Learning to Question: Categories of Questioning Used by Preservice Teachers During Diagnostic Mathematics Interviews

Developing appropriate questioning techniquesis an important part of mathematics teachingand assessment. This study examined thequestioning strategies used by 48 preserviceteachers during one-on-one diagnosticmathematics interviews with children. Eachparticipant conducted an audiotaped interviewwith one child, followed by an analysis andreflection of the interview. Data wereanalyzed to develop general categories ofquestions used by the preservice teachers. These categories included: 1) checklisting, 2) instructing rather thanassessing, and 3) probing and follow-upquestions. The analyses and reflectionscompleted by preservice teachers indicated thatusing the diagnostic interview format allowedthem to recognize and reflect on effectivequestioning techniques. Through an examinationof these categories of questions, we offersuggestions for teaching the skill ofmathematics questioning in preservice teachereducation courses.     

Preservice Teachers’ Perceptions of Mathematics Education in Urban Schools

This article reports findings from a study of preservice mathematics teacher education students and their beliefs about and experiences with students in an urban high school. The preservice teacher education students participated as mentors to a group of peer tutors in a mathematics tutoring program. Data collected from questionnaires and interviews reveal that the mentors had varied perceptions of tutoring program participants’ motivation, interest, and knowledge of mathematics. Mentors held varied perceptions of urban schools and what teaching mathematics in urban settings entails. Further, mentors reported that their work in the tutoring program had an impact on their strategies and plans for future mathematics teaching. Erica N. Walker is Assistant Professor of Mathematics Education in the Department of Mathematics, Science, and Technology and Research Fellow at the Institute for Urban and Minority Education at Teachers College, Columbia University.     

Curriculum design for inquiry: Preservice elementary teachers' mobilization and adaptation of science curriculum materials

Curriculum materials are crucial tools with which teachers engage students in science as inquiry. In order to use curriculum materials effectively, however, teachers must develop a robust capacity for pedagogical design, or the ability to mobilize a variety of personal and curricular resources to promote student learning. The purpose of this study was to develop a better understanding of the ways in which preservice elementary teachers mobilize and adapt existing science curriculum materials to plan inquiry‐oriented science lessons. Using quantitative methods, we investigated preservice teachers' curriculum design decision‐making and how their decisions influenced the inquiry orientations of their planned science lessons. Findings indicate that preservice elementary teachers were able to accurately assess how inquiry‐based existing curriculum materials are and to adapt them to make them more inquiry‐based. However, the inquiry orientations of their planned lessons were in large part determined by how inquiry‐oriented curriculum materials they used to plan their lessons were to begin with. These findings have important implications for the design of teacher education experiences that foster preservice elementary teachers' pedagogical design capacities for inquiry, as well as the development of inquiry‐based science curriculum materials that support preservice and beginning elementary teachers to engage in effective science teaching practice. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 47:820–839, 2010     

Investigating the Guidance Offered to Teachers in Curriculum Materials: The Case of Proof in Mathematics

Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed.     

Preservice Teachers' Stories Of Mathematics Classrooms: Explorations Of Practice Through Fictional Accounts

This report describes four preservice secondary teachers' fictional accounts about mathematics classrooms. The narrative structures and meanings of the preservice teachers' stories, written while the preservice teachers were enrolled in a secondary methods course, were examined with the goal of gaining insight into the preservice teachers' emerging identities as mathematics teachers. Although past research has examined experienced teachers' stories, little research, if any, has focused on stories written by preservice mathematics teachers or on intentionally fictional stories about mathematics classrooms. This report uses methods of narrative analysis to develop understandings about preservice teachers' storied identities and specifies areas for further investigation into the role of narrative in mathematics teacher education.     

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.     

The Role of Content Knowledge and Problem Features on Preservice Teachers’ Appraisal of Elementary Mathematics Tasks

The objective of this study was to examine the nature of preservice teachers’ evaluations of elementary mathematics problems using the Mathematical Tasks Framework (MTF), a model designed to discriminate among tasks according to their cognitive complexity. We also tested the relationship between mathematics content knowledge and problem length on the preservice teachers’ evaluations. Twenty-six undergraduate students enrolled in an elementary mathematics methods course at a large urban university were introduced to the MTF and cognitive complexity during a class lecture and were subsequently required to sort 32 mathematics problems according to the framework. Results demonstrated that overall, the preservice teachers had more difficulty accurately classifying problems considered to represent high levels of cognitive complexity compared to problems that were less complex. Those with strong mathematics content knowledge, as measured by a standardized test, were able to sort the problems more accurately than those with weaker content knowledge. Two open-ended items assessing content knowledge were not related to sorting performance. Finally, the preservice teachers were influenced by the surface characteristic of task length; the data indicated that the teachers tended to label short problems as less cognitively demanding and long problems as more so. Implications for preservice professional development include an increased emphasis on mathematics content knowledge as well as expert modeling of the identification of deep conceptual principles at the heart of the mathematics curriculum.     

日本中小学教师职前教育课程新变革

日本文部科学省自2019年4月1日起开始实施对中小学教师培训课程的变革。主要变革内容为提高教师信息活用技术和外语能力、强化教师的教育理解并关注特殊学生群体、增加对教师的综合学习时间课程的指导以及允许高校自主设置一定的培养课程,提高了教师队伍质量。而我国目前的教师资格考试制度存在种种弊端,例如教师准入门槛低、缺乏教学实践经验和理论知识的积累以及教师信息技术手段活用能力不足等问题。它山之石,可以攻玉,借鉴日本经验有益于我国发展教师队伍建设,提高我国教师专业素质。     

基于数学课程标准的小学数学教材调查分析

第八次基础教育课程改革倡导教师“用教材教”,而不是“教教材”．新教材使用至今10多年了,为了解教师对教材使用情况,调研了天津市河西区与郑州市金水区的523名小学数学教师,结果表明：教材能够比较好的体现数学课程标准的要求;注重对学生创新精神和实践能力的培养;内容丰富,容量恰当;难度基本合适;教材能够有效指导教师的教学;教材外观漂亮,出版服务比较好．结论教师总体认同教材,认为教材富有特色,尚需进一步改进．     

Loud and Clear: The Importance of Telling the Stories of African American Male Preservice Teachers

ABSTRACT

The shortage of African American male teachers has been a consistent issue in education. However, there is still much to learn about the experiences and perspectives of African American men on the teaching pathway. By placing a spotlight on the complex positioning of African American men in education, this essay expounds on the importance of capturing the stories of African American males enrolled in teacher education programs.     

Transition to Science Teacher Educator: Tensions Experienced while Learning to Teach Lesson Sequencing

This self-study investigated the tensions that I (Heidi) encountered when teaching elementary preservice teachers how to develop a coherent sequence of five science lessons. Four lesson planning components guided me in developing a series of lessons to support the preservice teachers with this exercise. Employing self-study methodology, data sources included preservice teachers' artifacts, an audio-recording of the preservice teachers discussing the planning of their lesson sequence, and two reflection journals, one kept personally and one kept collaboratively with my co-author and critical friend (Meredith). Findings indicate that a tension of telling and growth developed gradually during the three weeks of teaching. The collaborative journal revealed that this tension was promoted by two other tensions: confidence and uncertainty, and planning and being responsive. Implications regarding the need for explicit teacher educator coursework and reflective practice opportunities are discussed as potential avenues for Ph.D. programs to consider to lessen the tensions that doctoral students may experience during their transition into the role of teacher educator.     

新课程实施中数学教师面临的现实性挑战

新课程对一线数学教师提出了较高的要求.从试验区的情况看,需引起重视的问题是在教学实践中教师们面临着全面的现实性挑战,包括教学理念的更新与转变,教学目标的落实,课程内容的理解与把握,教学方式的探索与开发,教育技术的掌握与运用,教学评价方案的制定与实施等方面.     

数学课程改革与数学教师专业发展--专题研讨会综述

基础教育数学课程改革既需要专业化的数学教师,也能够促进数学教师的专业发展。但是,现实情况可能更为复杂,所以,需要研究者们不断地反思、改进数学课程改革与数学教师专业发展及其之间的关系：现实如何？问题何在？何以解困？批判的现实主义可能是研究者们所应把持的基本立场,如何处理好各方利益相关者之间的平衡可能就是问题所在,而理论建构和争鸣与实践尝试和探索及其激荡与互动也许就是解困之出路。     

新课程背景下中澳两国数学教师教学能力的比较研究——以加强数与代数学习之间的衔接为例

中国与澳大利亚最新的国家数学课程标准都特别强调数与代数学习衔接的重性。运用问卷,从以下四个方面分析、比较中澳两国数学教师在这一问题上的教学能力:相关数学知识,对数学课程标准理念的解读,对学生数学思考的理解,短期与长期的教学计划。结果表明,中澳数学教师在总体能力上水平相近,中国教师对于数学知识的理解更为清晰,而澳大利亚教师则在对学生数学思考的理解上表现得更好。与此同时,在推行国家数学课程标准时,教师教学能力是一个不容忽视的关键因素。     

数学文化在小学数学新教材中的实践研究——以西师版为例

数学教育本质上就是数学文化的教育.基础教育课程改革以来,各版本小学数学新教材已经将数学文化作为一个新的教学要求渗透于其中,这是《标准》的要求,也是教学的需求.国内已有多套教材在这方面做了有益的探索,以西师版小学数学教材为例说明:小学数学教材中数学文化的题材选取要体现多样化,数学文化的呈现形式可以图文并茂,数学文化有必要并且能够从低年级多维度渗透到小学数学教材中.     

Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom?

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and support the professional development of these teachers? Eighteen such textbooks for use by 7 to 11-year-old children in England were examined for their potential to help teachers attend to reasons. It was found that they were unlikely to point teachers towards reasons for patterns and procedures. Although some had the potential to help in introducing and structuring a lesson, they were unlikely to induce the teacher to address matters of understanding in their discourse. Their implicit message tended to be that mathematics education is about computational skill development through routines, algorithms and practice.     

Preparing Mathematics Teachers to Teach English Language Learners: What We Know and What We Can Do

Abstract

A recent issue of The Educational Forum contained eight articles theming the preparation of teachers for linguistically-diverse classrooms. This article extends that discussion, and in it this scholar introduces practicalities for mathematics teachers in linguistically-diverse classrooms, and provides suggestions for teacher educators whose target audience is prospective mathematics teachers. The author’s intention is to contribute to the discussion of supporting ELLs in mathematics classrooms, and to advance the praxis for teachers and teacher educators.     

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.     

教育类课程对职前数学教师作用欠佳的归因调查

教育类课程对职前数学教师教学知识的发展作用欠佳的原因是多方面的,既有教育类课程内容方面的原因,也有职前数学教师自身的原因,此外教授职前教育课程的教师的专业能力、教学方法也是不可忽视的原因.