Mathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an empirical base, elucidating its educational potential. To pursue this goal, a two-year ethnographic research study has been conducted in a selection of social media communities that exchange mathematical memes. In the paper, a twofold theoretical lens is used to investigate the phenomenon from a memetic perspective focused on the general characteristics of Internet memes, and from a cultural perspective considering the Web 2.0 environment. Analysis tools derived from the memetic and cultural theoretical background are applied to an instrumental case study, to reconstruct how mathematical memes activate the interaction among members of an online community. The investigation elicits key characteristics of the phenomenon, provides grounds to conceptualize mathematical memes as hybrid representations of mathematical statements, and sheds light on the traits of the epistemic culture they establish in the community.

Mathematical Internet memes are examples of how the creative thrust characterising the Web 2.0 environment reaches the field of mathematics, translating mathematical statements into a new digital form endowed with an epistemic potential that is capable of initiating a process of mathematical argumentation. The research presented in this paper aims to shed light on the creative process of mathematical memes, contributing to building a body of knowledge on mathematical memes that, prospectively, could enable educators to profit from these objects in their teaching. Theoretically, this is based on a widened concept of creativity that focuses on the connection linking digital culture with mathematics, and on distinguishing and merging three perspectives to disclose the meanings of mathematical memes. Methodologically, the process of mathematical memes’ creation is investigated through a reverse engineering approach on a dataset of about 2100 items collected in a 3-year-long ethnographic observation within online communities. The result is a heuristic action model of the creation process, that is validated by creating two new mathematical Internet memes that are shared online within the observed communities to explore if they retain the mathematical and epistemic characteristics of Web-found ones.

Understanding students’ opportunities in mathematics education requires tools that capture the social and cultural dimensions shaping their engagement with the subject. One way to conceptualise these opportunities is through the notion of mathematics capital, which encompasses the resources and dispositions that students bring to their mathematical experiences. This study introduces and validates a questionnaire designed to measure secondary students’ mathematics capital, adapting the well-established science capital framework to the mathematical domain. Grounded in Bourdieu’s concept of capital, the questionnaire operationalises mathematics capital across mathematical forms of cultural capital, mathematics-related behaviours and practices, and mathematics-related forms of social capital. The questionnaire was administered to 119 students in an Italian secondary school as part of a broader study on mathematical memes. Statistical analyses, including correlation tests and Cronbach’s alpha, confirm the instrument’s reliability and internal coherence, highlighting the influence of both school and extracurricular environments. The questionnaire provides educators with a practical tool to better understand students’ engagement with mathematics and to inform strategies for fostering equity in mathematics education. By making mathematics capital a measurable construct, this research contributes to discussions on how cultural and social factors shape students’ trajectories in mathematics and beyond.

This paper investigates the unexpected phenomenon that we call multiple documentational genesis, which occurred during a professional development program for in-service mathematics teachers, guided by researchers in mathematics education. It involves the proliferation of uncoordinated teaching materials created by teachers for their students based on the same initial input provided by researchers. To make sense of this phenomenon, we rely on a theoretical model combining the Documentational Approach to Didactics and the Meta-Didactical Transposition frameworks. We find that the logos component of the meta-didactical praxeology shared among the teachers participating in the program guided their documentation work in a way unforeseen by the researchers. Indeed, the teacher’s decision to distance themselves from the researchers’ initial input, perceived as non-coherent with their shared logos, led to a disruption in the co-learning partnership that had consistently characterised the program in prior years. This affected not only the sense of community among researchers and teachers but also the collaborative work among teachers themselves. The experimental findings informed new theoretical perspectives in the form of an adjustment of the theoretical model adopted for data analysis to the specific case of teachers participating in a professional development program.