神马作文网英语翻译Asking open-ended questions in class has many potential
来源：学生作业帮 编辑：神马作文网作业帮 分类：英语作业 时间：2024/11/11 22:48:20
英语翻译
Asking open-ended questions in class has many potential benefits:it can give students a chance to come to a result on their own,it can lead to new questions and deeper investigations of important concepts,and it can point to gaps in students’ understanding.Sometimes it even stimulates new research.Number theory,a subject in which conjectures can be easy to make but often difficult to settle,is particularly well-suited to asking students what they see in a particular example.This paper is the result of an innocent question and an unexpected answer from a number theory course.When the authors first submitted this article,they believed the work to be original.As it turns out,the majority of the work was a rediscovery of previous results,although the research experience was still a very positive one.
One of the standard topics in a first course in number theory is the Euler φ function,with φ(n) defined as the number of positive integers less than n and relatively prime to n.A famous theorem involving φ is Gauss’s theorem that the sum of φ(d) over the divisors d of n is n; that is,
Asking open-ended questions in class has many potential benefits:it can give students a chance to come to a result on their own,it can lead to new questions and deeper investigations of important concepts,and it can point to gaps in students’ understanding.Sometimes it even stimulates new research.Number theory,a subject in which conjectures can be easy to make but often difficult to settle,is particularly well-suited to asking students what they see in a particular example.This paper is the result of an innocent question and an unexpected answer from a number theory course.When the authors first submitted this article,they believed the work to be original.As it turns out,the majority of the work was a rediscovery of previous results,although the research experience was still a very positive one.
One of the standard topics in a first course in number theory is the Euler φ function,with φ(n) defined as the number of positive integers less than n and relatively prime to n.A famous theorem involving φ is Gauss’s theorem that the sum of φ(d) over the divisors d of n is n; that is,
在课堂上问开放式问题有许多潜在的益处：它可以给学生们一个自己总结的机会,可以引导出更多的新问题和对于重要观点更深层次的调查,可以专注于学生的理解.有时候甚至可以聚集新的研究.数字理论,是一个很容易提出猜想但是常常难以确定的主题,非常适合就某个特定的例子来向学生提问.这篇论文就是从一次数字理论课程由一个很无知的问题和一个未预料到的回答引起的.当作者第一次呈交这篇论文的时候,他们相信这是一个新出现的工作.尽管这个调查的经验仍然是有着积极意义的,当结果出来时,这个工作的大部分是从先前的结果中重新发现的.
数字理论的第一堂课其中的一个标准主题就是φ函数的欧拉,因为φ(n) 被定义为小雨 n 一样的正整数和 n 一样互质.一个有名的包含φ的理论就是高斯定理,该理论是φ的总和(d)的因子dnn,这就是说,
数字理论的第一堂课其中的一个标准主题就是φ函数的欧拉,因为φ(n) 被定义为小雨 n 一样的正整数和 n 一样互质.一个有名的包含φ的理论就是高斯定理,该理论是φ的总和(d)的因子dnn,这就是说,
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