Scrutinizing a Survey-Based Measure of Science and Mathematics Teacher Knowledge: Relationship to Observations of Teaching Practice

There is a clear need for valid and reliable instrumentation that measures teacher knowledge. However, the process of investigating and making a case for instrument validity is not a simple undertaking; rather, it is a complex endeavor. This paper presents the empirical case of one aspect of such an instrument validation effort. The particular instrument under scrutiny was developed in order to determine the effect of a teacher education program on novice science and mathematics teachers’ strategic knowledge (SK). The relationship between novice science and mathematics teachers’ SK as measured by a survey and their SK as inferred from observations of practice using a widely used observation protocol is the subject of this paper. Moderate correlations between parts of the observation-based construct and the SK construct were observed. However, the main finding of this work is that the context in which the measurement is made (in situ observations vs. ex situ survey) is an essential factor in establishing the validity of the measurement itself.     

Novice mathematics teachers create themselves

This study presents a qualitative research based on three narratives written by novice mathematics teachers. We examine their unique professional world during their first year of work. The methodology of narrative framework, on which this article is based, helps to gain better understanding of the need for novice mathematics teachers to have pedagogical knowledge. Findings reveal three themes of pedagogical knowledge: the attitude of novice teachers toward students with difficulties in mathematics; parents’ expectations of and involvement with novice mathematics teachers; teacher–student relations. The implications of the findings show that novice mathematics teachers are required to have not only content knowledge of mathematics but also, and above all, pedagogical knowledge. The implications of this study enable reassessment of emphases required in training mathematics teachers, as well as the assistance and support they need, especially as they launch their careers.     

A Case Study of Teacher Beliefs on Students' Beliefs about Multiple Representations

The mathematics education community, in its call for reform, underscores the importance of mathematics instruction emphasizing the use of multiple representations in the presentation of concepts. The focus of the study was how teacher beliefs affect their ability to implement a multiple representations curriculum. The novice instructor's attitude remained neutral while the experienced instructor's attitude remained somewhat positive. Of the eight students in the study, six of them showed a more positive attitude towards technology use and multiple representations by the end of the semester. The students increased their calculator use in both classes, particularly in the experienced teacher's class. Implications for further research were that teacher training is essential if reform curricula are to be properly implemented.     

Reconstructing elementary teacher candidates' understanding of mathematics and science content

This paper examines the mathematics and science content knowledge of elementary teacher candidates. Data are presented which demonstrate that many elementary teacher candidates enter teacher education seriously deficient in their understanding of the subject matter they will teach to elementary students. The authors argue that these candidates are weakly prepared in content because of deficiencies in the pedagogy practiced in traditional didactic mathematics and science courses. They describe a conceptual approach to teaching mathematics and science content and contrast this with a didactic approach. Data are presented which demonstrate that these conceptual approaches significantly improved novice teachers understanding of content.     

Promoting teacher learning: a framework for evaluating the educative features of mathematics curriculum materials

Educative curricula, curriculum materials that intentionally foster teacher professional development, can serve as a site for teacher learning through their use in daily instructional practices. The present article introduces a framework, Teacher Learning Opportunities in Mathematics Curriculum Materials (TLO-Math), for designing and evaluating mathematics curriculum materials’ educative features according to seven theoretically based variables: (1) mathematics content knowledge for teaching, (2) teacher knowledge of student thinking in mathematics, (3) teacher knowledge of disciplinary discourse in mathematics, (4) teacher knowledge of assessment in mathematics, (5) teacher knowledge of differentiated instruction in mathematics, (6) teacher knowledge of technology use in mathematics, and (7) teacher knowledge of mathematical community. Each variable is illustrated with a definition, guiding questions, discipline-specific literature, and examples from two sets of elementary mathematics curriculum materials. The development of the TLO-Math framework is a critical first step for further study of the use of mathematics curriculum materials as sites for teacher learning.     

韩国职前数学教师教育的评介与分析

韩国的数学教师职前教育体制有如下特点:类型多样的教师职前培养机构、严格的公立学校数学教师聘任制度、定期的教师教育机构评估制度.小学数学教师教育课程具有综合性、多样化特点;中学数学教师教育课程更重视学科知识.韩国数学教师职前教育对中国的数学教师教育有如下启示:建立多元的办学体制,致力于专业化的数学教师培养;以教师聘任制度和教师教育机构评估制度促进数学教师培养质量的提高;在学科课程和教学法课程之间寻求恰当平衡.     

Finding her way: a beginning teacher's story of learning to honour her own voice in teaching

This article examines the ways in which a collaborative action research design became the lens by which a classroom teacher and two university teacher educators examined the practice of a novice during her second year of teaching. Together the three authors tell a story of a young woman's struggle to find and honour her voice as a new teacher. Three overarching themes were identified from the date, including university preparation, formal/informal support networks and finding and honouring her voice. Findings revealed that the collaborative nature of this research provided for unintended praxis for all researchers. Ultimately, the teacher's quest for voice and ultimate articulation of self-as-teacher emerged as a result of her participation in this collaborative inquiry.     

A CASE STUDY OF THE IMPLEMENTATION OF CHINESE KINDERGARTEN MATHEMATICS CURRICULUM

In 2001, the Chinese Ministry of Education issued Guidelines for Preschool Education (GPE) (trial version) to call on early childhood practitioners to use a child-centered and play-based approach to teaching and learning. The guidelines also include mathematics within the science domain and described its standards in a way that significantly lessens the teacher’s role as knowledge disseminator. Instead, the guidelines encourage mathematics learning and teaching through play, self-discovery, and problem solving. This qualitative case study examined one kindergarten teacher’s implementation of and associated challenges in delivering mathematics lessons from a newly developed integrated provincial curriculum (PC) and the quality of instruction as influenced by using a curriculum that is organized around thematic units. The analysis of the curriculum, ten videotaped lessons, two teacher interviews, and other supporting documents, such as student work and teacher lesson plans, indicated that the teacher encountered difficulties implementing the PC as intended due to a number of factors, including inadequate curricular resources, incoherency of the curriculum design, and a mismatch between the mathematics standards and curriculum goals and the teacher’s instructional style and teaching philosophy. As a result, the quality of mathematics instruction was poor, especially in the areas of (1) using effective teaching strategies, (2) providing clear and accurate instruction with a positive attitude, (3) engaging students in sustained interactions with mathematical ideas, and (4) offering on-going assessment and feedback. To close, recommendations for curriculum refinement and professional development are provided.     

Linking reform-oriented experiences to teacher identity: The case of an elementary mathematics teacher

Novice teachers often have difficulty transferring what they learn in teacher education programs to classroom practice. This is especially true for elementary school teachers who are expected to teach mathematics with reform-oriented methods. The purpose of this longitudinal case study was to examine the experience of one novice elementary school teacher over a 3-year period, and understand the factors that supported her to enact a reform-oriented practice in mathematics as she transitioned from being a preservice to inservice teacher. Influential mathematics education models, her commitment to learning, and school-based contexts affected her teaching identity and practices. To conclude, an argument is made for teacher education experiences to explicitly address mathematics teacher identity to support the enactment of reform-oriented practices.     

PROFESSIONAL NOTICING PRACTICES OF NOVICE MATHEMATICS TEACHER EDUCATORS

The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those educating teachers. This research explores how novice mathematics teacher educators professionally notice as they engage in teaching experiments and create models of student’s mathematical thinking. Findings indicate the novice teacher educators are including some evaluative comments in their professional noticing practices but lack in-depth interpretive analysis about student thinking and rarely make connections between student’s thinking and the broader principles of teaching and learning. These findings provide evidence for the importance of supporting teacher educators with developing their abilities to professionally notice.     

Field experiences in secondary teacher education: Qualitative differences and curriculum change

This paper illustrates the nature of postlesson discussions between experienced and novice secondary science teachers during an early field experience. Analysis and appraisal of differences evident in these discussions suggests that novice secondary teachers experience significant variations in the substance and quality of field-based activities intended to help them develop competence in teaching. The author explores the potential of these variations to influence the development of pedagogical reasoning and the contextual influence of curriculum change in shaping experienced teachers' views of their role as teacher educators.     

Supporting novice elementary mathematics teachers’ induction in professional communities and providing innovative forms of pedagogical content knowledge development through information and communication technology

This paper reports on the needs identified as important to 27 novice elementary mathematics teachers and examines how Connect-ME, an online mathematics community, provides these supports. Qualitative data were collected using two focus groups and 16 telephone interviews. Findings validate the need for alternative teacher professional development (TPD) models and the value of professional communities and knowledge acquired through technology-facilitated learning. The results indicate that teachers actively seek formal and informal TPD experiences, opportunities for sharing and communicating, and access to quality resources. This study provides educational researchers and administrators with essential elements for effectively supporting novice elementary mathematics teachers.     

Certified But Not Qualified? EFL Pre-service Teachers in Liminality

Research on novice ESL/EFL teachers’ identity development often characterizes the teaching practicum/internship as a boundary-crossing period in which pre-service teachers move out of the sheltered environment of education to become in-service teachers in real classrooms. Nevertheless, many prospective teachers experience a prolonged pre-service period in which an examination-based selection mechanism is used to gatekeep teacherdom. Through the lens of liminality, the study explores the experiences of two Taiwanese pre-service secondary EFL teachers during a period filled with high-stakes recruitment examinations. By examining how the two participants negotiate their identities and learn about the profession amid the disheartening challenges and learning opportunities they face during liminality, the study gives voice to pre-service teachers caught in between institutional structures and allows them to articulate their struggles as well as their sense of agency in pursuing a teaching career. The findings yield practical implications for EFL teacher education and the examination-based selection mechanism.     

Curriculum strategy framework: investigating patterns in teachers’ use of a reform‐based elementary mathematics curriculum

The goal of this paper is to introduce the curriculum strategy framework as a way to characterize teachers’ interactions with curriculum materials. The framework focuses on three key interpretive activities: reading, evaluating, and adapting curriculum materials. Describing an individual teacher’s curriculum strategy involves identifying the manner in which a teacher engages with each of these activities before, during, and after instruction. This paper presents the results of a study in which the framework was used to identify patterns in the curriculum strategies of 10 elementary‐school teachers who were using a reform‐based mathematics curriculum for the first time. It concludes with directions for further research using the curriculum strategy framework, and implications of this work for curriculum designers.     

Designing a curriculum based on four purposes: let mathematics speak for itself

Trends in curriculum reform recognise the need to develop skills and competencies in addition to specifying what knowledge should be taught and when. However, a balance between skills and knowledge is sometimes difficult to achieve. In this paper which takes mathematics as the focus, we consider reform currently underway in Wales, from the perspective of a ‘knowledge approach’ and from the perspective of the Successful Futures report which is, we argue, driven more by a skills approach at the heart of which are ‘four purposes’: developing young people as ambitious, capable learners; enterprising, creative contributors; ethical, informed citizens; and healthy, confident individuals. Our interest is in the contribution that mathematics makes to the four purposes; and contribution that the four purposes make (or do not make) to the development of a school mathematics curriculum. After outlining the background and context, the paper consults literature and experts to consider what mathematics is and how the learning of mathematics can be seen to fulfil the four purposes. The study contributes to understanding the difficulties of re-contextualising school subjects from the academic disciplines and proposes that operating with a curriculum driven by big ideas or overarching statements places higher demands on teacher knowledge.     

Negotiating Voice Construction Between Writers and Readers in College Writing: A Case Study of an L2 Writer

Voice is co-constructed, a result of the “text-mediated interaction between the writer and the reader.” The present study, using the context of U.S. college writing, explores the complicated process by which an L2 novice writer—one who has a growing awareness of, yet peripheral access to, discourse practices—constructs a voice. Through interviews and a close analysis of a text, a comparison is made between the voice the L2 writer wished to project in an assigned paper and the voice constructed by two readers in the course of their anonymous readings of the paper. The significant gap between the L2 writer’s aims and the readers’ responses suggests that a writer’s view of her voice stems from the ways in which she conceptualizes discourse conventions, in association with her particular linguistic, social, and cultural background. The pedagogical implications of the L2 writer’s process of negotiating identity, and her struggles to learn discourse expectations, are discussed.     

美国综合大学中学数学教育专业的课程设置探析——以美国特拉华大学为例

人才培养质量在相当程度上取决于是否具有与之相匹配的课程设置.特拉华大学教师教育的培养目标为,培养反思性教学实践者.美国中学数学教育专业的课程设置的特点有:通识教育占主导地位、重视数学基础和数学的纵横联结、教育实践活动贯穿教育课程、教学评价凸显立体化.     

The organization of the mathematics preparation and development of teachers: a report from the ICMI Study 15

This article presents the results of an investigation carried out across 20+ country-regions under the auspices of ICMI Study 15 into the structures, approaches and general characteristics of the mathematics preparation and development of teachers. We use a global framework provided by the larger research literature on teacher education to contextualize the findings. The article provides an analytic perspective on (a) teacher education systems’ characteristics including institutional arrangements and regulations; (b) teacher’s recruitment, selection, and credentials; (c) teacher education programs’ structure and approaches; (d) teacher educators’ characteristics; and (e) the structure and content of the curriculum. This article highlights the important differences and similarities across systems that provide mathematics education and development to teachers. This article concludes with a discussion on implications for future empirical research on mathematics teacher education.     

Professional primary school teacher identity development: a pursuit in line with an unexpressed image

The results presented in this article are taken from a case study of novice primary school mathematics teachers’ professional identity development from the perspective of the teachers themselves. The empirical material was collected through self-recordings, observations and interviews. The results show how the professional identity development of these novice teachers becomes a pursuit in line with their image of a primary school teacher. To develop a sense of themselves as primary school teachers they need to establish their own criteria - individual (including graduation and personal knowledge) and social (the ability to work in one school, have colleagues and have a class of their own for which they do the planning and teaching). These criteria are shown to be both a precondition for and a part of professional identity development. The novice teachers’ image of what it means to be a primary school teacher directs their actions and becomes the goal of their professional identity development. Because of its high impact, student and novice teachers’ image of primary school teachers ought to be made visible in both teacher education and teacher induction.     

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．