Teachers’ Attitudes Towards Their Pupils’ Mathematical Errors

This article is mainly concerned with the didactical and the epistemological approach towards pupils’ errors in mathematics. The findings of an investigation into a representative sample of Cypriot teachers’ attitudes of errors in mathematics are presented. Although teachers draw on behaviourism as a way of understanding pupils’ errors, a considerable number of teachers seem to be influenced by both cognitive science error theory and the obstacle theory. Inferential statistical analysis revealed that teachers’ attitudes of errors are mainly associated with the attendance of a specialised INSET course in mathematics. Teachers who attended the INSET course in mathematics are generally more influenced by the cognitive science theory and the obstacle theory. Implications for the development of policy on teacher training are discussed. It is argued that with appropriate training teachers will be able to adopt a model of interpreting errors in mathematics based on the didactical and the epistemological approaches.     

Training higher education teachers’ critical thinking and attitudes towards teaching it

Teachers play a crucial role in attaining a major objective of higher education: fostering students’ critical thinking (CT). Yet, little is known about how to foster teachers’ own CT-skills and attitudes towards teaching CT. In a quasi-experimental study (N = 54), we investigated whether a three-session teacher training on (teaching) CT (n = 32) positively affected higher education teachers’ CT-skills and their attitudes towards teaching CT compared to a control condition (n = 22). The training consisted of explicit instruction on common reasoning biases combined with assignments focused on the teaching practice. Results showed that the training improved teachers’ performance on trained but not on novel CT-tasks. Also teachers’ ability to detect biases in a written student product improved; however, despite a small improvement, they still had difficulties in correctly explaining those biases. Possibly due to ceiling effects the training did not affect perceived relevance of teaching CT. Finally, perceived competence in teaching CT decreased temporarily after the first training session but this negative effect disappeared after the final third session. Future research should investigate ways to promote teachers’ ability to transfer trained skills to other CT-tasks, their ability provide feedback on students’ reasoning (i.e., bias explanation), and their attitudes towards teaching CT.     

学生所知道的 教师所知道的——理论、工具和结果

评估——无论采用何种形式——不得不建立在对不同水平和质量的理论思考基础之上。其中至关重要的是测验内容领域要依据教与学的过程来构建。其次,任务是评估相关内容结构的核心工具。因此,在设计对数学的教育评估时,按照合理的标识和特征对任务进行分类就成为一个息息相关的问题,也是一个巨大的挑战。本文重点研究PISA(国际学生评估项目的缩写,是以数学素养为目标的国际比较研究,包括在国家层面德国所做的许多调整)和COACTIV(德国教师数学知识和数学教学知识的一个代表性研究)。两者都旨在实现区分性评估(differentiated assessment),都考虑了评价内容和任务分析的不同方面。区分性评估结果使得我们能够获取有用的信息,进一步推动课堂教与学的发展。这些信息主要表现为两个方面:评估学生不同类型的知识,这些知识类型直接指向课堂教学与学习中存在的各种问题;探索教师知识对学生学习进展的影响,表明哪种教学行为是有效的。     

Variations of Symbolic Power and Control in the One-to-One Computing Classroom: Swedish Teachers’ Enacted Didactical Design Decisions

This study provides new insights into Swedish teachers’ didactical designs when handling two contemporary challenges regarding the new national curriculum and the increasing digitalisation of schools through one-to-one computing initiatives. The research questions consider how teachers organise physical and digital resources in their classrooms as well as variations in teachers’ pedagogical communication. From a study of 23 one-to-one computing classrooms (using tablets), some ethnographic-inspired methods were applied based on classroom observation and recordings of teachers’ teaching. The findings show two distinct forms of teachers’ classroom organisation that indicate different didactical designs used by teachers to integrate one-to-one computing into the classroom. Variations in teaching resulted in a shift of symbolic power and control from teachers to students, which exploit the potential of using one-to-one computing in the classroom.     

Elementary school mathematics teachers’ perception of their professional needs

This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.     

Pre-service teachers’ questions about the profession during mentoring group conversations

The use of mentoring group conversations as a tool to support pre-service teachers’ professional development has become more common. However, there is still a lack of research that shows how conversations are used to develop knowledge. The present paper is based on ethnographical observations of mentoring group conversations, and describes how pre-service teachers who participate in an obligatory mentoring model use their conversations as an arena in their search for professional knowledge. Three areas were focused upon during the conversations: the teachers’ role and teaching practice, conditions for professional development and conditions related to the profession. The pre-service teachers mainly used conversations to question, discuss, share and reflect over pedagogical and didactical dilemmas related to teaching activities in the classroom and to their own as well as other teachers’ behaviour and attitudes in different situations. The paper provides an insight into how a mentoring model can contribute to professional preparation.     

Primary Teachers’ Beliefs About Children's Development

The paper is a report of recent research on the beliefs about children's development held by a sample (n=28) of good teachers of primary school history. The argument centres on two questions, concerning: (1) good practice as the basis for the improvement of teachers’ practice generally; and (2) the applicability of psychological perspectives to teachers’ practice. Evidence is reported under four headings namely, teachers’ estimates of the ages at which children succeed on tasks, their ability to engage in task analysis, their view of children's error and their view of developmental accounts. The main conclusion drawn is that the answer to the two questions is negative and positive respectively. The implications of this conclusion for the implementation of the National Curriculum are discussed, leading to the claim that extra help and in‐service training for teachers is not merely desirable but strictly necessary.     

Beginning student teachers’ teacher identities based on their practical theories

In this article, we investigate first-year student teachers’ teacher identities through their practical theories and ask what these practical theories reveal about their emerging teacher identities? This study approaches teacher identity from a dialogical viewpoint where identity is constructed through various positions. The empirical part of this study analysed the practical theories of 71 first-year student teachers in order to determine what kinds of positions are involved in their teacher identity at the beginning of their teacher education and what positions are emphasised. The results showed that when student teachers begin their teacher education, the majority of positions concern didactical issues, that is, how to promote pupils’ studying and learning processes. In addition, student teachers’ teacher identities as teachers strongly emphasise the moral nature of teaching. Contextual issues about school and society and matters related to content, such as the curriculum, had little representation in first-year student teacher identities. On the basis of the results, the role of teacher education is considered in the process of promoting development of student teachers’ teacher identity during their studies.     

高校学生评教有效性的思考

学生评教作为高校教学质量评价的必要环节，已被一些高等院校纳入学校教学管理常规，并在实际的教学过程中发挥着不可替代的作用。文章分析了影响学生评教有效性的因素，提出了提高学生评教有效性的对策，以期最大限度地发挥学生评教的积极作用，促进高校教学质量的稳步提高。     

论继续教育中的普通话语音教学

普通话语音教学针对"中学教师"这一特殊教学对象,存在"因材施教"的实际需求.本文试图总结出部分教学经验,以便更好的为教学服务.     

A Survey of Opinion on Methods of Professional Development for Secondary Heads

This paper describes a school management development programme aimed at developing managerial skills and responsibilities across the whole school staff. The paper describes why there is possibly some antipathy to this topic for in‐service education and training (INSET). The approach chosen was to use teachers’ current managerial tasks as the focus for the development so that in conjunction with extant self‐study materials, teachers could design their own INSET appropriate to their current perceived needs.     

‘X is the odd one out,because the other two are more about the farmland’ – Dutch L1 student teachers’ struggles to reason about grammar in odd one out tasks

Grammatical knowledge is an important part of L1 language education. Nevertheless, teachers find it challenging to convey an in-depth understanding of grammar to their students. Previous research suggests that understanding might be stimulated by focusing on grammatical reasoning. The current mixed-methods study explores the grammatical reasoning of 108 Dutch L1 student teachers’ in odd one out tasks, showing that student teachers struggle with such reasoning tasks. A multilevel regression analysis indicates that their level of grammatical understanding as measured by a Test of Grammatical Understanding (TGU) and the elaborateness of student teachers’ argumentation significantly predict the quality of their grammatical reasoning. Student teachers’ performances were also compared to 14 year old pre-university students’ performances (N = 120). Contrary to what was hypothesized, senior student teachers did not manage to outperform junior student teachers, nor did student teachers outperform pre-university students. The paper discusses plausible reasons for these findings and explores how teacher education might need to shift focus to better develop student teachers’ grammatical reasoning skills.     

福建省高中高级职称教师（历史学科）新课程省级培训组织实施的分析与思考

开展高中高级职称教师省级培训,不断提升新课程背景下高中高级职称教师的教育教学能力,是我院中学教师继续教育的一项重要工作。文章从2009年福建省高中高级职称教师（历史学科）新课程省级培训的组织实施情况、问卷调查反馈、座谈交流等入手,对高中高级职称教师（历史学科）新课程省级培训进行梳理、分析与思考,为提升高中高级职称教师省级培训积累经验。     

Empowering teachers to implement a growth mindset

Research evidences the benefit of students holding a growth mindset. There is also increasing recognition of the influence of teachers’ beliefs on how students perceive their own abilities. Teacher and student beliefs are linked: despite this, there is sparse research investigating teacher mindsets. This research sought to evaluate training aimed at influencing teachers’ mindsets and effecting practice change. A mixed methods design was employed. Six training sessions were conducted across two phases. Phase one consisted of an initial training session to 37 participants. Phase two consisted of five sessions attended by 17 participants. Results found a statistically significant shift between pre- and post-measures of mindset which was maintained after three months. Evaluation indicated increased participants’ knowledge base and confidence. Key themes identified evidenced the impact of the training on sustained change to teacher mindset and practice. Limitations and implications for practice are considered.     

Enactive movement integration: Results from an action research project

In this article, we examine how to integrate movement into teaching. Through action research in four Danish primary schools, teachers and a researcher collaboratively developed movement activities in teaching. The result of the research is a didactical model for Enactive Movement Integration (EMI) containing six categories of bodily practices: to mime, dramatise, gesticulate, shape, imitate, and sense. These can provide pupils with sensory-motor, affective, and intersubjective experiences with the subject matter. We conclude that this didactical model can help teachers plan and conduct Movement Integration (MI) in a way that embraces the pupils’ embodied subjectivity and enactive engagement with the subject matter.     

Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory

In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues’ mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers’ prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.     

绩效导向初中教师培训模式的研究

教师培训是提高教师素质和能力的重要手段,也是推动基础教育改革、加快教育发展的重要举措。为了提高初中教师培训的实效性,文章针对目前教师培训所存在的问题,分析了初中教师群体的特征,从教师培训绩效角度,提出了一种切实可行的绩效导向式教师培训模式。     

冥想训练促进教师健康的探析

通过对冥想训练的内容、作用的分析,指出使用冥想训练来提升教师身心健康、缓解职业倦怠具有良好的可行性:优化教师的注意状态,预防教师情感耗竭;缓解教师的焦虑和抑郁,提高其情绪调节能力;增加教师的人际能力和人际支持从而提高其教学能力;提升教师的创造力和反思能力等。同时介绍了国外对教师实施冥想训练的方案MBWE的思路和内容,藉此为教师职业倦怠的预防和干预提供新的参考框架:通过发展支持性、非评判的空间来培养教师对健康和幸福的自我决定能力;让教师通过体验自身的存在来接纳自我、面对现实,从而能回应生活召唤,做出健康的抉择。