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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. 

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). 

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. 

We will focus on unpacking ‘current conceptions of validity’ and an argument-based approach to validation. 

The focus of this special issue is validity-related issues within mathematics education. This is an introduction to a broader set of articles focusing on validity-related issues in mathematics education. 

The purpose of this working group is to bring together scholars with an interest in examining the research on quantitative tools and measures for gathering meaningful data, and to spark conversations and collaboration across individuals and groups with an interest in synthesizing the literature on large-scale tools used to measure student- and teacher-related outcomes. While syntheses of measures for use in mathematics education can be found in the literature, few can be described as a comprehensive analysis. The working group session will focus on (1) defining terms identified as critical (e.g., large-scale, quantitative, and validity evidence) for bounding the focus of the group, (2) initial development of a document of available tools and their associated validity evidence, and (3) identification of potential follow-up activities to continue the work to identify tools and developed related synthesis documents (e.g., the formation of sub-groups around potential topics of interest). The efforts of the group will be summarized and extended through both social media tools (e.g., creating a Facebook group) and online collaboration tools (e.g., Google hangouts and documents) to further promote this work.