Qualified Pedagogical Reflection as a Way to Improve Mathematics Education

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments. May the teacher know what he teaches. May the teacher know how to teach. May the teacher be sincerely interested in teaching. Comenius     

A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development

This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator–researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implementing their own conjecturing activities during the workshops, the MTE-R fostered their professional learning and growth through reflection upon students’ performance. From the perspective of activity theory, this study examined the evolution of the MTE-R’s mentoring activities and tools whose design gradually changed from being based on the literature content toward being learner-centered activities with teachers as learners. Such evolution not only enhanced teachers’ learning outcomes, but also facilitated the MTE-R’s own professional growth in different areas, including mathematics, mathematics learning, mathematics teaching, teacher education, and, in particular, the extrapolation of generic examples for understanding mathematical concepts.     

论基于《标准》的职前教师专业能力形成机理

职前教师的专业能力培养是高等师范教育的基本任务。教师专业能力具有职业的特殊性,以解决教育教学实际问题为目标导向。《中学教师专业标准（试行）》把教师专业能力划分为六大领域,各领域之间具有相互支撑、相互促进的关系。作为职前教师的师范生需要发挥自身主体性,积极参与学习、实践和反思,指导教师需要为师范生提供支持,为其创设有利于各领域能力成长的学习环境。师范生六大领域专业能力的形成机理各有特点,需要师范生和教师的协同配合。     

Research-based and hands-on practical teacher education: an attempt to combine the two

This article, based on the analysis of responses given by 27 students in initial teacher education, gives an account of how education theory can be conceived by students as relevant to their teaching practice. Research on teacher education in many countries has revealed that students regard theory and practice to be inconsistent or to belong to different worlds in initial teacher education. This may have a potentially negative effect on the teachers’ opportunities for future professional development, as such development should be based on the ability to view one’s own teaching practice from a critical, theory- and research-based perspective. In the research and development project reported in this article, the PIL-project, the students’ teaching practice was chosen as the pivotal point for all the other activities involved in the teacher education programme. Results indicate that when questions emerge from the students’ own experience, theory is often found useful in discussing and understanding their practical experiences. The results further show that the students’ choice of theory when discussing their teaching practice is eclectic. Students tend to choose theory with direct relevance to their daily tasks in the classrooms. The implication for initial teacher education is that the educational theory taught should more often address the immediate challenges faced by the students doing their teaching practice.     

解读教师专业素养——基于专家教师和教研员的视角

在促进以发展学生核心素养为理念的课程改革中,教师专业素养至关重要.本文结合对专业素养、特别是教师的专业素养文献的介绍,描述了一项启发式研究(Elicitation Study).通过对上海地区一线教育研究工作者(主要指教研员和专家型教师)关于教师专业素养的观点的调查,研究刻画出他们对教师专业素养的认识,包括专业素养的主要成分;并且指出不同职称、学段的教育研究工作者对教师专业素养的不同观点.希冀能启发并指向在后续研究中提出更合理、更细目化的教师专业素养模型,促进教师专业的发展,最终达到发展中国学生核心素养的目标.研究结果显示,从一线教育研究工作者(以数学学科为例)的观点中,我们可以得到教师专业素养是一个多维度的概念,它包含教师知识等在内的诸多因素,以及这些因素交互作用所产生的个人特征;具有较高职称的、工作于高中学段的教育研究者对教师专业素养的观点与其他工作者有明显差别.     

发展性教师评价视域下高校青年教师评价机制的构建

发展性教师评价是以发展为导向的形成性评价,其根本目标在于提高教师的职业道德修养,促进教师创新素质提高,促进教师发展需要与学校发展需要的统一和融合。从发展性教师评价视域下观之,目前高校青年教师在成长过程中存在着专业化发展断层和评价指向偏差等问题。构建科学、有效的发展性教师评价机制,有利于高校青年教师的成长与发展。     

When Teaching Makes a Difference: Developing science teachers’ pedagogical content knowledge through learning study

It is a common view that developing teachers’ competence to restructure or reframe their knowledge and beliefs is inevitably a complex challenge. This paper reports on a research project with the aim to develop science teachers’ pedagogical content knowledge (PCK) through their participation in a learning study. A learning study is a collegial process in which teachers work together with a researcher to explore their own teaching activities in order to identify what is critical for their students’ learning. During one semester, three secondary science teachers worked in a learning study together with a researcher in a cyclical process in order to create prerequisites and further identify conditions for students’ learning. During the learning study, data were collected from video-recorded lessons and stimulated recall sessions in which the teachers and the researcher reflected on the lessons to analyze their development of PCK, their students’ learning and the impact of that knowledge on their own teaching. The results provide an insight into how the teachers developed their self-understanding in which they questioned their own epistemological beliefs, aims and objectives of teaching and taken-for-granted assumptions about science teaching and learning. As such, the study provides an understanding of teacher professional learning through a careful investigation of how teachers’ PCK is enhanced through their participation in the learning study, and further, how students’ learning might be developed as a consequence.     

Noticing Children’s Learning Processes – Teachers Jointly Reflect on Their Own Classroom Interaction for Improving Mathematics Teaching

One could focus on many different aspects of improving the quality of mathematics teaching. For a better understanding of children’s mathematical learning processes or teaching and learning in general, reflection on and analysis of concrete classroom situations are of major importance. On the basis of experiences gained in a collaborative research project with elementary school teachers, several ideas about a professional reflection on one’s own instruction activities are explained. The paper focuses on joint reflection between teachers and researchers on the participating teacher’s own classroom interaction by means of concrete examples. It becomes clear that changes of one’s own interaction behavior will take place only in the long-term. Nevertheless such a joint professional reflection should be an essential component of teachers’ professional knowledge in a natural way.     

美术教师专业化发展探析

美术教师专业化发展是教育发展的需要,也是教师发展的需要。在数码技术高度发达的现代社会,美术教师要注重自我的专业化成长,才能进一步适应社会发展及教育发展的需要,才能在教学过程中更好地引导学生进行美术活动,从而建立高尚的审美品格和正确的人生观、道德观,才能真正促进学生自身素质的发展。美术教师专业化发展体现在教学行为的转变、教学技能的发展、教学领导力的提升、自身文化底蕴的累积、专业技能的扩容和教科研能力的提高等多个方面。     

论幼儿教师实践智慧的优化策略

幼儿教师实践智慧作为关注幼儿成长需要、应对教学活动突发事件以及支持教师专业成长的重要因素,在引导幼儿身心成长和促进教师专业发展中起关键作用,是当前学前教育研究的热点领域。其优化途径和策略的探索发掘也是当前众多学者普遍关注的问题。基于对幼儿教师实践智慧存在价值与基本理念的认识,文章提出尊重幼儿教师个体的实践创造、加强幼儿教师的专业实践训练、建立幼儿教师实践智慧共享机制、鼓励幼儿教师进行实践反思与自我超越的优化途径和策略,旨在帮助幼儿教师在其专业实践中更好地获得、分享自己的实践智慧,促进专业成长,为幼儿成长提供更为优质的指导。     

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.     

Integrating the ontological,epistemological, and sociocultural aspects: a holistic view of teacher education

The three aspects of teacher change – ontological, epistemological, and sociocultural – are traditionally regarded as independent. Usually only the epistemological aspect is highlighted in formal teacher education. In this paper, I argue that a holistic and interdependent view of these aspects is needed. Thus, this paper aims to explore the process of teacher learning from a holistic perspective. Through deliberative discussions and selection, 13 ‘good’ teachers were interviewed in this study. The findings indicate that there may be a two-stage pattern (the II-VA model) that describes two different sorts of teachers. The first sort refers to those teachers who developed strong identities before beginning their teaching service and who tended to have a clearer educational vision which had a direct impact on their practices and professional development. As for the second sort, the teachers’ identities were vague in their first years of teaching, but their professional identities gradually developed within the referential community with affective and professional functions. These stages imply that we should replace ‘abstract theory’ with ‘subject reflection’ in the center of teacher education. Three kinds of reflection (theory-rationale, identity-integration and vision-accomplishment) are thus identified from a holistic view of teacher change.     

职业学校“学生评教”利弊分析

教师教学工作评价已经成为各级各类学校进行绩效管理的主要任务之一。职业教育学校因其发生发展的历程以及人才培养目标和培养模式的特色,在教师教学工作评价方面也应该呈现出不同的倾向性。目前将"学生评教"作为教师教学工作评价唯一方法存在很大的局限性,因此,将"教师职业评价"的概念及具体方法作为一种建议引入职业教育教师工作评价中对教师职业成长具有更重要的意义。     

The Promise of Teacher Inquiry and Reflection: Early Childhood Teachers as Change Agents

In this article, a preschool teacher and an early childhood teacher educator describe and analyze their work co-creating and co-facilitating an early childhood inquiry group over seven years. The group consisted of veteran lead teachers, assistant teachers, instructional coaches, and an outside teacher educator at an urban, public preschool in San Francisco, California. Using the framework of narrative inquiry and portraiture, the article tells the story of the group’s formation, its structure, and its benefits for the participants’ personal and professional growth. The authors argue that an inquiry group is a highly viable, home-grown form of professional growth that relies on the group as a forum for self-study and reflection. The inquiry group provided the teachers with an increased understanding of child development and instructional strategies, a trusting public forum for sharing and validating their inquiry and teaching, and a communal opportunity to make visible the voices of teachers, children, and families.     

反思能力是幼儿教师专业发展的关键

反思能力对幼儿教师的专业发展具有重要的推动作用。幼儿教师要想获得专业发展,必须深刻认识反思的意义,了解反思能力及幼儿教师专业发展,理解反思能力对幼儿教师专业发展的意义。     

In search of the excellent literature teacher. An inductive approach to constructing professional teaching standards

This study makes a contribution to the development of empirically based, domain-specific teaching standards that are acknowledged by the professional community of teachers and which, therefore, have a good chance of being successfully implemented and used for professional development purposes. It was prompted by the resistance on the part of many teachers to the one-size-fits-all teaching standards imposed on them from above. We, therefore, looked for an alternative and canvassed teacher opinion about what makes an excellent literature teacher. Because our standards will be used to evaluate the profession, we also wished to know to what extent teachers satisfy (or would like to satisfy) their own ideal, and which factors influence their professional development. Contrary to earlier studies, we found that the professional community of literature teachers hold widely shared ideas about what constitutes excellence in their profession. We also found that almost 40% felt that their own level of professionalism fell far short of excellence, but that their professional growth was primarily hampered by external, contextual factors. If the government wishes to promote teacher ‘excellence’, the infrastructure for professional development will need to change so that teachers can acquire the knowledge and skills embodied in the teaching standards.     

中小学教师的工作效能与专业成长

中小学教师的工作效能对于自身的专业成长和学生全面发展至关重要。考察中小学教师的工作效能,需要辨识教育者胜任工作的特征,考察影响其工作效能的多种因素以及评价中小学教师工作效能在实践中的不同模式。中小学教师工作效能的提升具有多层面的途径和策略,包括基于自我效能感的实践反思、基于专业(实践)共同体的同伴互助、基于学习型组织的学校管理变革。     

Teachers’ experience from a school-based collaborative teacher professional development programme: reported impact on professional development

The aim of this study was to find out how science teachers who have participated in a one-year school-based collaborative teacher professional development programme, perceive the programme’s impact on their professional development. Constant comparative analysis was used on data from three schools to generate the findings in this study. The results indicate that participating teachers perceived a clear effect on their teaching practice and ways of thinking about teaching science. In addition, the findings identify a positive effect on the teachers’ attitudes towards collaboration. The article further discusses how reflection seems to contribute to the teachers’ professional development.     

Professional primary school teacher identity development: a pursuit in line with an unexpressed image

The results presented in this article are taken from a case study of novice primary school mathematics teachers’ professional identity development from the perspective of the teachers themselves. The empirical material was collected through self-recordings, observations and interviews. The results show how the professional identity development of these novice teachers becomes a pursuit in line with their image of a primary school teacher. To develop a sense of themselves as primary school teachers they need to establish their own criteria - individual (including graduation and personal knowledge) and social (the ability to work in one school, have colleagues and have a class of their own for which they do the planning and teaching). These criteria are shown to be both a precondition for and a part of professional identity development. The novice teachers’ image of what it means to be a primary school teacher directs their actions and becomes the goal of their professional identity development. Because of its high impact, student and novice teachers’ image of primary school teachers ought to be made visible in both teacher education and teacher induction.     

Encouraging teacher development through embedding reflective practice in assessment

Learning to become a teacher is a developmental process, part of which is learning to become a reflective practitioner. The authors have implemented a structured approach to developing the habits of critical reflection, the purpose of which is to guide their university students (who are pre-service teachers) to progress through the stages of teacher development and to facilitate self-motivated professional growth. Their attempts to incorporate into these pre-service teachers' learning the ‘practice’ part of reflective practice have included the development of different kinds of practical and applied tasks. In turn, their attempts to incorporate the ‘reflective’ part of reflective practice have involved the embedding in assessment activities of different scaffolds for metacognitive reflection. Their innovative processes of embedding reflection in assessment have been guided by Dewey's and Schön's views of reflection, their own views of the teacher education process, and Brookfield's conception of ‘critical lenses’ which can be used as a scaffold to structure professional growth and development.