This is a response to a focus article by Briggs and Peck (2015) in issue 13(2). It should have been published in issue 13(3-4) alongside a rejoinder by Briggs and Peck that did appear. Due to an oversight, it was not published there and appears here. See issue 13(3-4) for a rejoinder to this response. Briggs and Peck (2015) propose what amounts to…

In assessing the utility of a test, two issues stand out: whether it provides information of interest to test consumers, and whether scores generated by the test assist in making good decisions. Validity addresses these two issues, making an assessment of test validity the single most important product provided by test developers. Unfortunately,…

In this paper, the authors complete the summative stage of the validity argument approach, then use their experiences to reflect on the validity argument as a method. They begin by evaluating the inferences and assumptions of the interpretive argument for the MKT measures. Then they examine both the form and the structure of the interpretive…

Validation efforts typically focus around what, exactly, is measured by an instrument(s), and whether what is measured corresponds to the theoretical domain(s) originally specified. The authors' goal for this article is to build instruments focused around measuring the mathematical knowledge used in teaching: not only the content that teachers…

In this article, the authors provide their critique on a set of papers that investigated Mathematics Knowledge for Teachers (MKT) assessment and the underlying theory and characteristics of the validity enterprise. Three types of assumptions and inferences--elemental, structural, and ecological--are discussed in these papers. These assumptions…

In this issue of Measurement: Interdisciplinary Research and Perspectives, Schilling et al. are explicit about the centrality of assessment design and development and psychometric analysis in validation. Schilling and colleagues, Kane (2004, 2006), other contemporary validity theorists and practitioners, and their predecessors typically discuss…

Schilling et al. (this issue) have done a commendable job in illustrating a comprehensive process of validating assessments of teacher knowledge (and, more broadly, other types of tests as well). On one hand, the concrete illustration of a process that often remains murky and incomplete is profoundly heartening, as it provides a rigorous model for…

In this journal issue, the authors of the focus articles have provided a suite of very stimulating and thoughtful articles. The overarching purpose of this research is to explore the application of principles derived from the view of validity proposed by Kane (2004) to their research on issues related to the measurement of mathematical knowledge…

The authors of this volume's stimulus papers have taken on the challenge of developing measures of teachers' mathematical knowledge for teaching (MKT). This task involves multiple decisions and considerations, including: (1) How does one specify the body of knowledge being assessed? What warrants are offered for those choices?; (2) How does one…

Teacher knowledge has been of theoretical and empirical interest for over two decades, and development of measures is overdue. The researchers represented in this volume have been breaking new ground by developing a measure of mathematical knowledge for teaching (MKT) without guiding precedents, and in the face of differing perspectives on teacher…

Operating from multiple literature bases in cognitive psychology, mathematics education, and theoretical and applied psychometrics, Schilling, Hill and their colleagues provide a systemic approach to studying the validity of scores of mathematical knowledge for teaching. This system encompasses an array of task formats and methodologies. The…

The author offers some thoughts on commentator's reactions to the substance of the measures, particularly those about measuring teacher learning and change, based on the major uses of the measures, and because this is a significant challenge facing test development as an enterprise. If teacher learning results in more integrated knowledge or…

In this article, the author echoes his co-author's and colleague's pleasure (Hill, this issue) at the thoughtfulness and far-ranging nature of the comments to their initial attempts at test validation for the mathematical knowledge for teaching (MKT) measures using the validity argument approach. Because of the large number of commentaries they…

This paper provides a summary of the authors' attempts to uncover links between their measures, classroom mathematics instruction, and student learning. This paper also provides evidence regarding one central critique of their measures: that multiple-choice assessments cannot validly represent the knowledge, skills, and judgment involved in actual…