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How teachers collectively address conflicting beliefs about reforms and come to privilege some over others is critically important in understanding instructional change and stability. The paper aims to discuss this issue.

Drawing on in-depth qualitative data gathered in interviews and observations of teachers’ formal collaboration time, this study focuses on teacher dialogue to examine the voicing and debate of teachers’ beliefs about reform efforts in their schools. Specifically, in two urban middle schools engaged in math instructional reforms, what are the conditions of teachers’ collaboration time that shape their dialogue about the feasibility of these reforms?

The findings reveal that the beliefs teachers voice vary widely depending on the topic of conversation. Teachers’ conversations about student achievement data and tracking elicited doubts about the possibility of instructional change, and conversations about other forms of student data and instructional strategies elicited a wider range of beliefs. Further, opportunities to meet with trusted colleagues as well as with wider groups provide teachers with different, but both useful experiences in exploring their own conflicting beliefs.

Avenues for shifting institutionalized beliefs about instruction in schools that have struggled to embrace equitable instructional practices for struggling students are discussed, along with implications for future research.

There is considerable research highlighting the characteristics of productive collaboration, but this paper provides a deeper understanding of the way teachers collectively negotiate beliefs about instructional changes in schools struggling to meet that mark.

This chapter provides a synthesis of the research project which investigated whether or not the most recent mathematics curriculum reform has reached the classroom and influenced classroom practice and student learning in the mainland China. Three types of evidence for change as a result of the curriculum reform were examined. These included the beliefs and perceptions of teachers about learning and teaching mathematics, the cognitive features of learning tasks and of classroom interaction that were implemented in classroom, and student learning outcomes. Two groups of elementary math teachers and their students participated in the study. One group had participated in the reform implementation in classroom for several years, and the other group had used the conventional curriculum when the project was conducted in 2005. About 150 videotaped class sessions were analyzed from 58 classrooms of the two groups. Survey methods were used to probe the changes in the beliefs and perceptions of teachers about teaching and learning mathematics. The student learning outcomes were assessed for three times with multiple measures of mathematics achievement. Findings of the project provide the converging evidence that the curriculum reform has resulted in some of the expected changes. Reform teachers were more likely to hold a dynamic view of mathematics and to indicate the importance to provide students the learning opportunity to hypothesize, to proof, and to communicate in learning mathematics. The reform classrooms used more learning tasks with higher cognitive demands. The teachers in the reform classrooms asked more questions that required students to describe procedures leading to their answers and the students in the reform classrooms raised more questions in learning mathematics. Students of the reform classrooms showed to have achieved a relatively more balanced development in different cognitive areas of mathematics achievement.

As early as 1928, Lewis Meriam’s research report to the Secretary of Interior indicated that American Indian and Alaska Native (AI/AN) schools were understaffed, had irrelevant curricula, and employed under qualified teachers. There continues to be a categorical need for professionally developed curriculum materials that reflect the local culture and language of AI/AN students. There is an equivalent need for instructional strategies that can succeed with AI/AN students. Over the past decade, reports (Deyhle & Swisher, 1997; Pavel, 1999; Swisher & Tippeconnic, 1999) have reinforced the need for educational programs for AI/AN schools and communities that are based on local culture and employ a group’s vernacular language as a part of schooling. This is a reversal from earlier more assimilationist models of education, which have been promulgated by the federal government through its policy on first language (other than English) and cultural exclusion. This call for programs based on culture and vernacular language is due, in part, to the persistent nationwide gap in the academic performance of AI/AN students and their non-native peers (Berlak, 2001).

The purpose of this paper is to explore what professional knowledge and competence (PKC) that knowledgeable others, namely, mathematics teaching research specialists (MTRS) in China, need to know, and how they may develop their PKC.

This study adopts mixed methods. A survey on PKC with 549 MTRS is utilized to examine MTRS’ perceived held and ideal PKC and perceived effective ways of developing their PKC. The responses to the open-ended questions on the survey were used to identify additional dimensions of PKC and ways of developing PKC. Multiple techniques of quantitative data analysis were employed to feature the characteristics of PKC and structure of the survey, and the relationship between background variables and perception of PKC. Collectively, this study paints a rich and comprehensive picture about Chinese knowledgeable others’ knowledge and competence, and its development.

The data analysis reveals that the participants appreciated the six-dimension model of MTRS’ PKC. They were confident with their PKC in general, but varied in different aspects. The factor analysis showed the six-dimension model could be further clustered into two components: knowledge about mathematics teaching and learning and competence in mentoring and educational leadership, and knowledge about content, assessing student learning, and use of technology. The participants perceived their learning through multiple ways including: learning through reading, attending specific training programs, attending and mentoring teaching research activities both school-based and across regions, observing and debriefing lessons, sharing within online learning communities. All these venues jointly contribute to developing MTRS’ PKC.

This is the first empirical study on MTRS’ PKC and its development in China based on such a large sample. The findings of this study not only contribute to an understanding of knowledgeable others in Chinese lesson study and providing suggestions for support of their development, but also provide implications for studies of practice-based mathematics teacher-educators globally.

Being numerate involves the ability to use mathematical knowledge meaningfully across multiple contexts allowing us to order our day, optimise our health and well-being, and function in technology rich environments. Addressing numeracy from the early years of learning, and across all areas of the education curriculum, is key to lifelong learning and quality of life. Being numerate, however, is more than mathematical knowledge; the language that underpins it heavily impacts how we become numerate. This chapter examines numeracy, or mathematical literacy, investigating how literacy can include, and exclude, students from opportunities to learn at school and beyond. This chapter will also examine how numeracy can be used to provide access to educational curricula and personalised goals for students with diverse learning needs in ways that many have ignored.

College placement assessments in the USA have underperformed in predicting college readiness. This has prompted a wave of reforms to placement practices and policies. Recently, student preparation for placement assessments has come to the forefront as a means for enabling better evaluation of college readiness. In this study, the authors explored the effects of an intervention aimed at preparing students for precollege placement assessments. The intervention focused on the provision of mathematics discipline-specific literacy skills because demonstrating mathematical mastery depends on students’ ability to read, understand and translate text into mathematical computations.

In this study, the authors used a randomized control trial design. The design enabled the authors to draw causal inferences while examining the effects of a placement assessment preparation intervention on mathematics placement and course outcomes. The authors also examined the intervention’s effect across incoming first-year college students with varying levels of readiness.

Findings demonstrated a positive and significant effect on assessment scores and placement for intervention participants with a stronger effect for those with higher levels of readiness. Intervention participants exhibited comparable academic success outcomes as those who did not receive the intervention.

Little assessment research has explored the intersection of mathematics and literacy skills in relation to college readiness assessment. In addition, findings support the utility of preparation for college placement assessments.

Over the past 20 years, research on the role of mathematical proficiency in academic and economic success has proliferated. Understanding how mathematical development and learning can be fostered in both in- and out-of-school settings is key to ensuring widespread numerical literacy. Much of what is known about how children develop mathematical knowledge and the educational practices that support such development come out of high-income countries. Widening the lens of research to include children and youth across languages, cultures, and contexts is essential to informing practices and policies across the globe. From pre-primary through primary grades, this chapter examines the increasing emphasis on supporting mathematical development in early childhood, efforts to move away from memorization-based instruction toward support of conceptual understanding, out-of-school influences on mathematical learning, and promising instructional practices.

Students with emotional and behavioral disorders (EBD) are known to experience academic deficits across core subject areas such as reading and mathematics. Until recently, less attention had been paid to the academic deficits of students with EBD. This was due, in part, to a common belief that academic deficits could not be addressed until problem behaviors were under control. However, within the past decade, we have seen an increase in studies investigating and documenting the academic characteristics of students with EBD and instructional practices that improve the academics of this population. This chapter discusses the general academic characteristics of students with EBD, how teachers can address the academic needs of students with EBD through specific instructional techniques (e.g., Direct Instruction, Strategy Instruction), and future directions and implications for practice.

In school improvement studies, randomized experiments are rare. A special problem is the assignment to the experimental and control groups, taking into account the different starting conditions at the schools in terms of school improvement competencies. The purpose of this paper is to take the example of an intervention study conducted in Baden-Württemberg, Germany, the extent to which the challenges involved with a quasi-experimental design were addressed is examined.

The intervention study was conducted with 54 math teachers (experimental group: n=29; control group: n=25) and their grade 7 and 8 classes (n=1,054) at 13 secondary schools. It aimed to increase teacher cooperation on teaching for promotion of students’ self-regulated learning. T-tests, Mann-Whitney tests, ANOVA, multilevel regression analyses were conducted.

At the beginning of the intervention, the teachers in the two groups did not differ significantly in prior cooperation on teaching processes and in attitudes toward cooperation. However, they differed in prior cooperation on school framework conditions and teaching processes. The intervention was effective in increasing teachers’ cooperation intensity on instruction, and teachers’ attitude toward binding cooperation. However, teaching processes did not change depending on experimental or control group.

Teacher cooperation practice was assessed only by teachers’ self-report. No indicators on the quality of the cooperation among teachers were included.

The paper discusses the challenges and limitations of conducting intervention studies on school improvement. Implications for further research are given.

This paper fulfils an identified need to study how quasi-experimental designs can be implemented in intervention studies on school improvement.

Teachers in the USA have been conducting lesson study for more than ten years since it was introduced from Japan in the late 1990s. Although interest in conducting lesson study in the USA is still strong and greater numbers of teachers have become involved in this professional learning, there are significant obstacles to conducting high quality and effective lesson study that enhances teachers’ content and pedagogical knowledge, as well as improving their instruction and student learning in classrooms. Because of the needs of improvement in lesson study in the USA, so it can be administered effectively and sustained, the purpose of this paper is to discuss the current status of lesson study in the USA, what high quality and effective lesson study is, and what ideas might be help to improve lesson study in the USA.

In this paper, issues that are common barriers to conducting effective lesson study, such as: US teachers’ misunderstanding or lack of understanding of lesson study; teachers’ insufficient knowledge of content, pedagogical content, curriculum knowledge; lack of support from administrators for lesson study; non‐systematic approach to implement lesson study; and having short‐sighted vision to conduct lesson study will be discussed. The discussions are based on the author's 12 years of experience working with teachers, schools, and school districts in the USA, interactions and information exchanges with other lesson study educators and researchers and professional development coordinators in schools and districts in the USA, and existing research documents in the USA. Through this discussion, the author attempts to provide suggestions for improving lesson study in the USA.

In order for lesson study to be successful, teachers need to think of lesson study as a way to improve their own learning as well as student learning. Spending more time studying mathematical content and curriculum, developing a strong pedagogical content knowledge with colleagues, and establishing a professional community of learning through lesson study will help it to be effective for improving classroom teaching and learning.

The paper provides some helpful suggestions for improving quality and effectiveness of lesson study in order to improve: classroom teaching – teacher's content, pedagogical content and curriculum knowledge; and student learning. The paper is particularly valuable for lesson study practitioners, and administrators and staff developers who are implementing lesson study in schools.