Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an algebraic structure to get a sense of those properties which form the basis of the fundamental definitions. We will explain the transition from examples to abstract algebra as a series of shifts of attention and in this paper we will use a case study to examine the initial shift, which we will call apprehending a structure, and examine how one student came to apprehend the structure of the commutative ring Z₉₉.     

教会学生对自己的一生负责——当前中小学生主要责任障碍及对策

责任障碍,是各种不负责任心理和行为的统称。这些障碍,有的表现为某种非正常的心理状态,有的表现为某些行为的失常。当前不少中小学生存在着各种各样的责任障碍,如破坏公物、乱扔纸屑、抽烟喝酒、拉帮结派、沉迷网络等。责任障碍,不仅影响学生健康成长,处理不当还会引起不良后果,甚至酿成悲剧。因此,学校和教师重视研究学生的责任障碍问题,显得尤为必要。     

苦难与生存:解读《平凡的世界》

路遥的长篇小说《平凡的世界》立足于特定的时间(1975—1985)和空间(陕北黄土高原),全景式地反映了这一时期陕北人民苦难的生存状态,以及他们如何从苦难中自我救赎,寻找生存之路。文章从时间和空间维度分别剖析苦难的生成,并理解主人公在苦难与生存间的救赎,从而把握这部现实主义巨著的精神内涵。     

Acceptance as a Normative Aspect of the Process of Coming to Understand Emotionally Charged Concepts: Upper-Secondary School Students Make Meaning of Gender

Previous research on how students’ acceptance of emotionally charged theories relates to their understanding is based on the measurement of acceptance and understanding as two separate variables. As an alternative, the present study takes a qualitative approach with the aim of exploring what 24 upper-secondary school students accept when they come to understand the concept of gender and how to justify gender-related statements. The results show how the students accept ideas about social structures, power, and emancipation, as well as ideas about essences, individual independence, and a natural order. As for their justifications, they accept ideals of equality and objectivity. By assuming that the ideas have positive connotations for the students, it becomes possible to understand them as engaged in negotiating norms that are brought to the fore in the interviews.     

Beginning to Understand Teaching as a Discipline

We explore the possibility of understanding teaching as a discipline in its own right, rather than as a domain that is ancillary to the many academic disciplines. While teaching looks easy and is widely regarded as easy, the image of teaching as transmission and the perspective of technical rationality mask the many ways in which challenging and engaging teaching represents a highly disciplined view. When extended to teacher education, the perspective of teaching as a discipline sheds powerful light on longstanding frustrations reported by those learning to teach. We argue for the conclusion that teaching is a discipline and that teacher education is the home of that discipline, with self-study as one of the central methodologies for making explicit the knowledge inherent in teaching seen as a discipline.     

如何把备学生真正落到实处

备课过程中,一定要“备”学生。然而在实际备课活动中,许多老师却并没有考虑到这一点,对学生学情缺乏深入细致的了解、思考与探究。本文在提倡“备”学生的基础上,提出如何去“备”学生和怎样“备”好学生的建议。     

有效教学理解的思路转向

有效教学概念是研究有效教学的逻辑起点和前提基础,通过对目前学术界关于有效教学各种定义的评述,指出对"有效教学"的理解有必要进行思路的转向.     

初中生如何认识及使用历史史料

在学习历史的过程中,史料是不可或缺的。初中生刚开始接触历史,借助史料可以更好地辅助教学。就初中生如何认识及使用历史史料的问题进行探讨,从了解史料的类型入手,培养学生辨别史料、使用史料的能力,从而达到帮助中学生学习历史的教育教学目的。     

谈如何帮助学生领悟“假说—演绎法”

面对新课程的新要求,教师自身对"假说—演绎法"的认识程度,将关系到学生领悟"假说—演绎法"的深刻与浅薄。教师对"假说—演绎法"的认识提高了,才能做到教学中有意识引导学生领悟"假说—演绎法",才会使有效引领的教学方法多起来。     

过程性评价对孔子“因材施教”教育理念的传承和发展

过程性评价是一种完整性、实时性、渗透性、连续性的评价方法,相比传统的终结性评价,过程性评价注重教学的过程,强调学生禀赋的不同,看重不同个体的差异性发展。通过研究其内涵特点和理论依据,发现过程性评价与中国古代孔子因材施教、因人而异的教育理念甚为相似,可以说,过程性评价是对孔子"因材施教"教育理念的传承,是中国古代传统教育理念在当代中国教育的反映。     

如何准确理解建构主义教学思想

本文在概述建构主义学习理论主要观点的基础上，从学习方式、合作学习、情境化教学和师生关系四个方面对建构主义学习理论作出澄清并进行分析，探讨了把建构主义学习理论与我国教育实践相结合的正确方法。     

Primary Caregiving as a Framework for Preparing Early Childhood Preservice Students to Understand and Work with Infants

Research Findings: This qualitative study explored the process through which a small group of preservice early childhood teachers engaged in primary caregiving as a framework for learning about early care and education with infants during an infant practicum course at a university-affiliated early childhood center in the United States. Based on multiple data sources, findings revealed that the participants found the primary care system to be beneficial to both infants and teachers. The student teachers gained a better understanding of the uniqueness of the infancy period, experienced the emotional rewards of a special relationship with an infant, and learned to provide individualized and relationship-based infant care and education, while the infants received the benefits of this care. The integration of hands-on practice enacting a primary care system in a responsive infant room, ongoing supervision, and a theory-to-practice seminar created an effective professional learning process for the student teachers, which helped them to grow as both infant teachers and early childhood professionals. Practice or Policy: These findings are a 1st step toward looking more deeply at 1 strategy as a promising practice for the future, offering implications for early childhood teacher education and new insight to the field.     

指导读书内化发展创造思维

语文既是人类思维活动的成果 ,又是人类籍以思维的工具。语文课堂教学是学生在享用人类思维成果的同时 ,学会运用思维成果 ,从而发展自己的思维能力。因此 ,围绕思维发展这一主线 ,从创造思维的独立性、求异性、广阔性着手 ,加强阅读教学 ,指导读书内化 ,是实现语文教育根本目的的需要 ,也是发展学生语文素质乃至整体素质的需要 ,更是培养创新人才的需要。一、指导读书内化 ,重视自我发现 ,培养思维的独立性。契可夫说 :凡是儿童自己能够理解和感受的一切都应当让他们自己去理解和感受。学生自我发现的知识 ,无疑印象更深 ,记得更牢。这就要…     

高校教师如何认识和处理教学与科研的关系

如何处理教学与科研的关系,是高校教师需要正确认识和处理的问题。教学始终是高等学校的中心工作,教学与科研需要协调发展,以科研促教学,把科研融入到教学过程中去,实现教学和科研的良性互动,促进教学质量的提高和教师自身的协调发展。     

以"学生随课参与教学评价"步入真实教学

学生随课参与教学评价具有形成性、同情性和公开性等特点,它按照"抽签--书面评价--口头报告"的程序进行,"口头报告"是非常关键的环节,它不仅可以培养学生的沟通能力,而且也使学生能够见证教师所做出的任何改变.这会促使教师认真对待教学,使学生诚服于教师的教学,是生成教师威信的可靠方式.     

如何理解任务型语言教学途径中的任务和练习

论述任务型语言教学的定义、任务的特点和练习的区别,讲明真实性语境是区别练习和任务的一个重要标准,提到为练习添加真实的语境使其转化为任务的方法。还重点论述任务和练习相互依存并不排斥的理由,对一线教师在实施任务型语言教学中把握好两者的关系有实际的指导意义。