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1. A model of students’ conceptions of equivalence.

   Wladis, C.; Offenholley, K.; Sencindiver, B. (July 2021, Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education)

   Inprasitha, Maitree; Changsri, Narumon; Boonsena, Nisakorn (Ed.)

   In mathematics education, much research has focused on studying how students think about the equals sign, but equality is just one example of the larger concept of equivalence, which occurs extensively throughout the K-16 mathematics curriculum. Yet research on how students think about broader notions of equivalence is limited. We present a model of students’ thinking that is informed by Sfard’s theories of the Genesis of Mathematical Objects, in which she distinguishes between operational versus structural thinking (e.g., 1995), which we conceptualize as a continuum rather than a binary categorization. Sfard also describes a pseudostructural conception, in which the objects that a student conceptualizes are not the reification of a process. We combine Sfard’s theory with a categorization of the source of students’ definitions, where stipulated definitions are given a priori and can be explicitly consulted when determining whether something fits the definitions, while extracted definitions are constructed from repeated observation of usage (Edwards & Ward, 2004). We combine these theories with inductive coding of data (open-ended questions, multiple-choice questions, and cognitive interviews) collected from thousands of students enrolled in a range of mathematics classes in college in the US, to generate categories of students’ thinking around equivalence. We see this model as a tool for analysing students’ work to better understand how students conceptualize equivalence. With this model we hope to begin a conversation about how students tend to conceptualize equivalence at various levels, as well as the ways in which equivalence is or is not explicitly addressed currently in curricula and instruction, and what consequences this might have for students’ conceptions of equivalence. 

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2. Born this way: individuality is seeded before birth and robust to environmental stress

   https://doi.org/10.32942/X2ZH27  

   Gallagher, James; Perkes, Ammon; Chang, Chia-Chen; Chirila, Emma; Kacevas, Karen; Laskowski, Kate (September 2025, EcoEvoRxiv)

   Consistent individual differences in behavior, known as behavioral individuality, are pervasive across the animal world and have major ecological and evolutionary consequences. Nevertheless, we still have a limited understanding of what drives individuality and how it emerges during ontogeny. Here, we subjected clonal individuals to a ubiquitous yet critical environmental challenge—the threat of predation—to disentangle the developmental mechanisms of individuality. Under such a salient environmental stressor, among-individual differences may collapse or expand depending on whether there is a single or multiple optimal strategies, demonstrating that individuality itself is a developmentally plastic trait. If, however, the environment does not impact among-individual variation, this suggests that individuality is determined before birth. We continuously tracked the behavior of genetically identical fish (Amazon mollies, Poecilia formosa), reared with or without predation stress, from birth through their first month of life. Predation shifted mean-level behaviors, with predator-exposed individuals swimming more slowly and spending more time near their refuges. However, the magnitude of individuality (as evidenced by repeatability) increased similarly over development in both treatments, indicating that individuality crystallizes robustly over time, even under stress and in a vacuum of genetic variation. Predator-reared fish also exhibited greater within-individual variability in refuge use, suggesting increased behavioral flexibility or disrupted developmental canalization in response to stress. Surprisingly, maternal identity, but not maternal behavior, was the strongest predictor of swimming speed, pointing to non-behavioral maternal effects as a key pre-birth source of behavioral variation. Refuge use however was not at all predicted by maternal identity, indicating that major fitness-related behaviors can have entirely different developmental mechanisms. Collectively, we show that individuality persists despite environmental stress and is seeded before birth through non-genetic factors. Even in the face of a shared environmental challenge, the behavioral trajectories of individuals are unique. 

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3. What Makes People Join Conspiracy Communities?: Role of Social Factors in Conspiracy Engagement

   https://doi.org/10.1145/3432922  

   Phadke, Shruti; Samory, Mattia; Mitra, Tanushree (January 2021, Proceedings of the ACM on Human-Computer Interaction)

   null (Ed.)

   Widespread conspiracy theories, like those motivating anti-vaccination attitudes or climate change denial, propel collective action, and bear society-wide consequences. Yet, empirical research has largely studied conspiracy theory adoption as an individual pursuit, rather than as a socially mediated process. What makes users join communities endorsing and spreading conspiracy theories? We leverage longitudinal data from 56 conspiracy communities on Reddit to compare individual and social factors determining which users join the communities. Using a quasi-experimental approach, we first identify 30K future conspiracists?(FC) and30K matched non-conspiracists?(NC). We then provide empirical evidence of the importance of social factors across six dimensions relative to the individual factors by analyzing 6 million Reddit comments and posts. Specifically, in social factors, we find that dyadic interactions with members of the conspiracy communities and marginalization outside of the conspiracy communities are the most important social precursors to conspiracy joining-even outperforming individual factor baselines. Our results offer quantitative backing to understand social processes and echo chamber effects in conspiratorial engagement, with important implications for democratic institutions and online communities. 

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4. We Have Never Been Sophisticated

   https://doi.org/10.31389/pop.370  

   Bradley, Clara; Weatherall, James Owen (June 2026, Philosophy of Physics)

   Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed, on the grounds that such theories posit “excess structure”. In an influential paper, Dewar [2019, “Sophistication about Symmetries”, Brit. J. Phil. Sci. 70: 485–521] introduces a distinction between “reduction” and “sophistication” as alternative ways of removing excess structure. In this paper we re-examine the distinction as Dewar draws it, and we argue that there is no physically or philosophically important distinction between what Dewar calls “reduction” and what he calls “internal sophistication”. We then argue that there are multiple notions of “reduction” in the literature that ought to be distinguished, both in motivation and in outcome. 

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5. We the swarm—Methodological, theoretical, and societal (r)evolutions in collective decision-making research

   https://doi.org/10.1177/26339137221133400  

   Garnier, Simon; Moussaïd, Mehdi (October 2022, Collective Intelligence)

   Collective decision-making constitutes a core function of social systems and is, therefore, a central tenet of collective intelligence research. From fish schools to human crowds, we start by interrogating ourselves about the very definition of collective decision-making and the scope of the scientific research that falls under it. We then summarize its history through the lenses of social choice theory and swarm intelligence and their accelerating collaboration over the past 20 or so years. Finally, we offer our perspective on the future of collective decision-making research in 3 mutually inclusive directions. We argue (1) that the possibility to collect data of a new nature, including fine-grain tracking information, virtual reality, and brain imaging inputs, will enable a direct link between plastic individual cognitive processes and the ontogeny of collective behaviors; (2) that current theoretical frameworks are not well suited to describe the long-term consequences of individual plasticity on collective decision-making processes and that, therefore, new formalisms are necessary; and finally (3) that applying the results of collective decision-making research to real-world situations will require the development of practical tools, the implementation of monitoring processes that respect civil liberties, and, possibly, government regulations of social interventions by public and private actors. 

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