美国《中学数学教与学》教材的特点及其对中国数学教师教育的启示

美国《中学数学教与学》是初中年级数学教师教育"数学教学法"课程的教材,其特点表现为:单元主题以数学教学理论为线索呈现,单元内容以具体数学知识为载体展开并且以参与式活动的形式组织教学活动.该教材对我国的数学教师教育有如下启示:数学教师教育课程应以数学知识为载体学习数学教育理论;数学教师教育教材应突出教学方式的示范性,体现做中学,在数学教学活动中学习数学教学方法;数学教师教育应注重教师学科专业素质的提升.     

Valid and Reliable Science Content Assessments for Science Teachers

Science teachers’ content knowledge is an important influence on student learning, highlighting an ongoing need for programs, and assessments of those programs, designed to support teacher learning of science. Valid and reliable assessments of teacher science knowledge are needed for direct measurement of this crucial variable. This paper describes multiple sources of validity and reliability (Cronbach’s alpha greater than 0.8) evidence for physical, life, and earth/space science assessments—part of the Diagnostic Teacher Assessments of Mathematics and Science (DTAMS) project. Validity was strengthened by systematic synthesis of relevant documents, extensive use of external reviewers, and field tests with 900 teachers during assessment development process. Subsequent results from 4,400 teachers, analyzed with Rasch IRT modeling techniques, offer construct and concurrent validity evidence.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

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.     

The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers’ knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this study is to explore whether elementary teaching candidates’ MCK and MPCK are associated with their opportunities to learn in mathematics courses and mathematics methods courses in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components.     

小学数学教师职前培养应重视的几个方面

数学教师的职前培养是数学教师专业化发展的重要环节,小学数学教师职前培养应重视以下几个方面:更新职前教师的数学教育观念;改进小学教育专业数学类相关课程的教学方法;深入研究高观点下的小学数学内容知识。     

Teacher candidates' growth in designing mathematical tasks as exhibited in their lesson planning

Abstract

In order to gain insight into preservice teachers' beliefs about planning for mathematics instruction, a study was carried out involving K‐8 teacher candidates enrolled in an elementary mathematics methods course. Doyle's (1992) notion of academic task and the research on pedagogical content knowledge served as the theoretical framework for this study. The teacher candidates submitted lesson plans at three intervals during a semester‐long methods course; the lesson plans were then coded based on candidates' planned uses of academic tasks. Analyses of the data revealed trends in these teacher candidates' design of academic tasks over the course of the semester. Recommendations and implications are pre‐sented highlighting the benefits of incorporating the knowledge base on academic task into a mathematics methods course as a means to con‐tribute to teacher candidates' developing pedagogical content knowledge via their designing of academic tasks in lesson planning.     

In Pursuit of a Connected Way of Knowing: The Case of One Mathematics Teacher

In this paper, we offer illustrations of a mathematics teacher’s difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher’s thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The paper is based on a sub-study that is part of a larger Colombian project, PROMESA (Creating Science and Mathematics Connected Learning Experiences that Open Opportunities for the Promotion of Algebraic Reasoning), which incorporated a Professional Learning Programme (PLP) seeking to integrate school science and mathematics teachers into working teams, in order to create science and mathematics connected learning experiences that considered the promotion of algebraic reasoning. The ‘challenging questions’ that emerged for this teacher, during the workshops of the induction stage of the PLP, became the driving force for her continued engagement in learning mathematics content in a connected way, as opposed to the compartmentalised content-item thinking that she had experienced as a school student. We provide illustrations of first steps in the development of a teacher’s mathematical understanding, which can support growth of mathematical knowledge for teaching.     

Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries

First findings of IEA’s “Teacher Education and Development Study in Mathematics (TEDS-M)” had revealed differences in the demographic background, opportunities to learn (OTL), and outcomes of teacher education between student teachers from different countries. Two hypotheses are examined: OTL and teacher background are significant predictors of mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) as outcomes. OTL effects are partly mediated by differential student teacher intake. Data from multi-level models support our hypotheses with respect to gender, high-school achievement, motivation, OTL in mathematics and the mediating effect of student teacher intake. Background affects only MCK but not MPCK.     

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.     

Pre-service Mathematics Teachers’ Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

This study examined pre-service mathematics teachers’ knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4–8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males’ knowledge scores are significantly higher than females’ scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers’ knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers’ positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.     

中美职前小学教师教育中数学课程的比较研究——以上海师范大学和纽约城市大学为例

教师教育中数学知识的获得是影响职前小学教师数学知识的主要因素之一,以我国上海师范大学和美国纽约城市大学小学教育专业本科培养的数学课程计划为个案,从数学内容类课程和数学方法类课程两方面研究发现,两国职前小学教师教育中各数学课程在学分要求、教学目标、教学内容和教学方法等方面存在差异。美国职前小学教师本科培养的经验,对我国职前小学教育专业本科培养的数学课程设置与实施应该如何加强联系小学数学课程与教学实际具有一定借鉴。     

高职院校学生数学素养现状及对策

目前,高职学生的数学素养存在的主要问题是：对数学文化缺乏认识,数学史知识贫乏,数学美鉴赏水平有限,数学语言转化能力差,思维、逻辑推理能力薄弱。要提高他们的教学素养,应从科学素质教育和数学文化的角度,更新高职数学教育理念;开设高职数学文化课程,改革高职数学课程体系;构建高职数学文化课程内容,深化高职数学教学改革。     

Development and use of a test instrument to measure biology teachers’ content knowledge (CK) and pedagogical content knowledge (PCK)

Research on teachers’ professionalism and professional development has increased in the last two decades. A main focus of this line of research has been the cognitive component of teacher professionalism, i.e., professional knowledge. Most of the previous studies on teacher knowledge—such as the Learning Mathematics for Teaching (LMT) (Hill et al. 2004), the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students´ Mathematical Literacy (COACTIV) (Baumert et al. 2010), and the Mathematics Teaching in the 21st Century (MT21) (Schmidt et al. 2007) studies—have been conducted in the field of mathematics teachers’ pedagogical content knowledge (PCK) and content knowledge (CK). There have been few comparable studies conducted with science teachers, especially biology teachers. To fill the gap, this study examines the development and use of instruments to measure biology teachers’ CK and PCK. In particular, this study describes a method to develop reliable, objective, and valid instruments measuring teachers’ CK and PCK in four steps by the use of empirical data of students. Additionally, the study explores whether CK and PCK might be measured as separate knowledge categories by using a paper-and-pencil test. This paper presents a theoretical model that guides test development and provides steps to develop and validate the instruments. Details are also provided regarding the computation of the Rasch scale score measures for 158 biology teachers. The results indicate that the instruments measured teachers’ CK and PCK in an objective, valid, and reliable way. This suggests that the new instruments can be used in combination with classroom observations to examine teaching quality and further its relation to student learning.     

RETHINKING FOOD UTILIZED AS MATERIALS FOR ART

ABSTRACT

Teaching mathematics in an early childhood program requires mathematical content knowledge and teacher self-efficacy, yet research has shown that early childhood educators often have negative attitudes towards mathematics and feel underprepared to teach mathematical concepts. The study reported here documents the reconceptualization of a graduate, preservice teacher education program, a program designed to address teacher anxiety and increase capacity to teach mathematics in a play-based early childhood setting. The study aimed to investigate: (1) the effectiveness of the mathematics component of the course in equipping teacher candidates to teach mathematics in early childhood, and (2) whether participation in the mathematics component of the course changed teacher candidates’ self-efficacy regarding mathematics. Findings show that both self-efficacy and content knowledge improved when teacher candidates had the opportunity to engage with play-based learning experiences that embed mathematical concepts. Furthermore, the focus on a learning trajectories approach supports the identification of developmental progression points in children’s emerging mathematical understanding, assisting with teacher candidates’ fine-grained observations, assessment of children’s learning, and authentic, individualized planning for learning.     

Comparing Knowledge Bases and Reasoning Structures in Discussions of Mathematics and Pedagogy

While teaching, teachers need to access both their knowledge of mathematics and knowledge of pedagogy. Practice-based materials afford teachers opportunities to reason about both mathematics and pedagogy within the context of teaching. Accepted systems exist for explaining and reasoning in the domain of mathematics; logic, procedures, and representations all serve as instances of mathematics that bear common meaning in the domain. In contrast, there is not an accepted well-structured system for reasoning within the domain of pedagogy; rather, it is an inherently interpretive act. This paper explores differences in knowledge bases and reasoning by examining discourse about mathematics and pedagogy in a practice-based teacher education course. Mathematics conversations featured greater depth of conversation, more challenges, and more echoes of previous claims. Pedagogical conversations were denser and featured more qualified statements and more evidence from personal values or opinions. Implications for the design of teacher education and professional development experiences are presented.     

新课程标准下数学课程资源的开发和利用

新课程理念下的数学资源有着广泛的内涵和外延,是保证新课程实施的基本条件。为了更好地为新课程的实施服务,必须开发和充分利用数学课程资源。数学课堂资源的开发和利用可以从以下几个方面进行：学生中的课程资源,教师中的课程资源,师生共有资源,校内能为数学课程服务的教育资源,校外能为数学课程资源服务的有效资源,现代教育技术手段;现代信息资源。     

Secondary School Mathematics Teacher's Professional Knowledge: A case from the teaching of the concept of function

This study examines the relationships between a secondary Mathematics teacher's pedagogical content knowledge and the dilemmas posed when teaching the concept of function. Alternative tools and procedures for analysing these relationships are used. The results illustrate the flexibility of her knowledge use in Mathematics teaching and how it is related to her knowledge of the pupils as Mathematics learners. In addition, it highlights the central role played by the teacher's knowledge about pupil comprehension in the content and organisation of her teaching agenda. The difference that the teacher establishes between exercise and problem shows her struggle with the two-fold understanding-memorisation of procedures as the content of a teaching dilemma. The results obtained suggest the need for secondary Mathematics teacher education programmes to adopt approaches that take into account the central role played by teacher knowledge about Mathematics learning, and the dilemmas generated when teachers have to reconcile objectives that are apparently contradictory during their teaching practice.     

Between the Academic Mathematics and the Mathematics Education Worlds

Change is always difficult, and there is no great doubt that teachers need time to come to terms with it. This fact is, however, too often forgotten. In the spirit of my earlier work, this paper is shaped by an action research perspective. It provides some insights into the learning experiences of a group of eleven experienced secondary mathematics teacher, who were enrolled in a Perspectives on Mathematics Education two semesters course, within the context of a Masters on Mathematics Teaching programme, held at a Department of Mathematics, in a Portuguese University. The first part of the paper highlights the conflicting pressures and stresses suffered, during the first semester course, by the participating teachers. Confrontation with new ideas about both mathematics and mathematics education, as well as work overload, had a damaging impact on the teachers’ self‐confidence and morale. The second part of the paper covers the second semester course by addressing three fundamental questions for teachers, which aimed at helping the students bridge the academic mathematics and the mathematics education worlds. Finally, brief scenarios of three participating teachers’ professional development throughout the course are discussed in order to illustrate the challenges they had to face and the possibilities the course (and the Masters programme) offered to promote individual change.     

Gender Difference in Teachers’ Mathematical Knowledge for Teaching in the Context of Single-Sex Classrooms

This study examines gender differences of teachers on their mathematical knowledge for teaching in the context of single-sex classrooms in Saudi Arabia. A translated version of the Mathematical Knowledge for Teaching (MKT) instrument (Learning Mathematics for Teaching [LMT], 2008) in Number and Operation Content Knowledge (CK) and Knowledge of Content and Student (KCS) scales were administered to 197 teachers (146 male and 51 female). Two-sample t test and multiple regression were conducted to compare the two groups and test the effect of teacher background variables. Female teachers significantly scored better than their male counterpart. Gender, years of teaching experience, and specialization significantly predicted teachers’ content knowledge, F(3, 187) = 13.180, explaining 41.8 % of the variance. Only gender and specialization significantly predicted teachers’ knowledge of content and student, F(2, 191) = 6.335, explaining 24.9 % of the variance. Further comparing items in the MKT instrument where female teachers outperformed male teachers confirmed that female teachers were better in attending to the content knowledge in the context of student’s learning.