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1.
What important ideas about forms of knowing mathematics should be included in mathematics methods courses for preservice teachers? Ideas are proposed that are related to categories in Shulman's (1986) framework of teacher knowledge. There is a brief discussion of the implications each idea holds for teaching mathematics, and some suggestions are given about experiences that may help preservice teachers appreciate these notions. One portion of Shulman's pedagogical content knowledge construct is knowing what makes a subject difficult and what preconceptions students are apt to bring. Three of the ideas offered for inclusion in a methods course are related to this aspect of pedagogical content knowledge: (1) Understanding students' understanding is important, (2) Students knowing in one way do not necessarily know in the other(s), and (3) intuitive understanding is both an asset and a liability. The last two ideas, are related to the other portion of pedagogical content knowledge, knowing how to make the subject comprehensible to learners. These ideas are (4) certain characteristics of instruction appear to promote retention, and (5) providing alternative representations and recognizing and analyzing alternative methods are important. Readers are asked to consider if the suggestions offered are appropriate and how they might best be taught.  相似文献   

2.
Since 2002, adult numeracy specifications have been introduced for the first time in England. This article investigates the relevance of Bernstein and Shulman's theoretical frameworks to teacher training using the new Level 4 adult numeracy teacher training programmes as an example. The article discusses Bernstein's theories relating to pedagogic methods of acquisition and transmission. It investigates the recontextualization process in which subject content and teaching standards may be translated into teaching approaches, which can be used by trainee teachers. It also investigates Shulman's model of pedagogical reasoning and action in relation to teacher training. The article bases its evidence on a research project, which evaluates teacher training courses in adult numeracy and literacy, and English for speakers of other languages in England. The article suggests that the two educationists' theories have significant relevance to the design and implementation of teacher training courses. It also suggests that they can be used alongside each other with each educationist's theories having their particular strengths. Bernstein's theories emphasize a rigorous approach to course structuring; Shulman's theories offer an insightful approach to how a trainee transforms subject and teaching standards knowledge and skills into possible teaching methods to help her learners understand the subject.  相似文献   

3.
This article examines relationships between various dimensions of teachers' professionalism, that is, pedagogical content knowledge and personal characteristics. Using Shulman's notion of pedagogical content knowledge (PCK) we explored the practical knowledge of twenty sex education teachers using in-depth interviews. It appeared that both core elements of PCK, teacher strategy and teacher style (PCK1) and teacher knowledge of student conceptions and learning difficulties (PCK2), are associated with one another in such a way that PCK2 is a prerequisite to PCK1. Furthermore, the PCK of sex education teachers is related to personal characteristics, personality and past experiences with sex education (as a pupil and as a teacher-in-training).  相似文献   

4.
This study sought to determine how experienced language teachers use analogies to help students comprehend a text on the course of their regular teaching routines. It is assumed that analogies constitute one important component of the content of teachers' practical knowledge in the context of reading-comprehension instruction. The framework of the study drew from Shulman's notion of 'pedagogical content knowledge'; the perspective was the analogy-provider (e.g. teacher or textbook author). Eight lessons taught by eight different teachers were observed and analysed for the presence of analogies. The frequent use of analogies, continuously under discussion in the literature about science education, seems at least open to question. The research suggests that teacher education programmes for language teaching should include information about developing and evaluating instructional analogies.  相似文献   

5.
This theoretical paper examines the concept of pedagogical content knowledge (PCK) and explores how it might contribute to conversations around quality teaching and learning in outdoor education. This paper begins by summarizing the historical and contemporary literature, including issues of definitions, curriculum, content, and pedagogy in outdoor education. We then review the concept of PCK, its history, and contributions to other subject areas, including mathematics. We present a framework for PCK from the field of mathematics education and propose a 'modified' PCK framework for outdoor education. We postulate that this framework might help articulate knowledge areas needed by a teacher of outdoor education, and how these differ from and are similar to those required in other subject areas. We conclude by exploring how the idea of PCK and the modified framework might add to existing understandings of what it means to provide high quality outdoor education teaching and learning experiences.  相似文献   

6.
《教育心理学家》2013,48(4):235-247
Research examining differences between expert and novice teachers is reviewed through the lens of cognition to outline and establish how features of the classroom are mentally represented. Studies are reviewed under Shulman's (1986b) framework characterizing knowledge bases necessary for teacher effectiveness, including content knowledge, pedagogical content knowledge, and general pedagogical knowledge. Inferences are made as to how teachers, varying in experience level, represent classroom events including curriculum planning, instruction, management, and communication. Implications for teacher education and professional development programs are discussed.  相似文献   

7.
In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.  相似文献   

8.
In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues’ mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers’ prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.  相似文献   

9.
通过对初中数学青年骨干教师L老师的叙事研究．研究者认为初中数学学科教学知识对学科内容知识量的要求是有限的,但对教师理解内容知识的深刻性有较高要求;实践与反思是形成学科教学知识的关键。L老师学科教学知识的生成途径有其独特的地方,值得其他教师借鉴和学习,可以概括为“二研五专”,即：研究教材、研题磨题、专业阅读、专题研究、专业现场、专题写作、专家引领。  相似文献   

10.
The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.  相似文献   

11.
Abstract

This article reviews research on pedagogies associated with the use of information and communications technology (ICT) in primary and secondary schools. We propose a framework for examining pedagogical practices based on an analysis of the nature of pedagogy as revealed in the literature. In the light of this framework we discuss empirical evidence of the use of different types of ICT in different subjects and phases of education. We identify pedagogical issues associated with ICT use and their implications for teachers' pedagogical reasoning and practices. The evidence suggests that new affordances provided by ICT-based learning environments require teachers to undertake more complex pedagogical reasoning than before in their planning and teaching that incorporates knowledge of specific affordances and how these relate to their subject-based teaching objectives as well as the knowledge they have always needed to plan for their students' learning. In addition the research shows that teachers' beliefs about the value of ICT for learning and the nature of successful learning environments are important in teachers' pedagogical reasoning  相似文献   

12.
《师资教育杂志》2012,38(3):325-338
ABSTRACT

This investigation examines the views of pedagogical content knowledge of 12 student teachers of mathematics drawn from three different training groups. Attitudes towards and understandings of pedagogical content knowledge were elicited using six Likert‐item statements whilst information on students' learning was obtained through open‐ended questioning. Differences between groups were apparent only in tendencies to give extreme responses and to adopt outlying positions. These differences may be attributable to differences in values or prior knowledge and to training parallels with the social construction of mathematical meaning. Indications of the acquisition of pedagogical content knowledge appeared in all training groups and seemed to be linked to a hierarchical view of mathematics; possible limitations for student learning are implied. Students' views also highlight the importance of reflection upon subject matter knowledge and awareness of learning processes when transforming mathematical ideas for teaching purposes. It is suggested that the role of prior learning is worthy of further investigation.  相似文献   

13.
Beginning teachers are entering the profession with increasing confidence in their ability to use digital technologies which has the potential to change the way teachers of the future make pedagogical decisions. This paper explores how pedagogical reasoning and action might occur in the digital age, comparing Schulman’s 1987 model with the reality for a small sample of digitally able beginning teachers as part of the emerging generation of teachers. The latter were examined through a multiple case study during their first year of teaching as they made decisions about using digital technologies within their teaching practice which gave an insight into pedagogical reasoning and action through the use of open‐ended interviews and observation. The conclusion drawn is that while the pedagogical reasoning and action model remains relevant, it was based on an assumption that teaching involves knowledge being passed from a teacher to their students, which was found to restrict innovation by digitally able teachers. A broader interpretation of knowledge and teaching within this model building on emerging learning theory could help reform practice once again, providing a framework for teachers in the digital age.  相似文献   

14.
In the current debate on pedagogical content knowledge (PCK), the term is used to refer to the context‐specific knowledge that teachers activate when reflecting on practice. Against the background of this debate, we conducted an empirical study and sought to answer the question of which knowledge experts and novices activated in assessing a videotaped lesson in relation to its effectiveness for learning. Our assumption was that the participants activate their PCK as a blending of content knowledge (CK) and pedagogical knowledge (PK) as suggested by Shulman's amalgam thesis. The participants (9 experts and 9 novices) were shown a lesson on optics, in which the law of refraction (Snell's law) was being studied. In a subsequent interview, the participants were asked to analyze the observed lesson. A qualitative and quantitative evaluation of the interviews showed that experts activated both CK and PK intensively and in this respect they differed significantly from novices. Further analysis of the expert statements also proved that they do not activate their CK and PK in isolation, but instead combine both kinds of knowledge together, in line with Shulman's amalgam thesis. © 2017 Wiley Periodicals, Inc. J Res Sci Teach 55: 44–67, 2018  相似文献   

15.
In this research I examined the enactment of liberatory pedagogy, a teaching practice that promotes equity for all learners, from the uniquely informative perspective of young women majoring in mathematics and elementary education. It is grounded theory that seeks to understand the role of personal identity and social location in learning and teaching. I collected data over a two-year period, following two young women from the final semester of their teacher education program to their first teaching positions. Three distinct influences inform the conceptual framework of this study: (a) the underrepresentation of women in mathematics; (b) the devaluing of elementary teachers' content and pedagogical knowledge; and (c) the marginalization of the education major and pedagogical knowledge. I ask research questions regarding the type of preservice education these women experience and how it informs their enactment of liberatory pedagogy. Themes among the findings include coping with being a stranger in both lands, the desire to know oneself as a learner, and enacting liberatory pedagogy as beginning inservice teachers.  相似文献   

16.
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.

Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research.

Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.

Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.

Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.  相似文献   

17.
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.  相似文献   

18.
Theories associated with teacher knowledge suggest that teachers transform subject content knowledge into pedagogical content knowledge in teaching to enhance the content comprehensibility. It is assumed that the connection between teacher content knowledge and curriculum is characterized by the content knowledge transformation. This study, using an interpretive research method combined with cognitive knowledge elicitation and mapping approaches, examined the subject-pedagogical content knowledge transformation process that was associated with the teachers' curricular decision-making in secondary physical education. Findings indicated that the teachers shared a common subject content knowledge base but demonstrated a personalized pedagogical content knowledge repertoire, suggesting that the teachers' pedagogical content knowledge was personally constructed even though they shared a subject content knowledge base. The classroom curriculum was closely connected to the pedagogical content knowledge base. In addition, the teachers' curricular decisions regarding content inclusion/exclusion were primarily based on their perceptions of student learning abilities. The findings may imply that enhancement of prospective teachers' pedagogical content knowledge should be emphasized in teacher preparation programs because it serves as a bridge linking the subject content knowledge with the curriculum delivered in classrooms.  相似文献   

19.
The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.  相似文献   

20.
Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.  相似文献   

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