Exploring the Development of Student Teachers’ PCK of the Multiple Meanings of Chemistry Topics

In chemical education, many secondary school students experience difficulties in understanding three mutual related meanings of topics, that is, the macroscopic meaning, the microscopic meaning, and the symbolic meaning. As a consequence, student teachers should be prepared carefully to learn how to teach this difficult issue. This article presents a naturalistic case study of the development of eight student teachers pedagogical content knowledge (PCK) of the multiple meanings of chemistry topics. The student teachers (all M.Sc.) participated in a teacher education program of which the initial phase focused on learning from teaching instead of learning of teaching. They were asked individually to choose and teach a chemistry curriculum topic with a focus on the macro-micro-symbolic issue. Research data were obtained by interviewing the student teachers individually before and after the lessons. The outcomes indicated a development of student teachers knowledge of teaching difficulties, for instance, too fast and mainly implicit reasoning between macro- and micro-meaning, and a dominant orientation towards the micro-meaning of topics. A development of knowledge of students difficulties was also indicated, for instance, difficulties in understanding the macro- and micro-meaning of reaction equations. Implications for the follow-up phases of the program are presented.     

Teachers’ construction of meanings of signed quantities and integer operation

Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. The specialized content knowledge (SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations form the foundation for the construction of SCK about representations used to teach integers. We report that teachers’ concerns about teaching the topic of integers implicate issues of meaning, although this may not always be explicitly acknowledged by teachers. We develop a framework of integer meanings synthesizing previous research, and describe how the framework allowed teachers to investigate a wide range of representations including contexts and thereby construct SCK in a professional development setting. Teachers constructed SCK by connecting various meanings of integers with one another and with representations including contexts. Teachers made two important shifts, from exclusively using the state meaning of integers to including the application of change meaning to representations and from exclusive use of formal models to including contexts to teach integer addition and subtraction. An implication of the study is that frameworks of meaning for key mathematical topics could be an important component of pre- and in-service teacher education.     

Aspects of negative numbers in the early 17th century

This paper argues that the questions, posed by researchers in the field of didactics of mathematics, require new historical research which mainly concerns the problems related to the emergence and evolution of concepts. Motivated by recent historico-didactical studies on negative numbers, the author explores two different types of problems through which these numbers started being used systematically in mathematics. The first problem deals with the correspondence between the terms of an arithmetical and a geometrical progression, which constitutes the theoretical basis of logarithms; the second deals with the application of algebraic syntactical ruies in the theory of equations. In the specific context of these problems, concepts, such as negative logarithm or negative root, were established in the early 17th century, long before the appearance of a general concept of negative quantity in mathematical textbooks. The analysis of these problems reveals the conventional character of negative numbers and poses certain questions about the meaning of the various concrete models, traditionally employed in their teaching (via temperature, debits and credits, etc.). Recent, large-scale empirical research has shown a major percentage of failure in understanding negative numbers and their operations; this fact is related to the meanings attributed to negative numbers during their introduction at school. The matter of revising traditional teaching models is considered in connection with a constructive learning hypothesis; there is a need for new problem-situations, which entirely justify the meaning of the concept that must be used and constructed by the pupil and allow a fruitful interaction with it. The case of negative numbers provides an illuminating example of the role historical problems can play in the creation of situations like these.     

“新工科”通识教育背景下的“名师研讨课”

"新工科"通识教育是连接传统通识教育与工科专业教育的桥梁,应以全面发展教育理念、结果导向理念、证据导向理念为核心。作为通识教育中"科技文明"板块的通识课程"名师研讨课",旨在通过邀请高水平的名师嘉宾,探索基于学生自主学习、名师指导、师生研讨的教学模式,使学生在领略名师教学风采和人格魅力的同时,提升学习、分析、表达、合作等综合素质能力,激发探索兴趣,挖掘研究潜能。文章对"名师研讨课"的课程定位、教学主题、教学方法、教学模式与教学内容等进行了介绍。     

Museum Experience — a Resource for Science Teacher Education

In this study, the researcher included an extensive science museum experience for the pre-service secondary science teachers within a teaching methods course to enhance their learning to teach science. The extensive museum experience covered four aspects: the visit, discussion with museum educators, the development of lesson plans, and practising teaching in the science museum. Twenty-one pre-service science teachers attended this course. Qualitative methods were used for data collection and analysis. The data sources included field notes, reports, diaries, and interviews. The findings show that this course connecting museum resources and context had created a novel situation for pre-service science teachers to learn how to teach science. The discourses with the museum educators also provided them with innovations in education beyond the gains from traditional teacher education. Through developing and practising teaching activities, they improved their understanding of the meanings and effective ways to use museum resources in science teaching. Pre-service science teachers reported that getting feedback from peers and observing modeling teaching was helpful. This course provided an alternative way to view how scientific activities were developed for junior high students. In general, the use of museum settings provides a new profile of learning and teaching course for pre-service science teachers in Taiwan. Based on the findings, this study makes suggestions for those science teacher educators who would like to use science museum resources and contexts to nurture prospective science teachers.     

Eighth grade students’ representations of linear equations based on a cups and tiles model

This study examines eighth grade students’ use of a representational metaphor (cups and tiles) for writing and solving equations in one unknown. Within this study, we focused on the obstacles and difficulties that students experienced when using this metaphor, with particular emphasis on the operations that can be meaningfully represented through this metaphor. We base our analysis within a framework of referential relationships of meanings (Kaput 1991; Kaput, Blanton, and Moreno, et al. 2008). Our data consist of videotaped classroom lessons, student interviews, and teacher interviews. Ongoing analyses of these data were conducted during the teaching sequence. A retrospective analysis, using constant comparison methodology, was then undertaken in order to generate a thematic analysis. Our results indicate that addition and (implied) multiplication operations only are the most meaningful with these representational models. Students also very naturally came up with a notation of their own in making sense of equations involving multiplication and addition. However, only one student was able to construct a “family of meanings” when negative quantities were involved. We conclude that quantitative unit coordination and conservation are necessary constructs for overcoming the cognitive dissonance (between the two representations—drawn pictures and the algebraic equation) experienced by students and teacher.     

Teaching Against the Grain as an Act of Love: Disrupting White Eurocentric Masculinist Frameworks Within Teacher Education

What is radical love in teaching? How can radical love incite change and transformation within teacher education? What does radical love entail to prepare critically minded teachers for urban schools? In this conceptual paper, we respond to these questions through our individual and collective experiences as social justice oriented teacher educators preparing students to teach in urban schools. We engage with our womanist ways of knowing (Walker in In search of our mothers’ gardens: womanist prose, Houghton Mifflin Harcourt, Boston, 2004) and “theory in flesh” (Moraga and Anzaldúa in This bridge called my back: writings by radical women of color, 2nd edn, Kitchen Table/Women of Color Press, New York, 1983) to collaboratively reflect and analyze our conversations, reflective journaling, meetings, and other telling moments about what it means to practice radical love in teaching. More specifically, we identify three central concepts of what love as an act of resistance or teaching against the grain entails: (1) vulnerability, (2) collective support and healing, and (3) critique. Through these concepts we offer a framework from which to practice radical love in teaching and work in solidarity with others to transform oppressive systems in urban (teacher) education.     

“无缝衔接”的教师教育理念及其实现

不同阶段教师教育之间保持良好的衔接是促进教师学习者实现持续发展的重要保证。现有教师教育衔接以机构整合、指导延伸和课程衔接为主,都存在一定的局限性或不足。无缝衔接的教师教育理念主张以教学为衔接点,以学习者的主动反思和知识建构为衔接机制,促进学习者原有知识、经验与新知识的衔接。     

The teacher-innovator: Models of teaching as the core of teacher education

A design for teacher education has been made around the concept of providing teacher trainees with the theoretical understanding of the major models of teaching and the clinical competence to employ them in the classroom. Research indicates that this design enables teachers to acquire the ability to radiate several models in the classroom regardless of their natural styles. While personal values do not appear to affect acquisition of the repertoire of models, conceptual level is related to repertory acquisition. The teaching behavior of cooperating (supervising) teachers is not related to the behavior of teacher trainees when practicing the models of teaching but is related to their more general teaching styles.

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Résumé Doter les futurs professeurs de la connaissance théorique des principaux modèles d'enseignement ainsi que de la compétence pour les utiliser en classe constitute le point central d'un programme de formation des maîtres. La recherche indique que ce programme permet aux professeurs d'acquérir la capacité d'utiliser en classe plusieurs modèles malgré leur style naturel. Même si les valuers personnelles ne semblent pas influer sur l'acquisition de la gamme de modèles, le niveau conceptuel est relié à l'acquisition de cette gamme. Le comportement en classe des professeurs (surveillants), lequel n'est pas relié à l'attitude des futurs professeurs lorsqu'ils pratiquent ces modèles d'enseignement, est plutôt fonction de leur style plus général d'enseignement.

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With Mike McKibbin, Michael Feller, Christina Gullion, Joe Kelly, and Gene Rude, all of whom contributed to the data collection and analysis and debate over substance. All are instructors at Teachers College.     

关于“教师职业专业化”概念的思考

目前国内对“教师职业专业化”的认识还处于初始阶段,对“教师职业专业化”概念的还模糊不清,给当前教师教育理论研究与实践都带来较大的影响和困难。“教师职业专业化”要求选择教师职业的人具备教师素质,包括以教师职业道德为基础的教育理念、教学经验、教学方法等个人的教育教学能力。明确认识“教师职业专业化”的内涵,以利教师教育事业健康发展。     

提高机械制图课堂效率之我见

提高机械制图课堂效率，教师要不断提高自身的专业知识水平。了解学生实际学习能力，教学中根据教学内容的不同，选择不同的教学方法。讲清概念，理清关系，深入浅出，化繁为简，运用计算机辅助教学，将抽象的概念转变成为生动、具体、形象的动画图形。合理分配课堂中的教学比例关系，突出学生的主体地位。     

关于"教师职业专业化"概念的思考

目前国内对"教师职业专业化"的认识还处于初始阶段,对"教师职业专业化"概念的还模糊不清,给当前教师教育理论研究与实践都带来较大的影响和困难."教师职业专业化"要求选择教师职业的人具备教师素质,包括以教师职业道德为基础的教育理念、教学经验、教学方法等个人的教育教学能力.明确认识"教师职业专业化"的内涵,以利教师教育事业健康发展.     

主体性与主导性相统一:思想政治教育的创新之基

针对当前思想政治教育面临的教学话语、教育理念、教学主体及教学评价等方面的创新困境,高校和思想政治教师应从多方入手,以学生主体和教师主导为依据,转化教学话语和教育理念,以主导性和主体性相统一为导向选择合适的教学模式、明确教学评价机制,促进学生主体性作用、教师主导性作用及二者相统一作用的实现,进而帮助思想政治教育提升教学效果,实现创新。     

Is experience the best teacher? A multilevel analysis of teacher characteristics and student achievement in low performing schools

The study investigated several teacher characteristics, with a focus on two measures of teaching experience, and their association with second grade student achievement gains in low performing, high poverty schools in a Mid-Atlantic state. Value-added models using three-level hierarchical linear modeling were used to analyze the data from 1,544 students, 154 teachers, and 53 schools. Results indicated that traditional teacher qualification characteristics such as licensing status and educational attainment were not statistically significant in producing student achievement gains. Total years of teaching experience was also not a significant predictor but a more specific measure, years of teaching experience at a particular grade level, was significantly associated with increased student reading achievement. We caution researchers and policymakers when interpreting results from studies that have used only a general measure of teacher experience as effects are possibly underestimated. Policy implications are discussed.

Effects of 3D Printing Project-based Learning on Preservice Elementary Teachers’ Science Attitudes,Science Content Knowledge,and Anxiety About Teaching Science

3D printing technology is a powerful educational tool that can promote integrative STEM education by connecting engineering, technology, and applications of science concepts. Yet, research on the integration of 3D printing technology in formal educational contexts is extremely limited. This study engaged preservice elementary teachers (N?=?42) in a 3D Printing Science Project that modeled a science experiment in the elementary classroom on why things float or sink using 3D printed boats. The goal was to explore how collaborative 3D printing inquiry-based learning experiences affected preservice teachers’ science teaching self-efficacy beliefs, anxiety toward teaching science, interest in science, perceived competence in K-3 technology and engineering science standards, and science content knowledge. The 3D printing project intervention significantly decreased participants’ science teaching anxiety and improved their science teaching efficacy, science interest, and perceived competence in K-3 technological and engineering design science standards. Moreover, an analysis of students’ project reflections and boat designs provided an insight into their collaborative 3D modeling design experiences. The study makes a contribution to the scarce body of knowledge on how teacher preparation programs can utilize 3D printing technology as a means of preparing prospective teachers to implement the recently adopted engineering and technology standards in K-12 science education.     

Sources of invalidity in measuring classroom behavior

The concepts of teacher effectiveness and teacher evaluation are growing in importance. Attempts to identify the classroom behavior of more and less effective teachers and evaluate the extent to which they reach pre-determined criteria of effectiveness have led to a heterogeneous array of statistical tools and measurement paradigms, many of which contain sources of invalidity. This paper (a) critically reviews past attempts to identify the behavioral correlates of effective teaching; (b) poses a systematic measurement framework for more effectively studying classroom behavior, and (c) identifies specific sources of invalidity in measuring the behaviors within this framework.     

A Review of Solution Chemistry Studies: Insights into Students’ Conceptions

This study has reviewed the last two decades of student conception research in solution chemistry pertaining to aims, methods of exploring students conception, general knowledge claims, students conceptions and difficulties, and conceptual change studies. The aims of solution chemistry studies have been to assess students understanding level of solution chemistry and in some studies compare understanding based on age and year at school or college. The methods of exploring students conceptions consisted of interviews, paper and pencil surveys (open-ended questions and multiple-choice questions), free writing and drawings and the validity of these methods have been highlighted. The general knowledge claims synthesized in this study are students (a) attending to mechanical events, (b) preference for everyday language usage over chemical language, (c) confusing solution chemistry with non-related concepts, (d) lack of sub-microscopic explanation for macroscopic observation, (e) difficulty with visualizing and representing sub-microscopic ideas, (f) difficulty with symbolic representations, (g) inconsistent explanations, (h) development of student understanding with age, and (i) development of conservation reasoning with age. To incorporate students conceptions, conceptual change studies have used strategies such as worksheet, analogy, collaboratively working with a teacher, hypermedia, and group exploration. The results of conceptual change studies generally have had a positive impact enabling students to consider their ideas and develop plausible models of solution chemistry. For improvement of student learning in chemistry, this review of solution chemistry studies sheds light on teacher thinking and capacity building with respect to explicitly incorporating students conceptions into chemistry curriculum; practicing research-based strategies; forging links among types of chemical knowledge; collaborating for experimental teaching; and conducting further research.     

The ontology of science teaching in the neoliberal era

Because of ever stricter standards of accountability, science teachers are under an increasing and unrelenting pressure to demonstrate the effects of their teaching on student learning. Econometric perspectives of teacher quality have become normative in assessment of teachers’ work for accountability purposes. These perspectives seek to normalize some key ontological assumptions about teachers and teaching, and thus play an important role in shaping our understanding of the work science teachers do as teachers in their classrooms. In this conceptual paper I examine the ontology of science teaching as embedded in econometric perspectives of teacher quality. Based on Foucault’s articulation of neoliberalism as a discourse of governmentality in his ‘The Birth of Biopolitics’ lectures, I suggest that this ontology corresponds well with the strong and substantivist ontology of work under neoliberalism, and thus could potentially be seen as reflection of the influence of neoliberal ideas in education. Implications of the mainstreaming of an ontology of teaching that is compatible with neoliberalism can be seen in increasing marketization of teaching, ‘teaching evangelism’, and impoverished notions of learning and teaching. A shift of focus from teacher quality to quality of teaching and building conceptual models of teaching based on relational ontologies deserve to be explored as important steps in preserving critical and socially just conceptions of science teaching in neoliberal times.     

Meta level in the teaching of unifying and generalizing concepts in mathematics

Certain concepts in mathematics were not invented only to solve new problems; their aim was mainly to find general methods to solve different problems with the same tools. Such concepts, as those of the axiomatic theory of vector spaces or groups or the modern definition of limit, will be called in this paper unifying and generalizing concepts. I will point out some epistemological specificities of these concepts and subsequently analyze their influence on teaching. I will explain the reasons which led me to the conclusion that it is necessary to introduce some meta aspects into the teaching of unifying and generalizing concepts, and I will present the theoretical framework I adopted for my purpose, in relation to other theoretical approaches. I will then present and analyze one example, from which I will draw conclusions about theoretical questions of evaluation in a long term experiment which includes a meta dimension for the teaching of unifying and generalizing concepts in mathematics.     

The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge

The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deduced from more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on the concept of chance illustrates this conflict. The interaction between teacher and students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the concept of chance is conceived of as a concrete generalization, which takes chance as a fixed and universalised pattern of explanation instead of unfolding potential and variable conceptual relations of chance or randomness and developing the theoretical nature of this concept in an appropriate way for students' comprehension.