In this rejoinder, the authors further detail their positions on the role of gaps analyses in mathematics education research as outlined in the previous 2 articles. They clarify areas of agreement and probe areas of disagreement, focusing on the benefits and dangers they see in either emphasizing educational disparities between groups or shifting…

There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused on measuring this knowledge. In this article, we describe an effort to conceptualize and develop measures of teachers' combined…

This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh's actions, this article…

The purpose of this article is to investigate the mathematical practice of proof validation--that is, the act of determining whether an argument constitutes a valid proof. The results of a study with 8 mathematicians are reported. The mathematicians were observed as they read purported mathematical proofs and made judgments about their validity;…

This article discusses issues associated with statistical testing conducted with data from clustered school samples. Empirical researchers often conduct tests of statistical inference on sample data to ascertain the extent to which differences exist within groups in the population. Typically, much school-related data are collected from students.…

As an alternative to statistical testing, effect size has a non-monotonic linkage with practical importance. Besides random variance and systematic bias, a proper interpretation of effect size hinges on its implication to outcomes of deductive and/or inductive enquiries. Consequently, a small effect size might suggest an important finding, and the…

The purpose of our article is to illustrate the use of mixed methods research as necessary to uncover maximum information and perspective, increase corroboration of the data, and render less biased and more accurate conclusions. This study used the case study method to closely examine the people, issues, programmes and topics related to the…

This research aimed to explore the attitudes of teachers of practically based subjects (arts and sports) towards ability grouping. Teachers from 45 secondary schools adopting different levels of ability grouping completed a questionnaire which elicited their responses to statements of beliefs about ability grouping and its effects. Overall, the…

Increasingly, academic institutions are being required to improve the validity of the assessment process; unfortunately, often this is at the expense of reliability. In medical schools (such as Leeds), standardized tests of clinical skills, such as "Objective Structured Clinical Examinations" (OSCEs) are widely used to assess clinical competence,…

Restorative Practices (RPs) in schools developed out of growing interest in Restorative Justice in the community. Schools looking for strategies to address disaffection, behaviour difficulties and violence were attracted by the key ideas: the need to restore good relationships when there has been conflict or harm; and develop a school ethos,…

The study reported in this article examines the nature of anxiety that undergraduate students experience in a research methods course and explores some of the factors that influence their anxiety levels. Two questionnaires measuring the attitudes towards research and the anxiety level were administered to 472 students enrolled in a research…

The application of educational research to practice remains an issue of concern, and yet there has been relatively little consideration of this in relation to reviews of research. While the professional user review hitherto represents the most relevant approach, this involves users applying the findings of an earlier review rather than carrying…

School systems may be usefully characterized according to Turner's proposed ideal types of sponsored and contest mobility. Germany is a critical case with respect to this typology because its secondary school system is stratified and selective, and yet it offers the opportunity for upward and downward mobility. Drawing on an analysis of a German…

Research on curricular choices has attracted widespread attention and merits increased investment by the research community. Multiple studies, publications, conferences, and a multicampus center (The Show-Me Project, n.d.) speak to the need to discuss what is taught in the classrooms and to whom, how, and when. Since the 1990s, with the creation…

Enacting the vision of NCTM's "Principles and Standards for School Mathematics" depends on effective teacher professional development. This 7-year study of 48 projects in the National Science Foundation's Local Systemic Change Through Teacher Enhancement Initiative investigates the relationship between professional development and teachers'…