In "International approaches to Science Assessment" Paul Black and Dylan Wiliam describe eight major elements of assessment systems and contrast some of the differences among these elements across seven countries. Of particular interest to the author is an issue that cuts across many of these elements, namely, what gets assessed as part of these…

The review by Black and Wiliam of national systems makes clear the complexity of assessment, and identifies important issues. One of these is "balance": balance between local and central responsibilities, balance between the weights given to various purposes of schooling, balance between weights for various functions of assessment, and balance…

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…

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…

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 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 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…

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…

The American Educational Research Association (AERA) 2007 Call for Proposals points out the need for researchers in education to look beyond their usual sources to other fields that have extensive experience in relevant theories and methods. In transitioning from a response to AERA's Call for Proposals to the text of these articles on Assessing…

The series of articles presented in this journal issue reports a systematic approach to judging the validity of a test within a framework recommended by Kane (2001, 2004a). The authors' approach effectively integrates quantitative and qualitative tools, showing the role of psychometric models in validation, and emphasizes the importance of clearly…

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…

According to Schilling, Blunk, and Hill, the set of papers presented in this journal issue had two main purposes: (1) to use an argument-based approach to evaluate the validity of the tests of mathematical knowledge for teaching (MKT), and (2) to critically assess the author's version of an argument-based approach to validation (Kane, 2001, 2004).…

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 series of papers presented in this issue about Mathematical Knowledge for Teaching (MKT) measures provide a clear and understandable presentation of the issues involved in the validation of new instruments. The authors' commitment to continuing validation studies leads everyone to believe their efforts will result in a high quality instrument.…

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…