This study investigated relationships between changes in certain types of coaching knowledge and practices among mathematics classroom coaches and how these explain changes in the attitudes, knowledge, and practice of the teachers they coach. Participants in this study were 51 school-based mathematics classroom coaches in the USA and 180 of the teachers whom they coached between 2009 and 2014. The participating coaches were recruited from schools that hired their own coaches independently from this research project. This study found evidence that improvements in coaches’ use of practices recommended by particular coaching models are related to improvements in teachers’ mathematical knowledge for teaching. The study also found that improvements in coaches’ self-assessment of their own coaching skills are related to improvements in teachers’ mathematics content knowledge for teaching, mathematics teaching practices, and attitudes about self-efficacy for teaching mathematics. The study did not detect relationships between changes in coaches’ mathematics knowledge and changes in teachers’ knowledge or practices.

We examined the impact of a state-mandated K-12 mathematics professional development course on knowledge, self-efficacy, and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics instruction. Inventories utilizing items from the Learning Mathematics for Teaching project measured changes in participants’ Mathematical Knowledge for Teaching (MKT) and an end-of-course self-evaluation enabled analysis of changes self-efficacy and beliefs. Statistically significant changes were found in all three variables. This study adds to our understanding of the potential usefulness of mandating large-scale professional development as a policy vehicle for influencing educators’ mathematics knowledge and beliefs.

This paper describes the effects of a professional development (PD) program – Developing Mathematical Thinking –on student achievement. Six Title I elementary schools with similar demographics, within one school district, werechosen to participate as either a treatment or comparison school. Three schools were chosen to participate inprofessional development that incorporates effective PD recommendations. All the teachers had to participate in allaspects of the PD, thereby eliminating potential self-selection bias. Using the state standardized achievement test as thebefore and after measure, results suggest improved student performance after professional development wasimplemented over a two year period.

In two studies, we examined the effect of professional development to improve mathematics instruction on the accuracy of teachers' monitoring of student learning. Study 1 was conducted with 36 teachers participating in three years of professional development. Judgment accuracy was influenced by the fidelity with which what was learned in the professional development. Study 2 was conducted with 64 teachers from 8 schools, which were randomly assigned to receive professional development or serve as a control. Judgment accuracy was greater for teachers receiving professional development than for teachers who did not and teachers were better to predict students' computational skills.

Mathematics classroom coaching is used across the United States as a means for improving instruction, with the ultimate goal of improving student learning. The job assignments of coaches can vary widely across schools and districts. Regardless of the various forms that coaching can take, there is the consistent expectation that a coach’s day-to-day work will positively influence classroom instruction. The study reported here attempts to gain a more complete picture of the job of an elementary mathematics coach based on the observation of seven coaches in five different districts for a day. We report the variety of ways we observed elementary mathematics coaches interact with teachers, and what roles and responsibilities they take on. Our analysis of these data led us to create a template for conducting observations of mathematics classroom coaching, which could be used by researchers seeking to conduct studies about coaching or by administrators seeking to document the day-to-day work of coaches.

Mathematics coaches represent a unique group of didacticians, or individuals who work with practicing teachers. Twenty-eight mathematics coaches participated in this exploratory study, which used video viewing to examine the coach–teacher dynamic. To gather data about participants’ views of effective coaching practices, we developed the Video Assessment of Coaching instrument, which provided coaches with opportunities to express their views of effective practice and implementation. The participants expressed views of effective coaching that often did not align with those of coaching authors. The significance of this research lies in its efforts to document the views that mathematics coaches develop as practitioners, as an early step in the examination of the relationships between the views of coaches and coaches’ effectiveness in improving teacher practice, knowledge, and attitudes.

Relationships between subject area knowledge of teachers and teacher practice are of interest in understanding the preparation and professional development of teachers as well as in assessing teacher performance. The study explores the relationship between Mathematics Knowledge for Teaching (MKT) and Inside the Classroom – Classroom Observation Protocol (ITC-COP) in a sample of 129 teachers from 25 school districts across seven states. Using linear and ordinal mixed models to account for a random district effect on ITC-COP measurements, modest relationships were identified between MKT and seven of eight different aspects of the ITC-COP.

I do not think any thoughtful researcher today believes that experiments or randomized field trials are the "gold standard" for addressing all the important questions in educational research. Yet, because these designs are now required by the 2001 No Child Left Behind Act (NCLB) and are being strongly encouraged in other federal legislation and funding initiatives, scholars, practitioners, parents, and researchers must devote time and energy to fighting these designs when they are inappropriate or irrelevant, which is often the case. Despite long-standing objections from prominent methodologists and reservations expressed by national groups and committees, key policymakers in the federal government are encouraging the pursuit of experimental designs primarily or exclusively (Eisenhart, 2005, p. 246).

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 our classrooms and to whom, how, and when. For example, the January 2007 issue of JRME focused on research related to the development, implementation, and evaluation of curricula (NCTM, 2007). Williams (2007) commented that one of the challenges we face as a field is determining what questions of practice are worth asking and how research on those questions can help advance the field. Since the 1990s, with the creation of Standards-based curricula, practitioners have had to choose between new and traditional curricula. In addition, the No Child Left Behind Act of 2001 has put pressure on schools to use curriculum materials that are research based and approved by the U.S. Department of Education (n.d.). These two milestones related to mathematics education justify making curricula issues an area that warrants the attention of both the research community and practitioners. The purpose of this article is to highlight advances related to curricular research; pose questions that require further investigation; and describe related, emerging subfields. First, we begin with a brief history of the events that have led us to our current state of curricular affairs. We will also explore a report released by the National Research Committee (NRC) in 2004 that challenged the research community to consider research on curricula issues differently than has been done in the past. Second, we discuss a recent study that illustrates the promise of new methodologies. Third, the Research Committee examines evidence on how the Standards-based curricula have impacted diverse groups of students, since a major goal of the Standards documents was to ensure that all students were provided access to highquality mathematics curricula. Fourth, as another example of progress in curriculum-