我国的区域发展政策选择之我见

区域发展政策是我国跨世纪发展的庞大系统工程，需要在实践中不断探索，不断创新。对此，作从指导思想、适用范围、实践经验、政策选择等五个方面提出个人的观点进行探讨。     

Varieties of discourse in supervisory conferences

The logic and substance of discourse between university supervisors and student teachers during post-observation supervisory conferences were studied in an elementary student teaching program in the United States. The findings describe these aspects of the discourse in relation to the program's goals and (a) the conceptual levels of supervisors and student teachers, (b) the content area of the lesson under analysis, and (c) the structure of the supervisor's role. Implications of the findings for research, program development, and for the preparation and training of supervisors are discussed.     

双语课堂教学语言的问题与对策

基于对双语教学与课堂教学语言的认识,根据为时九年的亲历双语教学督导检查,列举和剖析了双语课堂教学语言中普遍存在的四个问题:反馈语缺失或呆板、不当,课堂语言组织低能低效,情感缺失及不良语言习惯.从教育管理机构及教师个人角度提出了相应对策以确保提高双语教学实效.     

Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification

A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students’ mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students’ mathematical reasoning processes such as generalization and justification.     

Changing classroom culture,curricula, and instruction for proof and proving: how amenable to scaling up,practicable for curricular integration,and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are.     

Teaching multidigit multiplication: combining multiple frameworks to analyse a class episode

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher’s mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and ascending a priori analysis and an a posteriori analysis. This analysis shows a development of different didactical situations and some links between mathematical knowledge and pertinence. In the conclusion, the contribution of the frameworks from both French and Anglo-American origins is briefly addressed.