我对青年教师助课的认识和体会

<正> 高校的青年教师在独立开课前,一般总要经历一个助课的过程,这个过程对他们尽快胜任教师工作是至关重要的。我从事助课工作已有两年,其间遇到许多问题,也有不少思索和尝试,这里就助课工作的两个方面——跟班听课和教学辅导谈谈认识和体会。     

关于“数的概念的扩展”一节磨课的分析

为了实施浦东教育发展研究院“课堂改进计划”的目标，我校数学教研组经过多次的讨论和探索，最后觉得磨课的整个过程就是“课堂改进计划”最适当的实施环节．所谓磨课，就是某个教师在一定时期内，在大家的协助下，把某课教学当作科研课题，采取多种形式，运用科研方法，反复、深入地学习、研究与实践，使这个教师某课的教学成为水平较高的精品课．而要进行磨课，必须关注以下几个事件：1）作为磨课的课题，必须是相对独立的知识，所以往往是选择数学概念的引入或章节知识的总结；     

80 说课:平行四边形及其性质(第一课时)

主持人按：说课活动使教师把对教育教学理论的学习与现实的课堂教学结合起来,以现代教学论和学习心理学为依据,紧密围绕优化课堂教育过程设计来说教法,说学法．因此,说课是近年来各地教研部门十分推崇的一项活动,本栏也愿为老师们交流优秀的说课作品提供一席之地．本期推出第一篇说课作品．］教材分析、教学方法、教学目标等略叙．教学程序本节课的教学过程设计,是从“三性”出发,即“课堂流程的可操作性,知识目标的可接受性,学生主动学习的积极性”,我对整个教学过程作如下安排：１　趣味引入,初学目标通过模拟观察,直观演示（…     

初中数学单元复习课的策略性研究与实践

复习课是课堂教学重要课型之一,在初中数学教学中占有重要的地位,它对全面提高学生素质有着重要的作用．子日“温故而知新,可以为师矣．”在初中数学的每个单元、每个阶段的内容学习完成之后,进行一次系统的、全面的回顾与整理,是十分必要的．     

初三数学第一轮复习的实践与思考

面对初三的复习,尤其是第一轮复习——知识点的梳理阶段,很多学生总觉得有点浪费时间．要使学生真正体会到第一轮复习的方法——以点带面,形成知识网络结构,这就要求教师精心设计复习课的教学,让形象比喻成为现实．笔者以“一元二次方程的复习课（一）”为例,就第一轮复习进行了实践与思考．     

一轮复习课:起点和终点都是概念——以“相似三角形的判定与性质”复习为例

不同阶段的中考复习,在教学任务上有着较大的差异.与二轮专题复习的综合性相对应,一轮复习应凸显基础性,一般以知识点的梳理为教学任务.因此,在一轮复习课上,我们应以概念回顾为主要教学目标,通过适量的解题训练帮助学生梳理初中阶段所学的知识,形成较为完整的知识网络.近期,笔者以“相似三角形的判定与性质”为题开设了一节“起点和终点都是概念”首轮复习课,取得了较好的教学效果.现将这节课和笔者的些     

总复习时讲评课教学中的若干注意

高三总复习是数学教学的重要组成部分，讲评课是总复习教学的重要课型，但有许多教师对讲评课的重要性认识片面，注意不够，教学中存在诸多不足，因而课堂效率低下，影响了总复习的效果．笔者结合教学实践，谈谈讲评课教学中应该注意的几个问题．１注意明确目标在每一节课...     

求长必固本,欲远必浚源——高三数学复习课课堂变式教学探究

复习课是高三数学课堂教学中的主体课型．进入高三阶段总复习后,由于数学学科知识综合性增强,对运算能力、综合解题能力以及应用能力要求都有大幅度提升．如何根据本班学生的原有知识水平和思维特点,采用恰当的和行之有效的复习方式来提高课堂复习效率,是我们一直都在思考和探索的．     

立足基础 挖掘“缺失”——也谈试卷讲评课

试卷讲评是目前高三后阶段教学中的一个重头戏．试卷该如何讲评，是一个具有争议性的话题．最近新昌县举行了一次高三试卷讲评优质课活动．笔者有幸听了几位教师的讲评课，现对在这个活动中产生的一些看法和感悟进行阐述．     

近程空中目标航路研究

本文在等加速俯冲飞行假定下．分析了近程空中目标航路的特点，并据此提出了目标航路模型．经过投影变换，把目标航路模型转化为二次函数．从而使目标航路的滤波及预报问题得到简化．采用进推最小二乘(RLS)原理．给出了目标航路的在线滤波器及预报器．最后．对本文方法进行了仿真．并对仿真结果进行了分析．     

Preparing Science Teachers in an Era of Reform: Practitioners' Perspectives of Methods Courses

With recent national calls for the reform of science education have come standards that delineate not only science content but also assessment, pedagogy, and teachers’ professional development. If teachers must teach science differently, then teacher preparation must change. This study asked 31 inservice secondary science teachers to complete a survey about topics for inclusion in a secondary science methods course. Respondents ranked a list of prespecified topics and had an opportunity to suggest other topics for inclusion in the course. Results showed that the majority of prespecified potential topics were judged important enough by these teachers to warrant inclusion in a methods course, though no individual added topic appeared on more than two surveys. Results demonstrate that these teachers believe teaching many of the traditional topics in science methods courses is still needed. In addition, they advocated the inclusion of several topics that either represent recent technological and theoretical advances, or longstanding ideas that have recently received considerable attention.     

Pre- and in-service teachers’ perceived value of an experimental real analysis course for teachers

Prospective secondary mathematics teachers are usually required to complete several university advanced mathematics courses before being certified to teach secondary mathematics. However, teachers usually do not find these courses to be valuable for their teaching. We designed an experimental real analysis course with the goal of making real analysis content useful and relevant to teaching. Our approach was to ground the real analysis content in pedagogical situations that problematized a secondary mathematics topic, where the nuances of teaching secondary mathematics could be informed by the real analysis that was covered. The experimental course was implemented in a graduate teacher education programme with 32 pre- and in-service teachers (PISTs). After the course, we conducted focus group interviews with 20 of these PISTs to get feedback on how the course was valuable to their teaching practice. Many PISTs found the course to be valuable for teaching secondary mathematics, as well as for their understanding of secondary mathematics and real analysis.     

Chinese elementary mathematics teachers’ knowledge in mathematics and pedagogy for teaching: the case of fraction division

In this study, we investigated the extent of knowledge in mathematics and pedagogy that Chinese practicing elementary mathematics teachers have and what changes teaching experience may bring to their knowledge. With a sample of 18 mathematics teachers from two elementary schools, we focused on both practicing teachers’ beliefs and perceptions about their own knowledge in mathematics and pedagogy and the extent of their knowledge on the topic of fraction division. The results revealed a gap between these teachers’ limited knowledge about the curriculum they teach and their solid mathematics knowledge for teaching, as an example, fraction division. Moreover, senior teachers used more diverse strategies that are concrete in nature than junior teachers in providing procedural justifications. The results suggested that Chinese practicing teachers benefit from teaching and in-service professional development for the improvement of their mathematics knowledge for teaching but not their knowledge about mathematics curriculum.     

Improving Algebra Preparation: Implications From Research on Student Misconceptions and Difficulties

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of the arithmetic content they teach can dramatically, and sometimes negatively, impact their students' ability to transition to algebra. The purpose of this article is to bring awareness of some common algebra misconceptions, and suggestions on how they can be averted, to those who are teaching students the early mathematical concepts they will build upon when learning formal algebra. Published literature discussing misconceptions will be presented for four prerequisite concepts, related to symbolic representation: bracket usage, equality, operational symbols, and letter usage. Each section will conclude with research‐based practical applications and suggestions for preventing such misconceptions. The literature discussed in this article makes a case for elementary and middle school teachers to have a deeper and more flexible understanding of the mathematics they teach, so they can recognize how the structure of algebra can and should be exposed while teaching arithmetic.     

Teachers’ Practices in High School Chemistry Just Prior to the Adoption of the Next Generation Science Standards

Effective professional development that influences teachers’ classroom practices starts with what teachers know, understand, and do in their classroom. The Next Generation Science Standards (NGSS) challenge teachers to make changes to their classroom; to help teachers make these changes, it is necessary to know what they are doing in their classrooms just prior to NGSS adoption. An online survey was distributed to high school chemistry teachers to understand their teaching practices before NGSS was adopted as state standards. This article presents the findings of the survey in terms of the chemistry content, science and engineering practices, and engineering content currently taught in chemistry. Gaps in the current teaching practices as they relate to the standards at the time of the study and NGSS are discussed, which show a challenge for the transformation of science education, which the implementation of NGSS hopes to achieve. Implications for professional development are included.     

A Collaborative Effort to Improve University Engineering Instruction

This study focused on the instructional development of an assistant professor of environmental engineering in collaboration with science education and higher education faculty members. One semester of data was collected in the assistant professor's environmental engineering laboratory class as he endeavored to address his teaching goals. Data collection included pre and post interviews with the assistant professor, students, and program coordinator, and collection of course documents, such as the course syllabus and assignments. In addition, all of the classroom sessions were observed and videotaped, and a midsemester video stimulated‐recall interview was conducted. Results show the assistant professor made growth in the areas of questioning strategies, “think time” for students, increased class participation, and the implementation of a student‐designed field research project. Implications include that new professors can benefit from peer faculty support, and they and their students can benefit when the new professors recognize the complementary nature of research and teaching.     

Knowing more than their students: Characterizing secondary science teachers’ subject matter knowledge

Despite agreement among teacher educators, scholars, and policymakers on the importance of teachers’ subject matter knowledge (SMK), existing models provide limited information about the nature of this foundational component of teacher knowledge. The common assumption is that teachers need to know more about the science subject matter than their students are expected to learn, but what and how much more is underspecified. In order to more characterize science teachers’ SMK, we present the science knowledge for teaching (SKT) model, which has been adapted from the mathematics education literature to apply to science education. The SKT model includes three domains: core content knowledge, specialized content knowledge, and linked content knowledge. We used this model to explore the SMK new secondary chemistry teachers in South Africa and the United States drew on when they explained the conservation of mass and analyzed a related teaching scenario, two important tasks of teaching. Findings indicated these new teachers drew on knowledge from all three SKT domains in order to engage in these tasks of teaching. This result suggests the potential of the SKT model to characterize the nature of science teachers’ SMK and thereby better inform teacher preparation and professional development programs.     

课堂提问在大学数学教学中的意义

课堂提问是一种有效的教学组织形式,它既是重要的教学手段,又是完美的教学艺术.这篇文章以高等代数的教学为例,阐述了大学数学教学中课堂提问的重要意义.希望对年轻的教师能有所启迪和帮助.     

The Transparent and the Invisible in Professional Pedagogical Vision for Science Teaching

Science teacher educators use examples of practice to support teacher candidates (TCs) learning to engage in new forms of science teaching. However, interpretation of these examples assumes a level of expertise about practice TCs lack. This article describes a study designed to determine some of the differences between expert teachers' and TCs' professional pedagogical vision for science teaching. Specifically, the study examines what each group attends to (highlights) in examples of science teaching and how they interpret the events they attend to (codes). Both groups were asked to analyze video of classroom science teaching. Differences were found between TCs and expert teachers in terms of both highlighting and coding of science teaching practice. Four key areas of difference are described in detail: actor focus, questions, grain size, and enactment. The implications for science teacher education are discussed, in particular a set of tools and teacher education practices to support acculturating TCs into more a sophisticated professional pedagogical vision for science teaching. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis

In the United States and elsewhere, prospective teachers of secondary mathematics are usually required to complete numerous advanced mathematics courses before obtaining certification. However, several research studies suggest that teachers’ experiences in these advanced mathematics courses have little influence on their pedagogical practice and efficacy. To understand this phenomenon, we presented 14 secondary mathematics teachers with four statements and proofs in real analysis that related to secondary content and asked the participants to discuss whether these proofs could inform their teaching of secondary mathematics. In analyzing participants’ remarks, we propose that many teachers view the utility of real analysis in secondary school mathematics teaching using a transport model, where the perceived importance of a real analysis explanation is dependent upon the teacher’s ability to transport that explanation directly into their instruction in a secondary mathematics classroom. Consequently, their perceived value of a real analysis course in their teacher preparation is inherently limited. We discuss implications of the transport model on secondary mathematics teacher education.