Professional noticing of coordinated mathematical thinking

Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.     

Building a Professional Learning Community: Teachers’ Documentation of and Reflections on Preschoolers’ Work

This study describes teachers’ experiences in a preschool professional learning community (PLC) in order to gain understanding of the role of documentation in group learning. A central underlying assumption of PLCs is that teacher learning involves talking with colleagues about teaching and grappling with the issues embodied in everyday classroom life. We utilized a qualitative case study design in order to emphasize the situated and contextual nature of teachers’ professional learning in context. Data sources included the following: observations of PLC sessions, interviews with participating teachers, and the classroom documentation teachers shared during the sessions. We found that the incorporation of documentation in the PLC made implicit assumptions about children visible in order to be scrutinized. In addition, the teachers’ reflections on the documentation highlighted conflicting notions about teaching as either technical practice or inquiry. In contrast to traditional delivery approaches to teacher learning, we argue that PLCs focused on documentation encourage teachers to problematize practice rather than simplify it. The process of reflecting on children’s work made shifts in thinking about the nature of teaching possible.     

Wordsworth’s ‘We Are Seven’: Reflections on the Secondary English Classroom

English teachers select texts for the edifying qualities they possess: a good poem, novel or film can act both as a window looking out over different lives and as a powerful mirror for reflection. When teachers reflect on their professional practice, however, they generally look to education theory, to research or to action learning strategies. But if great works of literature strengthen a student’s empathetic, critical and reflective capacities, they can do the same for the English teachers who prescribe them. The article does not advocate for a rejection of pedagogical expertise in favour of pure literary criticism, but it does consider that these two aspects of English teaching can be brought together for the purposes of professional reflection and development. Using William Wordsworth’s lyric ‘We Are Seven’ as an example, it aims to illustrate how a close reading of the poem leads naturally and effectively from an analysis of content to more general considerations of why and how we teach.     

Changes in teachers’ beliefs after a professional development project for teaching writing: two Chinese cases

A plethora of research has found that teachers’ beliefs directly influence their classroom practices and teaching outcomes. While numerous studies in second/foreign language writing have examined the effectiveness of different innovative approaches on students’ learning to write, there is a paucity of research on writing teachers’ beliefs about these approaches and how their beliefs change in the process of their professional development. Such a lacuna becomes prominent in English as a Foreign Language contexts, especially in China, where there are numerous calls for changing the nature of classroom practices from product-focused to process- and student-centred instruction. In order to fill this gap, this brief article reports on a case study regarding changes in two Chinese English teachers’ beliefs after attending a professional development project for teaching writing. A key research question guides this study: What changes, if any, did the two teachers experience in their teaching beliefs during the project? Two writing teachers were voluntarily recruited for a case study. Findings show that the professional development project for teaching writing broadened the teachers’ understanding of different writing theories, provided a clear model of how to integrate these new approaches into regular writing courses, changed their instructional focus and shifted their perception of teachers’ roles in teaching practice.     

Teachers’ collaborative learning – development of teaching in group discussions

Teacher learning and the development of in-service education for teachers are both an active area of research and a broad challenge. In working as teachers, theory and practice are often seen as divided, or problems in teaching and the requirements of development are solved on the basis of experience. This study focuses on collaborative teacher learning as part of an in-service education course that supports teachers in connecting learning theories with practical knowledge and that aims to create new knowledge and practices for teaching. The starting points for the study are the changes of the curriculum and theories of learning. The aim is to analyse developing of teaching in teachers’ collaborative group discussions and how the theoretical knowledge of learning theories is connected with developing teaching practices. The research method of the study was data driven, systematic and qualitative analysis of the content of the discussion. The research data consist of video recorded group discussions of two teacher teams from the in-service education course meeting. The analysis focused on developing talk and further, on finding interconnections between the developing talk and the theories of learning. The analysis shows three different ways how the learning theories emerged in method developing talk. The findings indicate that theoretical knowledge can be used or left unused and imply that creating and changing teaching practices is challenging. However, the findings show that theoretical, research-based knowledge on learning theories can be applied to developing teaching practices in the teachers’ collaborative knowledge creation process. Long-term in-service education based on collaborative knowledge creation and supporting the interconnection of theoretical knowledge of learning and experience knowledge of teaching is a promising way to arrange and develop in-service education.     

An international online survey of the practices and perceptions of higher education professors with respect to the assessment of learning in the classroom

In a context where public action must demonstrate its effectiveness and efficiency, and where the links between teaching and the quality of learning are regularly highlighted, it seems relevant to identify the trends and logic that govern university professors’ decisions with respect to the modes of learning assessment favoured within the framework of their delivery of teaching services. Moreover, given that university teaching practices are changing rapidly due to the introduction of different views of the learning process, one might conclude that the same holds for assessment practices. Through our research work, we led to the development of a trilingual (English, French and Spanish) online survey devoted to an international investigation into the classroom assessment practices of higher education teachers. This survey proposes an online platform that will allow institutions of higher learning to document some of their current practices and to compare observed trends with what is happening elsewhere, in accordance with differing missions and traditions. These research notes are thus intended to describe the survey itself and to show how the questionnaire and individual items were structured, in addition to providing an overview of treatments within and between institutions that followed the testing.     

Profile of South African secondary-school teachers’ teaching quality: evaluation of teaching practices using an observation instrument

The need for quality teaching is reflected in the poor performance of students in international tests. Teachers’ practices and contextual factors could contribute to substandard quality of teaching in South Africa. Several studies indicate that successful learning is largely dependent on the teachers’ practices in class. The focus of the present research was to profile the effective teaching practices of 424 secondary-school teachers in the Gauteng Province, South Africa. Teachers were observed by trained observers using a valid and reliable observation instrument measuring six domains of effective teaching practices. Results showed that teachers find it difficult to differentiate in class and to activate learning. Additionally, teachers with more than 15 years of teaching experience scored lower than teachers with less experience, in all six teaching domains. Presumably, experienced teachers may lack motivation and/or insufficient training in implementing interactive and differentiated teaching methods that are needed for effective teaching practices.     

The impact of peer collaboration on teachers’ practical knowledge

Due to changes in Dutch mathematics education, teachers are expected to use new teaching methods such as enquiry-based teaching. In this study, we investigate how teachers design, implement and evaluate new methods for statistics teaching for 7^th-graders during a professional development trajectory based on peer collaboration. We monitored teachers’ development in a network of four mathematics teachers from the same school. By using a mixed-methods approach in which we combined data from interviews, concept maps and classroom observations, we describe changes in teachers’ practical knowledge. We found how the nature of these changes highly depends on teachers’ personal concerns that emerge during the trajectory. Some teachers considered their concerns as challenges stimulating their learning, while other teachers experienced their concerns as a reason to fall back to previous teaching methods. Based on our results, we give some recommendations for organising teacher networks.     

PERCEPTIONS AND PRACTICES OF CULTURALLY RELEVANT SCIENCE TEACHING IN AMERICAN INDIAN CLASSROOMS

This study explores the perceptions of culturally relevant science teaching of 35 teachers of American Indian students. These teachers participated in professional development designed to help them better understand climate change science content and teaching climate change using both Western science and traditional and cultural knowledge. Teacher perceptions of practices using culturally relevant instruction were evaluated. The data were analyzed both quantitatively and qualitatively. The results from the survey analysis show that the teachers’ existing practices of culturally relevant science teaching were limited in choosing topics relevant to American Indian culture. We found three common themes from the teachers’ perceptions of culturally relevant science teaching, meaning of culturally relevant science teaching, teaching strategies, and purpose of culturally relevant science teaching from the qualitative data. We also found that teachers with higher survey scores perceive culturally relevant science teaching differently than teachers with lower survey scores, specifically for the purposes and teaching strategies of culturally relevant science teaching. The results show that teachers with higher survey scores tended to perceive culturally relevant science teaching as a two-way learning process between teachers and students where the teachers can learn traditional science knowledge from the students. They also tend to perceive using concrete traditional science examples as effective teaching strategy for culturally relevant science teaching and building strong relationships with American Indian students as the most important purpose of culturally relevant science teaching. We also discuss common challenges faced by science teachers when trying to implement culturally relevant science teaching with American Indian students.     

A review of pedagogy related to information and communications technology

Abstract

This article reviews research on pedagogies associated with the use of information and communications technology (ICT) in primary and secondary schools. We propose a framework for examining pedagogical practices based on an analysis of the nature of pedagogy as revealed in the literature. In the light of this framework we discuss empirical evidence of the use of different types of ICT in different subjects and phases of education. We identify pedagogical issues associated with ICT use and their implications for teachers' pedagogical reasoning and practices. The evidence suggests that new affordances provided by ICT-based learning environments require teachers to undertake more complex pedagogical reasoning than before in their planning and teaching that incorporates knowledge of specific affordances and how these relate to their subject-based teaching objectives as well as the knowledge they have always needed to plan for their students' learning. In addition the research shows that teachers' beliefs about the value of ICT for learning and the nature of successful learning environments are important in teachers' pedagogical reasoning     

同课异构:教师实践知识习得的有效路径

作为教师学习的同课异构是教师实践知识习得的有效路径,体现了教师学习方式与内容变革的必然性。同课异构的真实性、情境性与互动性内涵及其对教师学习的意义,随着研究的深入而不断丰富。然而,同课异构的现实畸变却影响了其核心精神的实现和教师学习的有效性。为此,我们要构建展现教师的不同风格、面向教师的差异发展与构建教师学习文化的同课异构,使同课异构走向"实"、"精"、"新"。     

Facilitating a culture of relational trust in school-based action research: recognising the role of middle leaders

Abstract

Practices such as formal focused professional dialogue groups, coaching conversations, mentoring conversations and professional learning staff meetings have been taken up in schools and pre-schools as part of long-term action research and development activities to improve the learning and teaching practices. The development of relational trust has long been described in the literature as pivotal for the ongoing ‘success’ of such research and development in sites. In this article, we attempt to re-characterise relational trust as it is accounted for by participants in action research. We present data from a cross-nation study of middle leaders from Australian primary schools and Swedish pre-schools. Middle leaders are those teachers who ‘lead across’; they have both an acknowledged position of leadership or responsibility for the practice development of colleagues and a significant teaching role. The larger study examined the practices of middle leaders; and in this article we draw on interview data from one of the case-study sites that illustrate how colleagues in schools recognise the role middle leaders have for facilitating action research and teaching development. This article specifically presents excerpts from semi-structured interviews with 25 teachers, three principals, three executive teachers and three district consultants. Interviewees described how nourishing a culture of relational trust and mutual respect are critical features in the change endeavour. For them, the practices of the middle leader who facilitated the action research were instrumental in developing trust for teacher development. Analysis of participant accounts revealed five dimensions of trust: interpersonal trust, interactional trust, intersubjective trust, intellectual trust, and pragmatic trust.     

Science and Mathematics Teachers Working Toward Equity Through Teacher Research: Tracing Changes Across Their Research Process and Equity Views

We investigated secondary science and mathematics teachers engaged in a two-and-a-half-year professional development effort focused on equity. We examined how teachers conducting research on their own instructional practices—a central learning strategy of the professional development project—informed and/or constrained their views related to three strands of equity: teachers and teaching, students and learning, and students’ families and communities. Data collected included recordings of professional development seminars and school-site meetings, three sets of individual interviews with teacher researchers, and drafts and final products of the classroom research teachers conducted. From our qualitative analyses of data, we found that most teachers addressed at least two of the three equity strands in researching their own practice. We also found that most transformed their understandings of teachers and students as a result of their teacher research process. However, teachers’ views of families and communities changed in less substantive ways. We close with recommendations for other researchers and professional developers intent on supporting science and mathematics teachers in using teacher research to work toward equity.     

Implications of social network sites for teaching and learning. Where we are and where we want to go

This conceptual paper deals with some of the implications that the use of social network sites, though not originally developed and conceived for learning purposes, have for schools and academic activities when they are used as tools able to modify and innovate teaching/learning practices and academic culture. Beside the differences that characterize the two contexts, the attention that social network tools are progressively gaining in schools and higher education practices and pedagogies requires adjustments in learning and teaching that should be constantly considered by educators and policy makers. These environments are also presenting new and crucial opportunities for teacher training and teachers’ professional development. The purpose of the study is to reflect on some significant challenges and opportunities offered by social network sites, and how to exploit the latter, in relation to a number of themes. These themes have been identified as those that deserve better comprehension and further research investigation: communication between students and teachers and appropriate professional behaviours; pedagogical and technological challenges related to incorporating social networking practices into teaching and academic practices; how social networking can be exploited for teachers’ professional training and development. The study also provides some implications for policy and practice.     

Teachers’ Beliefs About Grading Practices and a Constructivist Approach to Teaching

We examined novice teachers’ beliefs about grading and constructivist teaching approaches. Adapting an existing instrument designed to assess preservice teachers’ grading beliefs that deviate from recommended practices, we administered the Survey of Grading Beliefs to 203 inservice teachers. Exploratory factor analysis resulted in a 3-factor model with a structure similar to that found in prior research; differences between the 2 samples were noted. Teachers who endorsed grading beliefs characterized as “academic enabling” tended to endorse constructivist teaching approaches. To better understand the underlying reasoning of the academic enabling factor, we conducted qualitative research with 6 additional teachers. Results revealed that teachers’ reasons for grading judgments were strategic, analytical, and thoughtful, not haphazard. This study provides empirical evidence about the nature of novice teachers’ beliefs about grading, how they relate to constructivist teaching beliefs, and how they may compare to the beliefs of preservice teachers.     

Interaction Between Science Teaching Orientation and Pedagogical Content Knowledge Components

The purpose of this case study is to delve into the complexities of how preservice science teachers’ science teaching orientations, viewed as an interrelated set of beliefs, interact with the other components of pedagogical content knowledge (PCK). Eight preservice science teachers participated in the study. Qualitative data were collected in the form of content representation, responses to an open-ended instrument, and semi-structured interviews. Preservice teachers’ orientation and PCK were analyzed deductively. Constant comparison analysis of how their orientation interacted with other PCK components revealed three major themes: (1) one’s purpose for science teaching determines the PCK component(s) with which it interacts, (2) a teacher’s beliefs about the nature of science do not directly interact with his/her PCK, unless those beliefs relate directly to the purposes of teaching science, and (3) beliefs about science teaching and learning mostly interact with knowledge of instructional strategies. Implications for science teacher education and research are discussed.     

Technology Integration into the Language Classroom: Developmental Trajectory of Beginning Teachers

This study adds to the current literature on teacher technology integration with an investigation into five beginning teachers’ technology use in the language classroom in their first two career-entry years. The longitudinal interview study reveals that these teachers went through a developmental trajectory of technology use towards using it for more diversified instructional purposes and with a greater orientation towards student learning over the years. The study also finds that the teachers’ developing understanding of technology use intertwined with their growing teaching competency and identity. It further finds that school culture not only had a direct influence on their technology use but also moderated the influence of teaching competency and identity on the nature of this technology use. This study concludes with suggestions for promoting research on the support needed for beginning teachers and the school culture in technology use.     

Teachers’ assessments of students’ learning of mathematics

This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students’ learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers’ knowledge of their students’ understanding of certain mathematical concepts is fairly limited. It then goes on to discuss this phenomenon in terms of a process that can hinder rather than promote learning. The research illuminates the position of teachers who appear to lack certain detailed information about their students which, it can be argued, could inform more effective teaching strategies. The paper concludes by exploring possible implications for similar situations where learning could be enhanced by more effective classroom assessment strategies and their use to inform future teaching and learning activities.