羟氨苄青霉素引起大疱性类天疱疮样疹

In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers’ content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers’ pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains that was mediated by the provision of cognitive activation and individual learning support.

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Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress:

Stichwort : Professionelle Kompetenz von Lehrkräften

Teachers who attempt to use inquiry-based, student-centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique and sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task but also begin to align students' disparate ideas and approaches with canonical understandings about the nature of mathematics. Research suggests that this is difficult for most teachers (Ball, 1993, 2001; Leinhardt & Steele, 2005; Schoenfeld, 1998; Sherin, 2002). In this article, we present a pedagogical model that specifies five key practices teachers can learn to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses. We first define each practice, showing how a typical...

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Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.

https://www.tandfonline.com/doi/pdf/10.1080/07370000802177235

Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

This article investigates teachers' subject-matter knowledge and its interrelations with pedagogical content knowledge in the context of teaching the concept of function. During the first phase of data collection, 152 prospective secondary teachers completed an open-ended questionnaire concerning their knowledge about function. In the second phase, an additional 10 prospective teachers were interviewed after responding to the questionnaire. The analysis shows that many of the subjects did not have a modern conception of function. Appreciation of the arbitrary nature of functions was missing, and very few could explain the importance and origin of the univalence requirement. This limited conception of function influenced the subjects' pedagogical thinking. Therefore, when describing functions for students, many used their limited concept image and tended not to employ modern terms. In addition, many chose to provide students with a rule to be followed without concern for understanding.

Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept

Factors involved in linking representations of functions

Interest in teachers' subject matter knowledge has arisen in recent years. But most of the analysis has been general and not topic-specific. This paper shows how one may approach the question of teachers' knowledge about mathematical topics. It demonstrates the building of an analytic framework of subject matter knowledge for teaching a specific topic in mathematics and then uses the concept of function to provide an illustrative case of a paradigm for analyzing subject matter knowledge for teaching. The choice of the aspects, which form the main facets of the framework, was based on integrated knowledge from several bodies of work: the role and importance of the topic in the discipline of mathematics and in the mathematics curriculum; research and theoretical work on learning, knowledge and understanding of mathematical concepts in general and the specific topic in particular; and research and theoretical work on teachers' subject matter knowledge and its role in teaching. An application of the framework in the case of the concept of function is described and illustrated by anecdotes drawn from a study of prospective secondary teachers' knowledge and understanding of functions.

Subject Matter Knowledge for Teaching and the Case of Functions.

Pedagogical content knowledge is made up of several components. In this paper we concentrate on one of these: teachers' planned presentations of the subject-matter. We deal with two main sources of this component of pedagogical content knowledge: knowledge about the subject-matter and knowledge about students. Illustrations are given in two mathematical domains: functions and undefined mathematical operations. The paper concludes with a discussion of the nature of teachers' knowledge and the interconnections between the three constructs: subject-matter knowledge, knowledge about students, and knowledge about ways of presenting the subject-matter.

Ruhama Even

Papers

Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept

Factors involved in linking representations of functions

Subject Matter Knowledge for Teaching and the Case of Functions.

Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter

The Professional Education and Development of Teachers of Mathematics