Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching

This article is based on one of the several case studies of recent graduates of a teacher education programme that is founded upon inquiry-based, field-oriented and learner-focussed principles and practices and that is centrally concerned with shaping teachers who can enact strong inquiry-based practices in Kindergarten to Grade 12 classrooms. The analysis draws on interviews with one graduate, and on video data collected in his multi-aged Grade 1/2 classroom, to explore some of the ways in which this new teacher enacted inquiry-based teaching approaches in his first year of teaching and to consider his capacity to communicate his understanding of inquiry. This article presents implications for beginning teachers’ collaborative practices, for the assessment of new teachers and for practices in preservice teacher education.     

寻找数学课程中研究性学习的切入点

将一题多解、一题多思作为在数学课程中实施研究性学习的切入点 ,有利于培养学生求异思维和创新思维的发展 ,从而在此基础上进一步提升研究性学习的质量与档次     

Learning in action: creating a community of inquiry in a healthcare organisation

The aim of this paper is to discuss an insider action research project concerned with establishing an audit team, with responsibility for addressing a clinical and social services ‘assurance gap’ at corporate level in a healthcare organisation. The focus of the research account is on the knowledge that was generated internally by establishing the aforementioned team underpinned by an action learning ethos, and through the observed evolution of this team into a community of inquiry. Using the stages within the experiential learning cycle to guide team interventions and our own critical reflection, the authors have different research roles in this study; one has responsibility for the design, recruitment, establishment and management of this audit team, while the other acts as academic advocate in context. The knowledge that emerged from this study and the learning therein has the capacity to be actionable, that is, at the service of both academic and practitioner communities.     

探究性教学在中学数学例题教学中的应用

探究性教学旨在以学生为教学主体,通过教师的积极引导,让学生能够更好进行数学实践活动,对数学知识的学习能有质的飞跃。本文通过对探究性学习在中学数学例题教学中的应用进行合理分析,提出了一些有效的建议。     

小学数学课堂教学设计与反思

教师在课堂教学前进行合理的教学设计,教学就已经成功了一半,同时,教师教学设计的好坏也直接影响学生的学习效果和学习能力的锻炼,因此课堂教学设计显得尤为重要。教学设计中,教师要努力为学生提供一定的动手素材和思想素材,同时把数学问题生活化,贴近学生生活实际,不仅使学生的思维能力得到训练,而且还可减少学生对数学的畏惧感和枯燥感,以便更好地激发出学生学数学的兴趣。     

Reframing one's teaching: Discovering our teacher selves through reflection and inquiry

Learning to teach is a highly complex and multidimensional process. This self-study, conducted collaboratively by a preservice teacher and a teacher educator, traces one preservice teacher's development and growth over a 2-year period. The study examines the complexities of learning to teach, as well as the complexities of assisting preservice teachers on their journey to becoming teachers. The data were derived from multiple sources including observation notes, journal reflections, dialogue journals, and the student's action research/self-study paper. The results provide insight into how preservice teachers think, the conflicts they experience, the fears they encounter, and the benefits they derive from systematically examining their teaching and their students’ learning. The article describes specific attitudes and dispositions that can impact growth and development. In addition, it discusses a variety of activities to foster reflection and inquiry.     

高职经济数学分层教学实践与反思

分层教学是一种适合高职学院现状的数学教学模式。它操作简单易行,成本低,效果好,很值得推广,但也有很多问题需要深入研究。它的重点是准确定位不同层次的教学目标,难点是C层教学的突破。这种教学模式对教师提出了更高的要求。     

Learning mathematics for teaching in the student teaching experience: two contrasting cases

Student teaching (guided teaching by a prospective teacher under the supervision of an experienced “cooperating” teacher) provides an important opportunity for prospective teachers to increase their understanding of mathematics in and for teaching. The interactions between a student teacher and cooperating teacher provide an obvious mechanism for such learning to occur. We report here on data that is part of a larger study of eight student teacher/cooperating teacher pairs, and the core themes that emerged from their conversations. We focus on two pairs for whom the core conversational themes represent disparate approaches to mathematics in and for teaching. One pair, Blake and Mr. B., focused on controlling student behavior and rarely talked about mathematics for teaching. The other pair, Tara and Mr. T., focused on having students actively participating in the lesson and on mathematics from the students’ point of view. These contrasting experiences suggest that student teaching can have a profound effect on prospective teachers’ understanding of mathematics in and for teaching.

Critical stance within a community of inquiry in an advanced mathematics course for pre-service teachers

Journal of Mathematics Teacher Education - This paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes...     

复杂性科学视野下的课堂教学行为研究:反思与重构

教师效能研究的消隐以及教师认知研究和教师生态研究的复兴表明,课堂教学行为研究从简单性范武向复杂性范式的转变是大势所趋。为了提高课堂教学行为研究的效益,在本体论模型上要实现从“简单小系统”向“复杂巨系统”的回归;在价值观操守上要实现从“探究普适性的客观规律”向“寻求情境化的教学意义”的转变;在方法论准则上要实现从“还原论方法”向“系统论方法”的升级。     

Learning environment,self-efficacy for teaching mathematics,and beliefs about mathematics

Learning environment research has a long history of significant relationships between the learning environment and student outcomes. This study investigated relationships between the learning environments of mathematics courses in a teacher education program and two outcomes, mathematics teaching self-efficacy and beliefs about mathematics. These two outcomes have been repeatedly shown to influence the future teaching practices of preservice teachers but, to date, their relationships with learning environment have been investigated neither with preservice teachers nor at all in the United Arab Emirates or wider Gulf region. The learning environment was found to be significantly related to preservice teachers’ mathematics teaching self-efficacy and beliefs about mathematics. Learning environments perceived more favourably by preservice teachers were associated with higher self-efficacy for teaching mathematics, but also with more-traditional beliefs, making these findings important for higher education institutes and teacher educators.

     

Using culturally relevant teaching in a co-educational mathematics class of a patriarchal community

The paper reports on the use of culturally relevant teaching in a class located in a patriarchal community. The paper is conceptualised around the notion that learners’ familiar context provided by the socio-cultural activities can facilitate mathematics learning and make it fun to learn. Data were derived from a lesson activity using semi-structured interviews, observation and video recordings. The findings reveal the prevalence of culturally oriented gender-related stereotypes such as tendency by boys to marginalise girls during the lesson activities and girls, in turn, attribute the treatment to their cultural beliefs and practices.     

Epistemological investigation of classroom interaction in elementary mathematics teaching

In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during the course of ritualized formats of communication, such as the funnel pattern, and is replaced by social conventions. Problems of understanding occurring during the interactively organized elaboration of the new knowledge require an analysis of the interplay between the social constraints of the communicative process and the epistemological structure of the mathematical knowledge. Specific aspects of the problem of meaning development are investigated in the course of two exemplary second-grade teaching episodes. These are then used to develop and discuss decisive requirements for the maintenance of an interactive constitution of meaning for mathematical knowledge.     

Programming-languages as a conceptual framework for teaching mathematics

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called ‘Logo’ adapted to objectify an enduring framework of mathematical experimentation.     

Intercultural language teaching as a catalyst for teacher inquiry

This study investigated how two teachers of languages, facilitated by university researchers, developed their practices with regard to intercultural language teaching. Taking a qualitative case study approach, we collected data from classroom observations, interviews, debriefing conversations, and guided reflective pieces written by the teachers. Findings indicate that the opportunities for teachers to inquire into their own practices shifted these teachers' approaches to language teaching to accommodate a curriculum expectation to develop students' intercultural communicative competence in plurilingual contexts. The study offers valuable insights for teacher education into the ways teachers' inquiries can support teachers’ responses to curricular change.     

BTI口译教学中的研究性学习和研究性教学

随着翻译学科的发展和"翻译专业本科教学质量国家标准"的出台,翻译本科专业人才培养的目标进一步明确。这对教师的教和学生的学都提出了新要求。本文以BTI的口译课程实践为研究对象,探讨把研究性学习和研究性教学方法引入口译课程之中,以期改变传统教学中以知识传授为主的教和学的方式,调动学生的主观能动性,依托学生的实践,使其理解口译工作的过程特点,提高学生口译能力。     

Developing critical reflection as a part of teaching training and teaching practice

Academics in universities can no longer teach in the ways that have been appropriate in the past. The paradigm has shifted from the dissemination of knowledge to a focus on the students and how to facilitate the best learning outcomes for them. This paper proposes that critical reflection is at the heart of being an effective teacher. It invites teachers to evaluate their own philosophies about teaching and to be critically reflective of their own practice. It is suggested that teachers need to learn how to be reflective practitioners through both self-evaluation and the use of collaborative strategies. It is no longer appropriate to focus solely on the 'what', but also on the 'how' and 'why'.     

课堂:作为学习共同体的内涵及特点

课堂,作为学习共同体,实质上是把教师和学生从一种"客位"的生活状态转向一种"主位"的生活状态.课堂作为学习共同体应该具有:教学目标的整体性、学习系统的开放性、学习过程的有序性、成员行为的主体性、师生关系的和谐融洽等特点.课堂,就是教学主体通过交往和对话构成的一个学习共同体,是开展教学活动的舞台,是教师和学生生活的主要场所.