英语翻译Student talk can lead to increased student mathematical

英语翻译
Student talk can lead to increased student mathematical knowledge and understanding in two interrelated ways.First,listening to students talk makes it possible for the teacher (and other students) to monitor students’ mathemat -ical thinking.Teachers can use information gleaned from student talk to inform their instructional decision-making practices,including problems to pose and follow-up ques-tions to ask (Franke,Fennema,& Carpenter,1997).Similarly,when students converse with each other,their talk makes it possible for students to gauge each other’s strate-gies and comprehension,providing opportunities for stu-dents to help each other build more complete mathematical understanding.Second,the act of talking can itself help students develop improved understanding.Describing,explaining,and justifying one’s thinking all help students internalize principles,construct specific inference rules for solving problems,become aware of misunderstandings and lack of understanding (Chi,2000),reorganize and clarify material in their own minds,fill in gaps in understanding,internalize and acquire new strategies and knowledge,and deve lop new perspectives and understanding (Bargh & Schul,1980; King,1992; Rogoff,1991).
Not just any kind of student talk is expected to be productive for supporting or challenging students’ think-ing.Providing explanations is positively related to achie -vement outcomes,even when prior achievement is controlled for,whereas giving only answers is not related or is negatively related to achievement outcomes (Webb & Palincsar,1996).Beyond providing answers,students must describe how they solve problems and why they propose certain strategies and approaches.Moreover,when describing their thinking,students must be precise and explicit in their talk,especially providing enough detail and making referents clear so that the teacher and fellow classmates can understand their ideas (Nathan & Knuth,2003; Sfard & Kieran,2001).

Student talk can lead to increased student mathematical knowledge and understanding in two interrelated ways.First,listening to students talk makes it possible for the teacher (and other students) to monitor students’ mathemat -ical thinking.Teachers can use information gleaned from student talk to inform their instructional decision-making practices,including problems to pose and follow-up ques-tions to ask (Franke,Fennema,& Carpenter,1997).Similarly,when students converse with each other,their talk makes it possible for students to gauge each other’s strate-gies and comprehension,providing opportunities for stu-dents to help each other build more complete mathematical understanding.Second,the act of talking can itself help students develop improved understanding.Describing,explaining,and justifying one’s thinking all help students internalize principles,construct specific inference rules for solving problems,become aware of misunderstandings and lack of understanding (Chi,2000),reorganize and clarify material in their own minds,fill in gaps in understanding,internalize and acquire new strategies and knowledge,and develop new perspectives and understanding (Bargh & Schul,1980; King,1992; Rogoff,1991).
学生讨论可以从两个相关方面 引导增加学生的数学知识和理解.首先,听学生讨论可以让老师（及其他学生）能够监听学生的数学思维.老师可以运用从学生讨论中获得的信息 为他们提供制定决策的实践,包括要展示的问题,以及要继续询问的问题.(Franke,Fennema,& Carpenter,1997).同样的,当学彼此交流,他们的讨论也可以让学生彼此判断对方的思路和理解,并提供机会让学生彼此更彻底的理解数学.其次,讨论本身可以帮助学生提高理解.描述,解释以及为自己的想法辩证,都可以帮助学生化规则为己用,构思明确的推理规则以解决问题,让他们意识到误解和缺乏了解,认识并分清他们自己头脑中的东西,填平理解的缺口,获取新的思路和知识,发展新的见解及理解.(Bargh & Schul,1980; King,1992; Rogoff,1991)
Not just any kind of student talk is expected to be productive for supporting or challenging students’ think-ing.Providing explanations is positively related to achie -vement outcomes,even when prior achievement is controlled for,whereas giving only answers is not related or is negatively related to achievement outcomes (Webb & Palincsar,1996).Beyond providing answers,students must describe how they solve problems and why they propose certain strategies and approaches.Moreover,when describing their thinking,students must be precise and explicit in their talk,especially providing enough detail and making referents clear so that the teacher and fellow classmates can understand their ideas (Nathan & Knuth,2003; Sfard & Kieran,2001).
并非任何学生讨论 对支持和挑战学生的思维 都会富有成效.因为解释与最后的成果是密切相关的,即便你已提前控制最后的成果,可是仅仅给出答案与成果并不相关甚至相反.所以学生除了提供答案,还要描述他们如何解决问题,以及他们为什么提出某种想法或者方法.此外,当他们描述问题时,学生必须保持他们的谈论详尽而明确,特别要提供足够的细节和详细的参考,这样,老师和别的同学才会理解他们的想法.