The purpose of this study is to identify the self-reported research-based instructional and assessment practices used by third through fifth grade teachers among rural school environments in Western Pennsylvania which have attained Adequate Yearly Progress (AYP) pursuant to statewide assessments. Specifically, this study examines the…

The Treatment Integrity Planning Protocol (TIPP) provides a structured process for collaboratively creating a treatment integrity assessment within a consultation framework. The authors evaluated the effect of the TIPP on the implementation of an intervention designed to improve the consistency of students' mathematics performance. Treatment…

This article offers an account of a doctoral insider research project that became problematic. The project was investigating mathematics teaching in a university in the UK, and by contrasting the research account with research diary entries pertaining to two interviewees, different interpretations of the interview data are evident. These…

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…

The Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project is a longitudinal study of student learning from two types of mathematics curricula: integrated and subject-specific. Previous large-scale research studies such as the National Assessment of Educational Progress (NAEP) indicate that numerous variables are…

Notes that students often find difficulty with the language used in the learning of and assessment of mathematics. Reports on a study that analyzes questions from a 1996 Higher School Certificate Mathematics in Society examination in New South Wales. Makes suggestions on changing the language of the assessment to make the mathematics in it more…

Presents an alternative to using a single-class-period test to assess a college student's knowledge in the mathematics area. Evaluation of student mathematical knowledge and understanding of concepts is improved when students are given opportunities to design problems and solutions, applying classroom-acquired knowledge to new situations. Such…