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1.

The seven articles that comprise this Special Issue examine the professional growth of mathematics and science teacher educators across different contexts and different foci of who is the teacher educator being studied. Despite these differences, a common thread running throughout these seven articles is the need for learning to be situated in collaboration with others. In this final article, we examine the contribution of these articles through two perspectives: that of the collaborative contexts supporting the professional growth of mathematics and science teacher educators, and the role of disciplinary knowledge as part of the purpose for teacher educators’ professional growth. We notice that collaboration can take on very different structures in supporting teacher educators’ professional learning due to the different purposes and roles of the teacher educators in the studies. We also notice that while collaboration figures as an important component in all of the studies, the disciplinary specific aspects of collaboration, i.e., how collaboration might be negotiated differently by teacher educators in mathematics and science, is still not well understood. Overall, these articles provide important insights that help to shed new light on the complex and multifaceted nature of teacher educators’ learning and growth and provide productive avenues for future research.

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This paper discusses two possible approaches to (-8)1/3. The first is that (-8)1/3 = 3(-8) = -2. The second is that (-8)1/3 is undefined. The pros and cons of each of these approaches are considered and some implications to teacher education are specified.This revised version was published online in September 2005 with corrections to the Cover Date.  相似文献   
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Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students and to interpret their talk and actions. Analysis of an interview with Ruth – an experienced elementary school teacher – after she observed two of her students solve a mathematics problem, suggests four types of her interpretation: describing, explaining, assessing and justifying. This analysis illustrates the complexity of the way Ruth hears her students, as is indicated even in the relatively simple case of describing. Using various sources of data we also analyze different characteristics of Ruth’s hearing for the describing and explaining types of interpretation and examine possible resources for her over-hearing, compatible-hearing, under-hearing, non-hearing and biased-hearing.  相似文献   
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This study investigates four seventh-grade teachers' awareness of students' tendency to conjoin or 'finish' open expressions. It also investigates teachers' ways of coping with this tendency. Three types of data were collected: 1) lesson plans, 2) lesson observations, and 3) post-lesson interviews. The analysis showed that the two experienced teachers were aware of this tendency and some of its possible sources, while the novices were unaware of either. Teaching approaches related to this tendency also differed considerably. In conclusion we analyze these teaching methods in light of the existing literature and discuss possible short- and long-term implications of the use of each approach.  相似文献   
5.
The Development of Teacher Leaders and Inservice Teacher Educators   总被引:1,自引:1,他引:0  
This article discusses the development of teacher leaders and inservice teacher educators whose role it is to promote teacher learning about mathematics teaching in the process of changing school mathematics. The Manor Program for the development of teacher leaders and teacher educators is used as a vehicle for addressing this issue. The article focuses on aspects of curriculum design, discusses the theoretical rationale for the learning opportunities provided by the program, and considers several problematic aspects encountered.  相似文献   
6.
This study examines the views of people involved in mathematics education regarding the commonly stated goal of using mathematics learning to develop deductive reasoning that is usable outside of mathematical contexts. The data source includes 21 individual semi-structured interviews. The findings of the study show that the interviewees ascribed different meanings to the above-stated goal. Moreover, none of them said that it is possible to develop formal logic-based reasoning useful outside of mathematics, but for different reasons. Three distinct views were identified: the intervention–argumentation view, the reservation–deductive view, and the spontaneity–systematic view. Each interviewee’s view was interrelated with the interviewee’s approach to deductive reasoning and its nature in mathematics and outside it.  相似文献   
7.
This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.  相似文献   
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