Cheating in School: What We Know and What We Can Do

This article discusses how integrating technology into microteaching exercises within teacher education programs can help develop reform-oriented and reflective teacher leaders.     

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。     

Learning to Teach with Mathematics Textbooks: How Preservice Teachers Interpret and Use Curriculum Materials

This study investigates how four prospective teachers interpret and use textbooks while learning to teach mathematics during university coursework and practicum teaching. Results indicate that prospective teachers had varied approaches to using textbooks ranging from adherence, elaboration, and creation. Factors influencing how they engaged with texts include their practicum classroom setting, access to resources, and their understanding of mathematics. Preservice teachers' attempts to modify textbook lessons raised pedagogical, curricular, and mathematical questions for them that were not easily answered by reference to the textbooks or teacher's guides. Findings indicate that the practicum can, however, challenge preservice teachers to be creative and flexible users of curriculum materials.     

Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know

In this article we offer a theoretical discussion of teachers' mathematics-for-teaching, using complexity science as a framework for interpretation. We illustrate the discussion with some teachers' interactions around mathematics that arose in the context of an in-service session. We use the events from that session to illustrate four intertwining aspects of teachers' mathematics-for-teaching. We label these aspects “mathematical objects,” “curriculum structures,” “classroom collectivity,” and “subjective understanding”. Drawing on complexity science, we argue that these phenomena are nested in one another and that they obey similar dynamics, albeit on very different time scales. We conjecture (1) that a particular fluency with these four aspects is important for mathematics teaching and (2) that these aspects might serve as appropriate emphases for courses in mathematics intended for teachers.     

Jewish Day School Wounds and What We Can Do About Them

This article is based upon a qualitative research study that examined 95 school stories written by Jewish female teacher candidates in an undergraduate education course. Many candidates wrote inspirational or humorous stories about growth and development or a special teacher. However, over one third of the narratives described painful Jewish day schooling episodes with insensitive teachers, stinging rebukes, or public shaming. The findings argue for the enhancement of Jewish educator preparation with attention to professionalization of classroom management and interrogation of assumptions from schooling biographies. This study challenges teacher educators in the liminal space of educator preparation as teacher candidates shift from personal lived schooling experience into professional practice.     

创新教育需要语文教师做些什么

语文教师如何在创新教育中发挥作用,首先要明确创新教育的内涵和外延,营造宽松、和谐、民主的课堂气氛,让学生敢于发现、敢于创新;其次要认清创新思维的规律,为培养学生创新精神理清思路;再次,要因地制宜地教给学生一些方法,为培养学生的创新能力建立高速通道。     

Educational Psychology: What Do We Teach, What Should We Teach?

Teacher education students sometimes question the value of educational psychology courses even though educational psychology textbooks are primarily concerned with understanding and improving classroom teaching and learning. A survey of current educational psychology textbooks and instructors reveals that (a) most texts cover a wide variety of topics, (b) instructors rate most of these topics as important, (c) there are large variations in depth of coverage among texts, and (d) all texts contain numerous classroom applications. The questionable reputation of the educational psychology course may stem from its broad coverage. A dozen or more topics in one semester may decrease the probability that most students will achieve a solid grasp of any one topic, leaving students uncertain about the course's meaning and applicability. A proposed solution is to offer the introductory course as a two-semester sequence, with the second course offered as an elective.     

Learning to Teach Elementary Mathematics: Ecological Elements of a Field Experience

Three elements of the ecology of a mathematics methodsfield experience were particularly important topromoting a shift in locus of authority thatprecipitated reflective thinking among the preserviceteachers: (a) an inquiry perspective, (b) the cohortgroup, and (c) school-university collaboration. Thearticle describes these three aspects of the ecologyof the field experience and provides the perspectivesof the mentor teacher, preservice teacher, and teachereducator. Also included are new challenges andproblems that arose with each aspect.     

我国数学教师职前教育研究综述

在数学教师职前教育的研究文献中,研究者进行了大量深入而细致的研究,在理论和实践、模式及内容上都取得了丰硕的成果.主要集中在以下几个方面:高师数学教育现状;培养目标;高师数学教育改革的理论建构;高师数学教育改革的实践.追溯教师专业化水平不高在对双专业理解水平偏低方面的渊源,奠定教师专业化形成与发展中对双专业深刻理解的基础,我们应在数学教师教育改革中为之做出不懈的努力.     

What Do We Know About Artistically Talented Students and Their Teachers?

This paper contextualises and summarises five research projects concerned with the education of artistically talented students in the United States. It reports on over ten years of research and describes the hypotheses, methods and findings of studies linked by their concern for the special needs of the artistically able. Finally, the paper points towards the next stages of the research.     

Learning to Learn to Teach: An ``Experiment' Model for Teaching and Teacher Preparation in Mathematics

This paper describes a model for generating andaccumulating knowledge for both teaching andteacher education. The model is applied firstto prepare prospective teachers to learn toteach mathematics when they enter theclassroom. The concept of treating lessons asexperiments is used to explicate theintentional, rigorous, and systematic processof learning to teach through studying one's ownpractice. The concept of planning teachingexperiences so that others can learn fromone's experience is used to put into practicethe notion of contributing to a sharedprofessional knowledge base for teachingmathematics. The same model is then applied tothe work of improving teacher preparationprograms in mathematics. Parallels are drawnbetween the concepts emphasized for prospectiveteachers and those that are employed byinstructors who study and improve teacherpreparation experiences. In this way, parallelsalso are seen in the processes used to generatean accumulating knowledge base for teaching andfor teacher education.     

The Development of Diploma in Education Student Teachers’ Mathematics Pedagogical Content Knowledge

Mathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the development of MPCK in their pre-service teachers. As part of a research study on the development of MPCK in primary school beginning teachers, a 16-item instrument was developed to measure some aspects of the MPCK for teaching mathematics at primary level. The instrument was administered to the 2003 Intake of the Diploma in Education student teachers at the National Institute of Education, Singapore just at the beginning of their programme. As they completed their methodology course in February 2005, the instrument was administered again. This paper will discuss the findings concerning their performance in these two tests, with reference to the overall performance as well as topic-specific and MPCK construct-specific performance. The findings indicate that student teachers at the beginning of their programmes are generally quite weak in their mathematics pedagogical content knowledge, as might be expected. There was significant improvement in some aspects of their MPCK on completion of their mathematics pedagogy course.     

Teachers and `Street Children': On Becoming a Teacher of Mathematics

The phenomenon of `street children' where youngpeople, for various reasons, live on thestreets of towns and cities is found all overthe world in varying degrees and forms. InSouth Africa, one approach to take care aboutthe plight of these children has been to set upand run what are referred to as `streetshelters'. One such street shelter, the onlyone exclusively for girls in the city ofDurban, is Tennyson House. In this paper Idescribe an innovative outreach programmeintegrated with a university curriculum inwhich a group of pre-service teachers takingmathematics education as a major were involvedin teaching mathematics to girls at TennysonHouse. From the vantage point of a mathematicsteacher educator in the programme, I describeand reflect on what was experienced and learnedfrom the intervention in terms of threeaspects: learning about learners; learningabout teaching (mathematics) and learning aboutrelationships.     

Effects of an Online Mathematics Curriculum for English Language Learners

This study measured the effects of an online supplementary mathematics curriculum designed for middle school English language learners who speak Spanish as a first language. A randomized experiment measured the achievement differences between middle school English language learners who used the Web-based HELP Math (Help with English Language Proficiency) curriculum and students who used other technology-based programs. Three hundred and ninety-six students participated. Both groups made statistically significant gains from pretest to posttest within their respective curricula, but no main effect was found between the two groups. Post hoc analyses revealed that students with higher levels of English proficiency, who participated in the comparison condition, performed significantly better than students in the HELP Math condition, while students with lower levels of English proficiency performed better in the HELP Math program (although these differences were not statistically significant). Findings are interpreted with caution due to the truncated length of the intervention.     

Secondary Teachers and English Language Learners (ELLs): Attitudes,Preparation and Implications

The education of language-minority students is a constitutional right. Throughout this article, the authors synthesize recent literature addressing two main questions: (1) What are secondary teachers’ attitudes toward English language learners (ELLs)? and (2) To what extent are secondary teachers being prepared to teach content effectively to this student population? Secondary teachers’ attitudes about ELLs vary, but are generally positive. The lack of teacher preparation—especially at the secondary level—to teach ELLs effectively is widespread. Thus, it is not surprising that secondary teachers feel ill-prepared to scaffold or differentiate instruction to meet these students’ language and academic needs. Since attitudes, preparation, and practice are interrelated, the authors also provide numerous implications for future practice at various levels: teacher-preparation programs, school district support, and classroom teaching.     

Science and Mathematics Efficacy Beliefs Held By Practicing and Prospective Teachers: A 5-Year Perspective

A compilation of results from three studies, conducted over a 5-year period, compare and contrast efficacy beliefs held by prospective and practicing teachers toward science and mathematics instruction. Particular attention is directed toward confidence and accountability factors. The theoretical background is derived from Bandura's model as well as the locus of control construct. Recommendations for teacher education programs are offered.     

如何让学生用数学语言说话

学生通过用数学语言说话可以培养数学感觉,还可以培养数学感情.数学语言基本单位分为5类:词素,单词和词组,句子和句群,段落,篇章.语言表达是人类能够交流思想、传播知识的前提,是人类社会能够赖以存在的必要条件之一.数学的应用和数学的思维过程也就是对数学符号的操作过程,是主体借助于语言符号而认识和再现以及改造现实世界的过程.     

对提高中学数学教师数学修养的思考和尝试

提高中学数学教师的数学修养在塑造人的过程中具有不可替代的作用.在实际调查中我们发现:一方面,教师们对提高自身数学修养水平的热情很高;另一方面,在涉及到具体数学知识时,教师们又往往把自己的眼光仅局限在个人所讲授或熟悉的具体中学课程中,而对关系“较远”的内容则倾向于采取回避和应付的态度.提高教师自身的数学修养是解决目前数学教育中种种弊端的关键.在实际教学中可采用如下方法加强数学教育中数学类课程:(1)加强对数学内容的数学思想和方法论的讲解;(2)加强数学计算和论证的训练;(3)加强与中学数学课程的结合.     

教师专业化与数学教师的继续教育

教师专业化要求教师在整个专业生涯,具备相应的人格、学问、教育观念和教学技能,这四者之间的动态有机组合体现了教师职业的本质,形成了不同的教师特征.特别是教育观念和教学技能两个要素,是区别于其他行业人员而充分体现教师独有的职业特征.而多数数学教师也恰恰在教育观念和教学技能两方面比较薄弱.根据教师专业发展阶段理论,以及对北京市中小学数学教师的调查,反思数学教师的继续教育,须在教育观念的转变、教学技术的培训、教学模式的革新等方面有所加强.