis, (2) Introduce the steps and purpose of statistical investigation, (3) Guide students through the statistical investigation process, (4) Link investigative questions to word problem types to solve, and (5) Build understanding of variability throughout.

Reports on diagnostic testing of eighth grade students' performance using two different methods. Concludes that the computer version was significantly more difficult than the other. Suggests that students may perform mathematics differently due to the characteristics of the mediums used. (RT)