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Mathematics education needs measures that can be used to research and/or evaluate the impact of professional development for constructs that are broadly relevant to the field. To address this need we developed the Priorities for Mathematics Instruction (PMI) survey consisting of two scales focused on the constructs of Explicit Attention to Concepts (EAC) and Student Opportunities to Struggle (SOS) – which have been linked to increased student understanding and achievement. We identified the most critical assumptions that underlie the proposed interpretation and use of the scale scores and then examined the related validity evidence. We found the evidence for each assumption supports the proposed interpretation and use of the scale scores. 

This paper provides a brief introduction to the set of four manuscripts in the special issue. To provide a foundation for the issue, key terms are defined, a brief historical overview of validity is provided, and a description of several different validation approaches used in the issue are explained. Finally, the contribution of the manuscripts to further articulating argument-based validation approaches is discussed, along with questions for the field to consider. 

The purpose of this working group is to continue to bring together scholars with an interest in examining the use of and access to large-scale quantitative tools used to measure student- and teacher-related outcomes in mathematics education. The working group session will focus on (1) updating the workgroup on the progress made since the first working group at PME-NA in Tucson, Arizona, specifically focusing on the outcomes of the Validity Evidence for Measurement in Mathematics Education conference that took place in April, 2017, in San Antonio, (2) continued development of a document of available tools and their associated validity evidence, and (3) identification of potential follow-up activities to continue this work. The efforts of the group will be summarized and extended through both social media tools and online collaboration tools to further promote this work. 

As early as Descartes (1637/1970), logic and reason have been positioned as tools for individuals to advance their own understanding. By contrast, argumentation is an interactive, social exercise used for persuasion, collective cognition, and to advance shared knowledge (Mercier & Sperber, 2011, 2017). When one advances an argument, subjects it to the tests and challenges of others, and responds to questions and counterarguments, one’s thinking improves (Mercier & Sperber, 2017). Through argumentation, groups produce correct solutions more often than individuals (Moshman & Geil, 1998) and individual accuracy improves as well (Castelain, Girotto, Jamet, & Mercier, 2016). Since it was formally introduced by Kane (1990, 1992), the argument-based approach to validation has been promoted in the field of educational and psychological measurement as the preferred method for validating interpretations and uses of test scores (AERA, APA, & NCME, 2014; Kane, 2013; Schilling & Hill, 2007). Scholars continue to debate the best approaches for developing and supporting validity arguments, however (for examples, see Brennan, 2013; Kane, 2007). 

Abstract The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates. 

Abstract We report the observation of gravitational waves from two binary black hole coalescences during the fourth observing run of the LIGO–Virgo–KAGRA detector network, GW241011 and GW241110. The sources of these two signals are characterized by rapid and precisely measured primary spins, nonnegligible spin–orbit misalignment, and unequal mass ratios between their constituent black holes. These properties are characteristic of binaries in which the more massive object was itself formed from a previous binary black hole merger and suggest that the sources of GW241011 and GW241110 may have formed in dense stellar environments in which repeated mergers can take place. As the third-loudest gravitational-wave event published to date, with a median network signal-to-noise ratio of 36.0, GW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar structure of gravitational-wave generation, and the existence of ultralight bosons within the mass range 10⁻¹³–10⁻¹²eV.