Factors that influence teachers learning to do interviews to understand students' mathematical understandings

Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics teachers to use interviews to understand their students' mathematical understandings as well as to prepare teachers to use technology-intensive curricula. This study examined the influences on three high school mathematics teachers as they learned to use task-based interviews to understand students' mathematical understandings. The areas of teacher knowledge and conceptions that influenced the teachers we studied were: teachers' mathematical understandings and knowledge of technology and the perceived importance of curriculum topics; teachers' views of knowing mathematics; teachers' perceptions of students' characteristics and needs; and teachers' perceptions of interviewing and the role of questioning in interviews. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Interfacing of Preservice and Inservice Experiences of Reform-Based Teaching: A Longitudinal Study

This article contrasts four elementary teachers who were graduates of a teacher education program that incorporated a reform-based mathematics methods course. The report provides results from a four-year longitudinal study that extended from the time that the participants were preservice teachers until the end of their second year of teaching. The article provides background information of each teacher, vignettes from her teaching, excerpts from interviews, and an analysis of each teacher's case. Results from the case studies indicate that two of the four teachers sustained their cognitively-based conceptions about mathematics teaching and learning, and implemented these conceptions into practice. The analysis suggests that there were several factors that influenced the teachers' conceptions and the choices they made in their teaching: personal commitment, professional strength, curriculum, planning, assessment, beliefs, knowledge, and support from school administration. The article concludes with implications for teaching and questions about the nature of what might be required in the beginning years of teaching if new teachers are expected to implement reform-based mathematics teaching practices. This revised version was published online in August 2006 with corrections to the Cover Date.     

创建合作教师文化:师徒教师教育模式的运作与实施

教师文化是在学校教师群体内形成的独特的价值观、共同的思想和信念、职业精神和行为准则、规范等。师徒教师教育模式基于缄默的教学知识理念,是人际互动理论的合作教师文化的体现。师徒模式在合作的教师文化中运作,其有效实施会促进合作教师文化的生成和建构。通过师徒模式创建合作教师文化不仅对教师的发展和持续成长产生重要影响,而且为课程与教学改革的有效实施和顺利推进提供重要保证。然而,学校在实施师徒模式的过程中存在着人为的合作、肤浅的合作、顺从的合作等不容忽视的问题。     

Fast Kids,Slow Kids,Lazy Kids: Framing the Mismatch Problem in Mathematics Teachers' Conversations

Abstract

This article examines the social nature of teachers' conceptions by showing how teachers frame the “mismatch” of students' perceived abilities and the intended school curriculum through conversational category systems. This study compares the conversations of 2 groups of high school mathematics teachers addressing the Mismatch Problem when implementing equity-geared reforms. Although East High teachers challenged conceptions that were not aligned with a reform, South High teachers reworked a reform mandate to align with their existing conceptions. This research found that the teachers' conversational category systems modeled problems of practice; communicated assumptions about students, subject, and teaching; and were ultimately reflected in the curriculum. Because East High teachers supported greater numbers of students' success in advanced mathematics, this study considers the relation between teachers' understandings of student learning and the success of equity-geared math reforms. In addition, this study contributes to the understanding of how teacher conceptions of students are negotiated and reified in context, specifically through interactions with colleagues and experiences with school reform.     

Learning to Teach Mathematics: Questioning, Listening, and Responding

This paper reports a study designed to explore prospective teachers' learning to teach mathematics in the complex context of a university-based curriculum and instruction course. The course, taught with a focus on inquiry, used prospective teachers' weekly interactions with students as springboards for investigations of mathematics, teaching, and learning. A framework of questioning, listening, and responding is used to analyze prospective teachers' understandings and the tensions they experienced. The difficulties and tensions prospective teachers face in turn pose challenges and tensions for teacher educators. This revised version was published online in July 2006 with corrections to the Cover Date.     

Student teachers' conceptions of how to recognise a “Good” primary science teacher: Does two years in a teacher education program make a difference?

Several studies have suggested that preservice teacher education has little impact on student teacher conceptions about various facets of teaching and learning. Most of these studies refer to generic teaching and learning, and very few have related to primary science in particular. To explore this area eight primary student teachers were interviewed on six occasions during the first two years of their Bachelor of Teaching degree. This paper reports the findings from part of these interviews. It describes the (sometimes changing) conceptions which these eight students held about how they would recognise a “good” teacher of science and the people and experiences they believed influenced the formation of these views. The differential impact of past and present teachers and the teacher education program revealed possible implications for practica and science curriculum units in particular, if teacher education is going to have an influence on preservice teachers' conceptions about teaching and learning.     

Integrating academic and practical knowledge in a teacher leaders' development program

This study examines an attempt to encourage integration of knowledge learned in the academy with knowledge learned in practice as a means to challenge educational practitioners' — teacher leaders and inservice teacher educators — existing conceptions and beliefs, and promote intellectual restructuring. The article centers on two components of the Manor Program for the development of teacher leaders and educators. The first component focuses on expanding academic knowledge, by helping the participants become acquainted with studies on students' and teachers' conceptions and ways of thinking in mathematics. The second component focuses on the integration of knowledge learned in the academy with knowledge learned in practice by conducting a mini-study.This revised version was published online in September 2005 with corrections to the Cover Date.     

从中学教师的专业智能水平看教师教育课程改革

中学教师已有的专业智能水平普遍低于应有的水平,这与我国教师教育课程设置存在的问题密切相关。由此出发,教师教育课程设置应体现如下构想:拓宽通识课程,整合学科专业课程,加大教育课程比例。     

Conceptualizing Teachers' Ways of Knowing

This article addresses issues related to the ways teachers learn mathematics and the teaching of mathematics and the relevance of those ways to their professional development. Preservice teachers' understanding of school mathematics lacks sophistication, a situation that needs to be addressed in mathematics teacher education programs. What is critical is the means by which they encounter and explore the mathematics they will be teaching. Fundamentally, their mathematical experiences need to be congruous with the kind of teaching we would expect of a reflective, adaptive teacher. The article contains both practical and theoretical considerations of how these experiences might be structured. Theoretical orientations for conceptualizing teachers' belief structures are offered as a foundation for conceptualizing teachers' ways of knowing. The moral dimension of teacher education is considered as a backdrop for understanding how teachers come to know.This revised version was published online in September 2005 with corrections to the Cover Date.     

高师计算机课与中学数学新课程整合的探究

在高师数学系计算机课中整合中学数学新课程,以在职和职前教师能胜任中学数学新课程的教学为研究出发点,选用中学数学新课程充实深化重组计算机课程内容,实施计算机支持的协作学习的六个步骤：教师创设情境和提出问题、教师分析问题和明确方法、学生自主探索和寻求解答、小组协作学习和解决问题、师生总结和评价成果及教学反思,培养学生基于信息技术平台更有效地学数学与教数学的能力,提升他们的信息素养和数学素养．     

让学生“动”起来,追求有效而有活力的课堂

《新课程标准》指出:有效的数学学习活动不能单纯地依赖模仿与记忆,教师应该向学生提供充分从事活动的机会,引导学生主动参与、亲身实践、独立思考、合作探究。而现在的课堂往往忽视了学生的个性和思维的发展,过于强调知识的记忆与模仿,有时甚至为了追求分数,采取题海战术,严重压抑了学生的主动性和创造性,使数学课堂缺乏生命力。如果老师能利用儿童好动的天性,利用形式多样的活动促使他们积极地投入到数学学习中来,将取得事半功倍的效果。     

Preparing teachers for realistic mathematics education

A shift in mathematics education in the Netherlands towards the so-called realistic approach made it necessary to prepare prospective teachers for a type of curriculum different from what they experienced as pupils. This article describes the characteristics of a preservice programme aiming at this goal and presents an analysis of the development of the student teachers' views of mathematics and mathematics education during the programme as well as their classroom behaviour. This analysis is based on two research studies. The first was a longitudinal study in which the student teachers were followed during years by means of questionnaires and interviews. The second was a study in which graduates from this programme were compared with graduates from a more traditional preparation programme by means of two teacher questionnaires and a pupil questionnaire, the latter measuring the pupils' perceptions of the actual teaching behaviour of the graduates. The teacher education programme appeared to be successful in changing the student teachers' views of mathematics education, especially in the direction of a more inquiry oriented approach, and in promoting effective teacher behaviour in the classroom. As far as their facilitating role as a teacher is concerned, the student teachers seemed to go through a two-stage learning process. Most of them reached the first stage, in which they realize that pupils have different preferences for learning and that a variety of possible explanations for problems should be offered. However, only a small number of student teachers seem to reach the second stage, in which they recognize the principle of building on pupils' own constructions, an important feature of realistic mathematics education. Possible explanations for the low impact of the programme, as well as solutions are discussed.     

A comparative analysis of primary teacher professionalism in England and Finland

Policy‐makers' conceptions of teacher professionalism currently differ markedly in England and Finland. In England they are shaped by agendas associated with the drive to raise standards and ‘commercialized professionalism’ whilst in Finland they are influenced by notions of ‘teacher empowerment’. This article analyses findings on the theme of teacher professionalism derived from re‐interviewing a sample of English and Finnish teachers in 2001 as a follow‐up to earlier ethnographic research in six schools in each country during 1994–1996. Issues of professionalism are addressed through three broad themes: the impact of curriculum and pedagogical reforms; working together to implement these reforms; and accountability and control. It is argued that in each country teachers' conceptions of their professionalism were undergoing reconstruction. These conceptions were shaped by past and present ideology, policy and practice and displayed multiple and situational dimensions.     

Prospective elementary teachers' comprehension of mathematics instruction

This article reports on a study that investigated prospective elementary teachers' knowledge and convictions regarding content, pedagogy, and pupil needs as well as on their rationales for the teaching of mathematics. Data collected through journals is qualitatively analysed and interpreted to understand common views on ‘ideal’ mathematics classes. The findings are used as a basis for a broader sociological discussion of the school's role in a changing environment. Participants in this study tend to value mathematics classes mainly in terms of the degree of pupil enjoyment. Consequently, they comprehend the teacher's role as beyond instruction: the teacher as an entertainer. This is discussed by confronting the two conceptions of school as a locus for serious learning, and of school as a ‘playhouse’. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effective Professional Development in Science and Mathematics Education: Teachers' and Facilitators' Views

This study compares the views of teachers and professional development facilitators about effective professional development (PD). We analyzed interviews with 72 teacher participants and 23 PD facilitators involved in nine science and mathematics PD projects. The teachers' themes for characterizing effective PD included classroom application, teacher as learner, and teacher networking. Similarly, the PD facilitators discussed effective PD as having classroom application and experiences for teachers as learners. In addition, PD facilitators shared the need to develop collegial relationships with teachers and improve teacher knowledge. These views correspond to some of the standards and recommendations described in policy and research documents on effective PD. Criteria of effective PD in these documents that the participants did not mention included: (1) challenging teachers' content and pedagogical content knowledge with transformative learning experiences, (2) encouraging teacher leadership for sustained support, and (3) focusing on student learning by instructing teachers on how to use student data to inform their teaching practice. Our findings have implications for designing PD that reflects the criteria of standards-based reform.     

The emerging of teachers' conceptions of new subjects inserted in mathematics programs: the case of informatics

The changes in mathematical curricula induced by the introduction of informatics in school represent the general framework of this research. In particular we focus on the teacher's role by analysing the different choices taken by mathematics teachers when faced with a curriculum reform induced by the introduction of informatics in secondary school courses (age 14–16). Our hypothesis is that these choices are the consequence of conceptions teachers have about informatics and its teaching in relation to the teaching of mathematics. Thus, through a case study research method, we focus on mathematics teachers' conceptions of informatics and its teaching. An attempt is made at outlining a typology of these conceptions, based on the different orientations identified.     

Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs are a good place to start the process of redesigning mathematics curricula so that school mathematics will pay more than lip service to problem posing. Data are presented and analyzed showing that teacher education students can recognize the need for problem posing both in their own programs and in school mathematics curricula. Examples of problems posed by teacher education students are presented and discussed. An active learning framework for interpreting the role of problem posing in mathematics classrooms is presented.     

An Evolution of Mathematical Beliefs: A Case Study of Three Pre-K Teachers

This case study involved examination of the evolution of mathematical beliefs of three prekindergarten teachers. The researcher followed three teachers at one school in west Alabama over the course of 6 months as they implemented a new mathematics curriculum in their pre-K classrooms. Interviews were conducted prior to implementation and at the end of the school year. Classroom observations were done throughout the implementation process. Three themes emerged from the data (a) math resources for the pre-K classroom, (b) pushing beyond—thinking mathematically, and (c) instructional strategies used the pre-K classroom. These themes revealed how all of the teachers' perceptions of early childhood mathematics curriculum and instruction evolved during the course of the study. These findings have implications for early childhood teacher education programs and professional development.     

关于师生互动中教师对话行为的思考

教师对话行为是影响师生互动效果的关键因素。当前教师对话行为中主要存在提问不均一、讨论不规范及评价不合理等问题。改变教师不合理的师生观、强化教师对新课改理念的学习领悟及提高教师教学能力水平是克服教师对话行为问题的重要举措,是构建良好师生互动的保障所在。     

北京市基础教育课程改革实验学科教学监控与评价报告

采用问卷法、访谈法、测验法及资料分析法等方法对北京市小学一年级至四年级和初中一年级课程改革实验进行监控与评价,结果表明:四年来,北京市基础教育国家课程改革实验的成绩主要表现为国家课程计划和目标总体上得到落实,教师教学观念和教学行为发生了显著变化,学生语文基础知识和技能掌握较好,小学生数学计算技能依然保持优势;存在的主要问题是教学任务过重与计划课时不足的矛盾依然存在,学习方式存在认识误区与实践偏差,学生阅读能力普遍较低,初中一年级学生数学基础知识和技能掌握还存在较大差距,学生基础学科学习过早两极分化,教学质量评价改革滞后于教学改革,教师培训工作落后于课程改革发展的需要。