Paul Newton (2010), with his characteristic concern about theory, has set out two different ways of thinking about the basis upon which equivalences of one sort or another are established between test score scales. His reason for doing this is a desire to establish "the defensibility of linkages lower on the continuum than concordance."…

This article presents the author's rejoinder to thinking about linking from issue 8(1). Particularly within the more embracing linking frameworks, e.g., Holland & Dorans (2006) and Holland (2007), there appears to be a major disjunction between (1) classification discourse: the supposed basis for classification, that is, the underlying theory…

"Linking" is a term given to a general class of procedures by which one represents scores X on one test or measure in terms of scores Y on another test or measure. A recent taxonomy by Holland and Dorans (2006; Holland, 2007) organizes the various types of links into three broad categories: prediction, scale aligning, and equating. In…

Newton's article (2010) makes three main contributions to the literature. First, it is transatlantic, bringing together literatures that have been dealing with similar problems, using sometimes different methods and certainly with distinctive educational, cultural perspectives. He points out that neither of these literatures has all of the…

The article "Thinking About Linking" by Newton (2010) presents a novel philosophical perspective on the way that educational assessments should be linked. Newton starts by describing the linking framework as it was characterized in various publications and identifies a cross-cultural dimension in the definitions and uses of test…

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…

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…