The Role of Mathematics Teachers' Content Knowledge in their Teaching: A Framework for Research applied to a Study of Student Teachers

The authors develop and explain a framework toguide research on the relationship betweenmathematics teachers' knowledge of content andtheir teaching. The framework istwo-dimensional. The dimensions are (a) theelements of teaching and (b) the processes ofteaching in which knowledge of content is ofconsequence. The interplay between the elementsof teaching and the processes of teaching isdiscussed theoretically, consideringconnections to existing literature about therole of teachers' subject matter knowledge.Three vignettes from the authors' work withpre-service secondary mathematics teachersinvestigate further the relationship betweencontent knowledge and effective mathematicsteaching. The vignettes also serve toillustrate the complexity of investigationsinto this relationship. Direction is offeredfor use of the framework in future research.     

Preparing Elementary Pre-Service Teachers from a Non-Traditional Student Population to Teach with Technology

This article documents the development of a two-stage curriculum intended to improve elementary teacher candidates’ understanding of technology integration. Most students in the program came from low-income districts and lacked technology experience. The first stage of the curriculum consisted of a prerequisite basic technology skills course offered by the Computer Science Department. This was then followed by an online educational technology course offered by the College of Education. The objectives of the authors in this article are twofold. The first is to describe the rationale, procedures, and design of a two-stage curriculum, as a pedagogical model for teaching elementary teacher candidates to teach with technology, with the goal of preparing a new generation of teachers who are capable and comfortable applying a broad range of advanced technologies to meet the learning needs of their students. The second objective is to share the authors' findings from the evaluation, which employed mixed methodologies, after the students completed the online educational technology course. The results showed that an online educational technology course contributed to the candidates’ development of Technological Pedagogical Content Knowledge and improved their attitudes and beliefs on their technology integration practices.     

美国MKT研究的缘起、发展及启示*

数学教师需要具备怎样的数学知识才能教好数学？美国Ball研究团队MKT概念的提出为这一问题提供了当前最好的答案。本文详述了美国MKT研究的缘起、研究的过程、MKT的结构模型,以期对我国数学教育研究有所启示。     

Secondary Teachers and English Language Learners (ELLs): Attitudes,Preparation and Implications

The education of language-minority students is a constitutional right. Throughout this article, the authors synthesize recent literature addressing two main questions: (1) What are secondary teachers’ attitudes toward English language learners (ELLs)? and (2) To what extent are secondary teachers being prepared to teach content effectively to this student population? Secondary teachers’ attitudes about ELLs vary, but are generally positive. The lack of teacher preparation—especially at the secondary level—to teach ELLs effectively is widespread. Thus, it is not surprising that secondary teachers feel ill-prepared to scaffold or differentiate instruction to meet these students’ language and academic needs. Since attitudes, preparation, and practice are interrelated, the authors also provide numerous implications for future practice at various levels: teacher-preparation programs, school district support, and classroom teaching.     

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.     

Mathematics Teaching as a Deliberate Practice: An Investigation of Elementary Pre-service Teachers' Reflective Thinking During Student Teaching

In this case study I examine the reflectivepractices of two elementary pre-serviceteachers during their student teachinginternship. I extend current views ofreflective practice to create a framework for a`deliberate practitioner'. With this framework,I investigate the pre-service teachers'thinking with regard to reflective processesand how they use their pedagogical contentknowledge in their practices. My findingsindicate that the pre-service teachers usetheir pedagogical content knowledge inanticipating problematic events, and inreflecting on problematic events ininstruction. However, limits in pedagogicalcontent knowledge and lack of confidence impedethe pre-service teachers' reflection while inthe act of teaching. They were more likely toreflect on their practices outside of the actof teaching. Implications for teacher educatorsand pre-service teachers are discussed.     

Exploring ICT Use and TPACK of Secondary Science Teachers in Two Contexts

The aims of the study were to census and compare the technological pedagogical and content knowledge （TPACK） of secondary science teachers and their most used information and communication technology （ICT） in two contexts, Taiwan and Shaanxi Province in China. A questionnaire was employed to examine secondary school science teachers＇ most used ICT and their TPACK in science teaching. Eight hundred and six secondary science teachers from Taiwan and 164 teachers from Shaanxi participated in the study. The analytical results showed that multimedia was the most used ICT in Taiwan, followed by PowerPoint （PPT）, Internet platforms, and interactive whiteboards （IWBs）. In Shaanxi, PPT was the most used ICT reported by science teachers, followed by multimedia, IWBs, and Intemet platforms. The findings indicated that in Taiwan, science teachers＇ TPACK was statistically significant in relation to different types of ICT, whereas in Shaanxi, science teachers＇ TPACK did not demonstrate significant difference. In Taiwan, science teachers who reported their most used ICT to be multimedia were found to show significant differences in TPACK according to gender and teaching experience. In Shaanxi, science teachers who reported their most used ICT to be PPT did not show any significant difference on TPACK by gender; however, they showed significant differences on TPACK in regard to teaching experience. The research implications of this study are provided below along with suggestions for future research.     

Content-Related Knowledge of Biology Teachers from Secondary Schools: Structure and learning opportunities

Teachers’ content-related knowledge is a key factor influencing the learning progress of students. Different models of content-related knowledge have been proposed by educational researchers; most of them take into account three categories: content knowledge, pedagogical content knowledge, and curricular knowledge. As there is no consensus about the empirical separability (i.e. empirical structure) of content-related knowledge yet, a total of 134 biology teachers from secondary schools completed three tests which were to capture each of the three categories of content-related knowledge. The empirical structure of content-related knowledge was analyzed by Rasch analysis, which suggests content-related knowledge to be composed of (1) content knowledge, (2) pedagogical content knowledge, and (3) curricular knowledge. Pedagogical content knowledge and curricular knowledge are highly related (r_latent?=?.70). The latent correlations between content knowledge and pedagogical content knowledge (r_latent?=?.48)—and curricular knowledge, respectively (r_latent?=?.35)—are moderate to low (all ps?<?.001). Beyond the empirical structure of content-related knowledge, different learning opportunities for teachers were investigated with regard to their relationship to content knowledge, pedagogical content knowledge, and curricular knowledge acquisition. Our results show that an in-depth training in teacher education, professional development, and teacher self-study are positively related to particular categories of content-related knowledge. Furthermore, our results indicate that teaching experience is negatively related to curricular knowledge, compared to no significant relationship with content knowledge and pedagogical content knowledge.     

Pedagogical content knowledge of French as a foreign language: differences between pre-service and in-service teachers

Pedagogical content knowledge (PCK) is an important predictor of educational quality. PCK develops from various sources, such as teaching experience. Studies investigating the effects of teaching experience on PCK development mainly focus on the question whether experienced teachers differ from novices in the amount of PCK. In a mixed methods study, we study both quantitative and qualitative differences between pre-service and in-service teachers’ PCK. Total scores on a paper-and-pencil instrument are used as a measure of French PCK. To analyse the participants’ PCK in a qualitative way, answers are coded in four categories and the prevalence of answers in each category is compared between groups. Furthermore, the nature of answers is studied. No differences on our quantitative PCK measure are observed. The qualitative analysis shows that in-service teachers have more difficulties with conceptual knowledge, while showing more practical knowledge of students’ understanding than pre-service teachers.     

Pedagogical Reasoning: Issues and Solutions for the Teaching and Learning of ICT in Secondary Schools

Confusion has developed over the role of ICT in schools as a result of conflicting messages from government-led initiatives and changes in the technology. Amidst the ongoing debate about the purpose and rational for ICT in schools a subject has evolved called ICT (Information and Communications Technology), IT or Informatics. Whilst the nature and content of the subject has been fairly clearly defined with significant agreement between specifications from a range of countries, the pedagogy is still unclear. The analysis that I present here of the pedagogical reasoning process as it applies to ICT teachers who are implementing the ICT curriculum in England reveals the basis of the difficulties in teaching ICT and leads to the identification of issues for the development and integration of theories and practices for learning and teaching ICT. These issues are discussed in relation to developments in pedagogy in other curriculum areas, notably science, and an agenda for developing a pedagogy for ICT is proposed.     

Collaborative Effort to Develop Middle School Preservice Teachers’ Mathematical Knowledge

Abstract

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses, two in mathematics and one in mathematics education, worked together to more explicitly link course materials, assignments, and the pedagogical approaches. Collectively, the courses were designed to address the five components of preservice teachers’ mathematical knowledge for teaching (PT-MKT), and to model effective teaching practices. Using their collective experiences co-planning and implementing these course adjustments were made in the subsequent year. The instructors were pleased by their implementation and student outcomes in all three courses.

We describe how each component of the PT-MKT framework was approached in these courses and discuss challenges experienced by the instructors, who were part of a larger effort to develop and implement a middle school teacher preparation program. The information shared is based on data collected as part of a program evaluation effort, and is bolstered by the instructors’ recollection of events. Overall, the instructors enhanced the curricula and their instructional practices and found that the attention placed on developing PT-MKT support the mathematical development of middle school mathematics preservice teachers.     

近二十年我国中小学教师心理健康研究的文献计量学分析

对收录在中国期刊网上的784条中小学教师研究的论文题录进行计量学分析发现：中小学教师心理健康研究总体上呈现上升的趋势,但近年来有所下降。研究论文发表在主流心理学学术刊物上数量并不多,研究水平需要提高。在基金资助上,国家级项目相对总体基金项目来说较多,省部级、厅局级项目在逐渐增多,校级项目有待提高。在合作方式上,主要以个体研究为主,合作较少,与中小学合作更少。核心作者逐渐形成。研究力量的机构分布主要集中在高等师范院校,中小学较少。从研究内容看,高校与中小学研究的区别较大,高校着重实证研究,中小学侧重对策与综述研究。     

Learning from Rookie Mistakes: Critical Incidents in Developing Pedagogical Content Knowledge for Teaching Science to Teachers

While there is a growing literature focused on doctoral preparation for teaching about science teaching, rarely have recommendations extended to preparation for teaching science content to teachers. We three doctoral students employ self-study as a research methodology to investigate our developing pedagogical content knowledge for teaching science to teachers during a mentored internship in an elementary teacher professional development program. With our mentor, we examine critical incidents in the experience that supported new insights about teaching teachers and about ways in which beginning teacher educators need to develop their existing pedagogical content knowledge for teaching science to students in order to teach science effectively to teachers. We emphasize ways in which doctoral internships can support this learning and how our respective cultures shaped our interactions with and perceptions of teachers as learners.     

Choosing Content and Methods: Focus Group Interviews with Faculty Teachers in Norwegian Pre-Service Subject Teacher Education in Design,Art, and Crafts

The study is aimed at generating knowledge on how faculty teachers reflect and justify their choice of subject content logic in teacher education, exemplified by a concurrent pre-service Subject Teacher Education in design, art, and crafts. Focus-group interviews generated data. Three topics were discussed: too many choices, different logics, and avoiding confrontation. Faculty teachers expressed various understandings of content knowledge (CK) and pedagogical content knowledge (PCK), linked to the teachers' intuitive and reasoned reflections and preconceptions through the anchoring effect and attribute substitution. The study contributes to the knowledge base by reframing problematic sides of education, and by expanding the understanding of CK and conditions for PCK by exploring the thread between educational psychologist Lee Shulman and psychologist Daniel Kahneman.     

优秀中小学教师胜任特征分析

探索优秀中小学教师成长规律和胜任特征,对青年教师的专业发展有借鉴价值。阅读了15名优秀中小学教师的传记,提取他们在专业成长和教书育人工作中发生的典型事件,运用关键事件技术和内容分析法,依照事件主题、教师工作活动类型,对其进行分类、整理和胜任特征编码。数据分析结果表明,优秀中小学教师工作中发生的关键事件,集中表现在与学生课下交流、日常上课、上公开课、获得荣誉、撰写教学论著等方面。他们成为名师的主要途径包括坚持自学、反思总结、向名师学习、上公开课等。这些教师从教原因各异,但都有强烈的成就动机,关爱学生,通过勤奋努力变得杰出。他们具备的胜任特征,相互紧密关联,其行为模式在相似情境下具有一致性。     

怎样的评价可以促进教师潜心育人:来自中小学教师专业表现的实证证据

教育评价事关教育发展方向,影响教师潜心育人的专业表现及学生全面发展。为考察问责式和发展性两种教师评价对教师专业表现的不同影响,本研究采用问卷法,调查了我国中西部2354名县镇及乡村中小学教师,构建潜变量结构方程模型,探究教师所感知的教师评价方式、对评价的态度、教师的专业学习及专业表现之间的关系。结果发现:问责式教师评价对教师专业表现影响的直接效应不显著,但通过教师对评价反馈的态度和专业学习,显著负向影响教师专业表现;发展性教师评价对教师专业表现的总效应、直接效应和间接效应皆为显著正向影响。这提示不同教师评价对教师潜心育人专业表现的影响机制是不同的,在制定和改革教师评价方案时需要综合考虑。     

Profiles of middle school science teachers: Accounting for cognitive and motivational characteristics

Teachers play a critical role in successfully implementing science education reforms in the United States to provide high-quality science learning opportunities to all students. However, the differentiated ways in which teachers make decisions about their science teaching are not well understood. This study takes a person-centered approach by applying latent profile analysis to examine how cognitive (pedagogical content knowledge) and motivational (instructional goal orientations, self-efficacy beliefs, and reform values) characteristics combine to form science teacher profiles in middle school. Predictors of profile membership (bachelor's degree, school %FRL) and both teacher (science instructional practices) and student (science achievement, engagement, and self-efficacy) outcomes related to the teacher profiles were also examined. Five science teacher profiles were identified (severely discouraged but reform oriented, discouraged but reform oriented, conventional, confident and mastery oriented, and confident with multiple goal approaches) that represented unique configurations of cognitive and motivation characteristics. Additionally, findings showed that the teacher profiles were significantly related to three dimensions of science instructional practice including communication, discourse, and reasoning. Finally, the teacher profiles were significantly related to student science achievement and motivational outcomes. Implications for differentiated approaches to teacher professional learning and supports for science instruction are discussed.