Developing Self-Efficacy in Teaching Mathematics: Pre-Service Teachers’ Perceptions of the Role of Subject Knowledge

ABSTRACT

Two major concerns in mathematics teacher education are the role of subject matter knowledge and the development of self-efficacy in pre-service teachers. This article brings these issues together in an exploration of the interaction between pre-service teachers’ perceptions of their subject matter knowledge and their accounts of university and placement experiences as potential sources of self-efficacy. Reporting on a group of ten pre-service teachers in Norway, we explore variations in the ways in which they perceived the role of subject knowledge in relation to experience, particularly “mastery experiences”, over a period of nearly two years. We suggest that recognition of the role of “understanding why” in mathematics is crucial in the experience of mastery, and that there is a need to focus more on the role of subject matter knowledge in all sources of self-efficacy in teaching mathematics.     

AHA Moments of Science and Mathematics Pre-service Teachers

This research study explored pre-service teachers' (PST) reflections of their student teaching experiences through AHA moments. Participants included 37 pre-service teachers enrolled in mathematics and science student teaching seminars. Qualitative methods were used to analyze PSTs' written and verbal responses to questions regarding AHA experiences. Four themes emerged related to PSTs' AHA moments: a greater awareness of PSTs' identity as teachers, the importance of knowing their students, the realization of inconsistencies in their own and their students' beliefs, and the importance of anticipating students' misconceptions. The potential for using an AHA moment assignment, as presented here, appears to support reflection among PSTs; however, it is not clear these PSTs used judgments and analysis, both integral elements of the reflective process.     

Number Sense Strategies Used by Pre-Service Teachers in Taiwan

This study examined number sense strategies and misconceptions of 280 Taiwanese pre-service elementary teachers who responded to a series of real-life problems. About one-fifth of the pre-service teachers applied number sense-based strategies (such as using benchmarks appropriately or recognizing the number magnitude) while a majority of pre-service teachers relied on rule-based methods. This finding is consistent with earlier studies in Taiwan that fifth, sixth, and eighth grade students tended to rely heavily on written methods rather than using number sense-based strategies. This study documents that the performance of pre-service elementary teachers on number sense is low. If we want to improve elementary students’ knowledge and use of number sense, then action should be taken to improve the level of their future teachers’ number sense.     

Misconceptions of Turkish Pre-Service Teachers about Force and Motion

The purpose of this study was to diagnose the misconceptions held by pre-service physics teachers about force and motion. The secondary aim of the study was to detect whether misconceptions vary according to gender, educational level, and culture. The study was conducted with 79 student-teachers attending to one of the largest faculties of education in Turkey. Force Concept Inventory (FCI) was used to diagnose student-teachers’ misconceptions. FCI is a conceptual test consisting of 29 multiple choice items. Each wrong choice for each question reflects a specific misconception about the force and motion concepts. Data from the study was analyzed by using frequencies, t-test, and ANOVA for making comparisons according to gender and years of education. Results of the study showed that student-teachers of physics hold very strong misconceptions about impetus and active force. No significant differences were found between male and female students’ scores on the concept test. The results also showed that misconceptions about force and motion decreased through the years of education. However, they did not disappear completely. Findings of the study are very similar to the other research findings conducted on the subject in other countries. Student-teachers’ conceptions about Newton’s Third Law, on the other hand, were significantly better than those observed in other research done in other countries such as the US and Finland.     

A Comparison of Preservice Teachers' Mathematics Anxiety Before and After a Methods Class Emphasizing Manipulatives

The changes in levels of mathematics anxiety among future teachers in two different mathematics materials and methods classes were investigated. The changes were a function of using: (a) Bruner's framework of developing conceptual knowledge before procedural knowledge, and (b) manipulatives to make mathematics concepts more concrete. The sample included 87 preservice teachers enrolled in mathematics methods courses. Two strategies were used to gather data both at the beginning and ending of each quarter. First, future teachers completed 98-item, Likert-type questionnaires. Second, some of the factors that influence the levels of mathematics anxiety were determined through the use of questionnaire-guided narrative interviews. Multivariate analysis of variance was employed as the quantitative measure for comparing mathematics anxiety both at the beginning and ending of the quarter. Data revealed a statistically significant reduction of mathematics anxiety levels (p < .05). Tukey's HSD was used to determine that a significant difference in mathematics anxiety levels occurred between the classes in the fall and winter quarters. Results of the study have implications for teacher education programs concerning the measurement of mathematics anxiety levels among future teachers and the determination of specific contexts in which that anxiety can be interpreted and reduced.     

Engaging Pre-Service Teachers in Read Alouds

ABSTRACT

Today, reading aloud is considered ‘a significant component of instruction across grade levels’; particularly as a tool for teaching reading in elementary classrooms. It is basically an essential literacy practice for all student teachers to understand how to implement. In this study, authors understand the importance of modelling effective read-aloud practices and they demonstrate how they support engagement in reading and writing instruction with undergraduate students. Student teachers responded to the read alouds using reflective essays, and tables. Themes emerged that indicated that the use of read alouds in the undergraduate classrooms enhanced their understanding of identity, pedagogy, and empathy.     

Interconnecting Content and Community: A Qualitative Study of Secondary Mathematics Teachers

The publication of the National Council ofTeachers of Mathematics initial Standards(1989) has acted as a catalyst to beginreforming the way mathematics is taught in theUSA. However, the literature regarding reformmovements suggests that changing oureducational systems requires overcoming manybarriers and is thus difficult to achieve.Reform in mathematics education, like reformmovements in other areas of education, has thusbeen slow to take hold. One structure that hasbeen shown to support educational reform,particularly instructional reform, has beenteacher community. This paper discusses aprofessional development intervention thatattempted to start a professional communityamong a group of secondary mathematics teachersthrough in-service work on mathematical problemsolving and technology. The results of thisstudy suggest that the use of mathematicalcontent explorations in professionaldevelopment settings provides a means to helpmathematics teachers build professionalcommunities. Together, these two components –mathematical content explorations and teachercommunity – provided these secondarymathematics teachers with a strong foundationfor engaging in the reform of their mathematicsclasses.     

Teacher Education in Britain: a JET symposium with politicians

ABSTRACT

This paper reports on a symposium with the participation of the editor and deputy editor of the Journal of Education for Teaching and two senior British politicians on the current situation of teacher education in Britain. Topics discussed include: control and accountability, the influence of political and bureaucratic forces, the threat from unelected, non‐responsible bodies, threats to institutions, to the links of teacher education with higher education and the threat of the deskilling of the teaching professions. A concluding section considers the possibility that the policy of the Government is failing through its own structural defects and the possibility of the profession's subsequent recovery.     

Understanding Teacher Educators and Their Pre-Service Teachers through Multi-Media Case Studies of Practice

The challenges facing those who seek to prepare mathematics teachers are well established in the literature. Most of the research to date has focused on the perceptions and understandings of pre-service teachers, but not on the perceptions and understandings of teacher educators. In this study, we explore how four teacher educators understand their pre-service secondary teachers as the pre-service teachers attempt to make sense of teaching through the investigation of a multimedia case study of practice. We found that the teacher educators adopted two different implementation strategies: one strategy tended to be open-ended and exploratory; the other was more focused on the teacher educators' goals of anticipating student understanding and developing mathematical content knowledge for teaching. We also found that, in using the case study, teacher educators elicited pre-service teachers' thinking about the complexities of the teacher's role in small group work, about the value of explicitly revealing the teacher's reflections on the lessons, about the role of planning and preparation, and about the limits of pre-service teachers' abilities to understand and appreciate students' thinking and to extend lesson ideas. Both teacher educators and their pre-service teachers gained perspectives on the role of a teacher's mathematical content knowledge. These results imply that multimedia case studies of practice can serve as vehicles for revealing the knowledge and practice of teacher educators, as they engage in supporting the professional development of pre-service teachers.     

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.     

数学教师继续教育课程需求分析

中学数学教师继续教育课程需求类多面广,较受欢迎的有数学教育课程、数学教育技术课程,极少有进修数学科学课程的愿望.在数学教师继续教育过程中:应保持数学教育课程、数学教育技术课程和数学科学课程设置的合理比例,继续教育课程类型与相应的教学模式相对应,重视数学教师继续教育校本课程的研发.     

基于教学隐喻的职前国际汉语教师转化性学习初探

职前国际汉语教师的教学信念在经过一个学期的课程学习之后,绝大部分都有了转变,转变的结果呈现出人本主义倾向,转变的过程蕴涵了丰富的情感。教学隐喻视角的研究对职前国际汉语教师培养的启示在于:隐喻是促进职前国际汉语教师批判性反思的有效途径;要充分重视并有效利用职前国际汉语教师的先前经验;在职前国际汉语教师的培养中要探究有深度的学习内容和方式。     

Engaging Pre-Service Teachers in Multinational, Multi-Campus Scientific and Mathematical Inquiry

Pre-service teachers from Texas and Indiana in the United States and from Queensland, Australia, observed the Moon for a semester and compared and contrasted their findings in asynchronous Internet discussion groups. The 188 pre-service teachers were required to conduct inquiry investigations for their methods coursework which included an initial Moon observation assignment, an Internet Moon discussion, and a final project. The Moon context was chosen for its motivating capability, its inherent interdisciplinary makeup, its inclusion in the National Science Education Standards, and its ability to be viewed worldwide. This study was of a mixed method research design and involved pre-service teachers’ journals, summative reflections, Internet discussions, final projects, and the Lunar Phases Concept Inventory (LPCI). Analysis of the qualitative data was conducted through the exploration of patterns and themes that illustrated pre-service teachers’ conceptual development, and the LPCI was administered as a pre/post assessment. We found that our project led to increased knowledge concerning the mathematics and science involved with understanding the Moon and its phases. We also found that it was beneficial to have Internet discussions with pre-service teachers from around the world, but it was not without its problems (e.g., coordinating schedules and lack of participation by some participants). We discovered that pre-service teachers’ exposure to the new uses of technology for teaching and learning did not necessarily translate to their planning to adopt similar techniques in their own classrooms.     

文科学生高等数学学习焦虑心理及对策研究

高等数学学习焦虑心理是影响文科学生数学学习效果的一个重要情感因素,对高数学习产生负影响。本文分析了焦虑的定义、分类、焦虑对高数学习的影响及焦虑产生的原因,同时,结合作者的实际教学经验和文科学生的实际情况,提出了克服和减轻学生高数学习焦虑的可行性策略。     

准数学教师专业化程度调查研究

数学与应用数学和小学数学教育这两个师范专业学生的专业化发展情况总体良好,在P<0.05水平下被测的专业理念、专业知识、专业技能和专业情意等4个维度均不存在差异,在P<0.1水平下专业知识和专业情意存在显著差异.在数学师范生的教师专业化教学中:应强化学生对教师专业化的正确认识;课堂教学中展示教学方法;优化课程结构,加强学科联系;加强实践性教学;丰富评价体系.     

Engaging Prospective Elementary Teachers in Lesson Study

This paper discusses the ways in which teacher educators can effectively engage prospective teachers (PTs) in lesson study during mathematics methods courses. Evidence from this work suggests that engagement in lesson study provides PTs with opportunities to strengthen their knowledge about mathematics, students, and pedagogy. More specifically, the results demonstrated that lesson study helped PTs to engage in deep and thoughtful discussions about mathematics, reflect on their teaching, and make effective changes to their lessons that showed noticeable improvements in student learning. Recommendations from this work provide specific methods-course suggestions on the implementation of lesson study as a model for PTs' professional and practitioner development, including strategies and guiding questions that teacher educators can utilize to help deepen PTs' knowledge about mathematics, teaching, and student learning.     

西藏地区中小学数学教师认识信念的调查研究

本研究选取西藏地区353名中小学数学教师作为研究对象,通过问卷调查、访谈的方法,采用描述性统计、独立样本t检验和单因素方差分析等探索西藏中小学数学教师认识信念的现状和背景因素差异。研究发现:西藏中小学数学教师的数学认识信念总体上呈进步倾向,在教师自身认识信念上则存在显著的学校位置差异,并且职称对数学教师的数学认识信念、教龄对数学教师的学生信念、学历对数学教师的数学学习信念和数学教学信念均产生一定影响。     

卓越教师培养视角的师范生信息化教学能力课程重构

作为教师教育课程体系的重要组成部分,现阶段的信息化教学能力课程,忽视了"师范生"与"中小学教师"的角色差异,与中小学信息化教学改革的现实需求相脱节,不利于培养师范生的信息素养和信息化教学能力,难以有效地支撑卓越教师培养,亟须重构。立足"互联网+"时代背景,在课程调研基础上,梳理分析了师范生信息化教学能力课程建设与实施现状,明确了课程重构的基本原则,并以"信息化教学技术与方法"课程为例,从教学目标、教学内容、教学资源、教学模式、教学活动、教学评价等维度阐述了课程重构的设想,旨在从"过程"和"结果"两个层面有效地支撑卓越教师培养。     

职前科学教师TPACK的自我效能感研究

应用国外成熟量表工具对307位职前科学教师进行调查,探索其TPACK自我效能感,研究发现:研究对象无论是在性别维度,还是在院校层次维度,抑或是在学历层次维度,TPACK自我效能感大多没有显著性差异,但各个维度分量表和总体得分都不高。在研究基础上建议"拓宽视野,促使职前科学教师全面、科学地认识技术变革;增加技术支持教学的实践机会;引导职前科学教师在研究中发现技术发挥的作用;促进同伴互助,提升TPACK自我效能感"。