初中农村教师数学知识状况及来源的调查研究——以勾股定理为例

初中农村教师所给出勾股定理的证明方法或思路都是正确的,但是这些证明方法或思路大多来自于教材;"教科书"和"自身的教学经验和自我反思"是初中农村教师发展数学知识的两个主要来源,其次是"作为学习者的经验",接下来是"专业书刊"、"和同事的日常交流"、"课堂听课和教研活动"、"教学辅导资料"、"在职培训"、"网络资源"和"职前教育".促进初中农村教师数学知识发展需要做到:充分利用发展数学知识的一些常见途径,不断扩充发展数学知识的途径.     

Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment

The aim of this study was to investigate how participation and reification of ideas about mathematics teaching are constituted in on-line discussions when prospective primary mathematics teachers analysed video-cases about mathematics teaching. Prospective teachers enrolled in a mathematics methodology course participated for 4 weeks in two virtual learning environments that integrated the analysis of video-clips, on-line discussions and writing essays about key aspects of mathematics teaching. Three aspects were considered relevant to explain the prospective teachers’ learning: the way in which the theoretical information was used to frame and to interpret the events from mathematics teaching; the characteristics of engagement with others participating in the on-line discussions and the role played by prospective teachers’ beliefs. Possible reasons for the importance of these features include the specific questions posed in on-line discussions and the use of video-clips of mathematics teaching. These findings are considered useful in designing virtual learning environments and the kinds of tasks through which the understanding of mathematics teaching and learning-to-notice skills can be developed.     

小学数学探究式课堂教学的探讨

在新课程改革的背景下,教师逐渐意识到探究式教学方式在课堂教学中的重要性,通过探究式教学,不仅可以有效发挥学生在学习以及课堂教学中的主体作用,进而促进学生专业能力以及综合素质的提升,而且有助于学生在进行探究式学习的过程中提高其思考、分析以及解决问题的能力,进而实现课堂高效教学。在小学阶段的数学教学中采用探究式的教学方式,可以充分调动学生数学学习兴趣,使其自愿参与到数学课堂教学中,同时,促使学生自主思考和分析学习中的数学问题,进而获得探究及创新能力的发展。     

Exploring Teachers’ Meta-Cognitive Skills in Mathematics Classes in Selected Rural Primary Schools in Eastern Cape,South Africa

Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving.     

小学数学教学中学生学习兴趣培养的策略分析

对于小学阶段的学生来说,需要具有良好的逻辑推断与理解能力,因此,教师要以学生兴趣为主,为学生提供更为创新有趣的教学模式。本文将以小学数学教学中学生学习兴趣培养的重要性和意义为切入点,对课堂教学提高学生学习兴趣的策略进行简要探讨和分析,为广大教师提供借鉴。     

基于学习进阶的幼儿教师数学核心经验模型建构

幼儿教师数学核心经验主要是指教师在教学实践中形成的数学领域至关重要的概念、能力或技能,对于幼儿的数学学习和教师的数学教学具有至关重要的作用。幼儿教师作为基本的学习者,其专业发展过程符合学习进阶的各项准则,不同职业发展阶段的幼儿教师有着各自不同的进阶轨迹。学习进阶强调学习是一种不断积累和发展的过程,并倡导为不同阶段的学习者设计不同的进阶框架,这为有效推动幼儿教师数学核心经验的发展提供了充分的理论参考。本研究在厘清幼儿教师数学核心经验内涵与结构的基础上,依据学习进阶的主要观点,建构幼儿教师数学核心经验的经验模型,并提出相应的教师培养策略,主要包括加强数学核心经验的学习共同体建设、制订数学核心经验的阶梯式成长方案和完善数学核心经验的质量监测指标。     

Becoming a Teacher of Mathematics

For many years I have engaged future mathematics teachers in activities that focus on emotional dimensions of their learning. Even those teachers who were able to reconstruct themselves as learners of mathematics had difficulties with changing their practice. Through a series of autobiographical stories, I examine my own experiences as a teacher and a learner. These stories—one from a computer class, one from a workshop for elementary teachers, one from college, and one from eighth grade—serve as data from which I draw themes that capture the tensions that I experience as I teach. Sharing these tensions with mathematics teachers has had an impact on the way the teachers talk about their teaching and promises to change how they teach. The paper is written to encourage teacher educators to adopt the practice of sharing teaching and learning stories with their students.     

Prospective teachers’ skills of attending,interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos

This study explores prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Prospective teachers analyzed the mathematics instruction of two teachers through four video clips and proposed alternative instructional ways to support the teaching and learning of mathematics. The results indicated that as prospective teachers examined the teachers’ instructional practices, they increased their level of attending and interpretation to content-specific aspects of instruction rather than focusing on generic dimensions of the instruction. When they watched and compared different characteristics of teachers’ mathematics instruction, they provided more detailed and mathematical instructional suggestions.     

What measures of program quality tell us about the importance of executive function: implications for teacher education and preparation

In recent years, increased attention has been given to executive function and its relationship to the overall learning and development of young children. Because of this, it is essential that educators have the skills needed to effectively facilitate the development of executive function throughout early childhood. The focus of the current paper is to provide early childhood practitioners, teacher educators, and researchers with (1) background information about executive function, and (2) findings from a recent large-scale study that provide preliminary information about specific aspects of the learning environment that may support executive function development. In addition, a discussion surrounding implications for practice, particularly related to supporting pre- and in-service teachers as they acquire the skills needed to effectively support young children’s development of executive function skills, is provided. Finally, potential avenues of future research that focus on understanding the role of the learning environment on executive function development are outlined.     

高中教师代数教学知识的调查研究

代数是中学数学课程的重要部分.在高等代数知识方面,教师能理解一些基础而重要的概念,并掌握公式算法.但理解涉及逻辑知识的一些符号表示的复合命题时有困难.在学校代数知识方面,大多数教师显示出扎实的代数基础知识与技能,特别是常规问题的解法明确,运算准确.高中数学教师具体较为扎实的学校代数与高等数学中有关代数的知识,但在理解学生的学习困难,错误概念等方面有待提高。     

成为批判反思型教师:内涵及其途径——托马斯大学Stephen D.Brookfield教授访谈

斯蒂芬.D.布鲁克菲尔德(Stephen D.Brookfield)教授从批判理论的传统出发来探讨教师的反思。他将反思看作教师不断学习、探究自己教学的方式。当教师开展批判性反思时,他们实际上是对自己作为成人学习者有更清晰的意识;通过反思,教师持续地了解自身,了解他们与同事的关系,了解他们如何对学生施加影响。批判反思型教师不断质疑自己带到教学中的前提假设,尤其是课堂中的权力关系及其相互转换;确保课堂中的权力和权威被负责任地使用从而有助于支持学生的学习,而不是被误用或滥用而使学生感到不公或无益,或者是被胁迫或压制。他提出,每一位教师都可以运用从学生那里收集来的反馈信息、同事的感受、理论学习和对自身经验的反思这四条途径来探查自身的教学假设,寻求教学实践的改善。     

Contradictions,dialectical oppositions and shifts in teaching mathematics

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is οn the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging contradictions and we elaborate on the construct of dialectical opposition to understand the nature of these contradictions and their potential for teacher learning. We provide evidence that discussions about contradictions and their dialectical character in the two groups support teachers to engage differently in mathematics teaching and learning and carry potentials for shifts in the practices that evolve in their classrooms. Our study addresses empirically in the context of mathematics teaching the philosophical claim about the role of contradictions as a driving force for any dynamic system.     

互动教学在弹性力学教学中的实践与探讨

“工程弹性力学”是一门具有代表性的理工科专业课,课程具有重要的工程应用价值,同时也具有一定的理论深度。传统的以教师讲授为主的教学方法较为依赖教师的经验技巧,课堂气氛难以充分活跃,学生也容易陷于抽象概念和复杂公式,而对知识脉络的掌握较为欠缺。基于BOPPPS有效教学法,以学生视角作为教学设计的“参考系”,开展了“引入、学习目标、前测、参与式学习、后测、总结”的渐进式教学环节设计。借助智慧教学互动工具,在多个环节增加了教与学的互动,提升了教师对学生实时学习状态的把握,同时,形成的教学大数据能够为调整和改进教学提供有效依据。     

Using mathematics strategies in early childhood education as a basis for culturally responsive teaching in India

The objective of this small study was to elicit responses from early childhood teachers in India on mathematics learning strategies and to measure the extent of finger counting technique adopted by the teachers in teaching young children. Specifically, the research focused on the effective ways of teaching mathematics to children in India, and examined teachers’ approach to number counting. In India, children were taught by their parents or by their teachers to use fingers to count. The qualitative study conducted by the researcher further enriched the topic with first‐hand comments by the teachers. Although the finger counting method was not the only process that teachers would adopt, it was embedded in the culture and taken into consideration while infusing mathematics skills. The teachers confirmed adopting the Indian method of finger counting in their teaching strategy; some specified that the method helped children to undertake addition and subtraction of carrying and borrowing, as counting by objects could not be available all the time. Although the study is limited by its small sample to the unique mathematics learning experience in India, it provides readers with a glimpse of culturally responsive teaching methods and an alternative mathematics teaching strategy.     

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.

     

融合内容的教学知识之课例研究

借鉴Kahan等的教学过程和基本要素研究框架,以情意原理、序进原理和活动原理作为解析课堂教学的框架,调查师范生融合内容的教学知识的实然水平。师范生的教学水平大致分布在三个等级上,师范生对学与教的理解有明显的缺失。如果师范生对知识的发生发展过程认识较为深刻,那么知识教学的序列安排就与知识发生的历史过程拟合得较好;如果师范生对做数学的一般机制有一定的体会,那么学生思维过程的设计就与历史上人们做数学的活动经验较为相似。数学发生发展的知识是影响师范生课堂教学水平的重要因素之一。     

基于有效教学的小学数学教学设计例谈

有效教学是对当前课堂存在各种问题的一种理性思考。试图根据学生学习数学的特点,从教材处理、问题设计、导学组织和练习设计四个层面来展开,以发展学生的数学学习经验和规划解决数学问题的步骤为着眼点,提出有效教学的教学设计思路和方法。     

Elementary School Teachers' Beliefs about the Role of Technology in 21st-Century Teaching and Learning

Technological advancements have led to changes in the expectations placed on K-12 teachers. Teachers are now expected to better equip students with 21st-century skills, making it important to understand teachers' beliefs about the role of technology in teaching and learning and the skills their students need to be successful. Using a qualitative approach, the current study explores these beliefs among a group of urban elementary school teachers in the southeastern United States. Results suggest that, although teachers see the value of technology for teaching and learning, they require more guidance on what constitutes 21st-century skills and how to effectively integrate technology.     

Teaching anxieties revealed: pre-service elementary teachers’ reflections on their mathematics teaching experiences

Over the last 50?years, there has been ample research dedicated to mathematics anxiety in contexts of teaching and learning. However, there has been less attention focused on pre-service teachers’ anxieties about teaching mathematics in classroom settings. This study analyzed pre-service teachers’ reflections at the conclusion of an elementary mathematics field experience in order to determine common themes surrounding anxiety-related events based on mathematics practice-teaching experiences. Through qualitative analysis of pre-service teachers’ reflections using open and axial coding, three categories and ten themes surrounding elementary pre-service teachers’ anxiety-related events based on mathematics practice-teaching experiences emerged. Some of the themes presented were ones that increased pre-service teachers’ anxieties for teaching mathematics, whereas other themes reflected aspects of the field experience that decreased anxiety for teaching mathematics. Based on the themes revealed in this study, suggestions for strategies and materials that could be developed for university mathematics methods courses are discussed. Novel perspectives for considering mathematics teaching anxiety, such as locus of control and future time perspective, are shared.     

STAFF DEVELOPMENT AND “THE FOURTH REVOLUTION”

The paper‐‐an abbreviated version of the author's Conference address‐‐argues that we are in the midst of a learning revolution with which all of us, academics and students alike, must come to terms. The lecture and the printed word, as the sole means of communication in tertiary education for the large percentage of teachers and students, may be challenged. As student needs diversify, teachers will no longer be able to function using traditional skills but will need to develop new skills. It should be their duty to acquire these skills before they begin a life time of teaching