摘自 http://www.timhsu.net/courses/generic/proof.pdf   或 http://www.timhsu.net/courses/generic/how-to-lecture.pdf

怎样上一堂数学课

How to give a math lecture

本节给出数学课的一个简单指引,也就是,当你在数学课上讲授定义,定理,证明和例子时的一个呈现方式。

This section gives a brief guide to giving a math lecture, i.e., a classroom presentation where you are teaching definitions, theorems, proofs, and examples to a class of students.

一、将你说的话都写下来。数学课和其他任何公开发言(比如文学课,沙龙,政治演讲)的最大差别在于你

必须将你说出的话都给写下来。这是因为不像其他的科目,数学通常不是那种你可以用语言和模糊的方式交流

而不用处理细节的学科。 所以,如果你想你的听众能理解的你讲的话,那你就必须将他们写下来。

1. Write down everything you say. The main difference between a math lecture and almost any other kind of public speaking you can think of (a literature lecture, a sermon, a political speech)

is that you must write down everything that you say. This is because, unlike almost any other subject, math generally doesn’t have an underlying kind of intuitive sense to it that you can communicate

verbally and vaguely without dealing with details. Therefore, anything that you want your audience to understand must be written down.

二、写一次,说两次。作为一个规则,当你在写黑板的时候,说出你将写下的内容,写完后再说一次你写下内容。

2. Write it once, say it twice. As a rule, it often helps your audience if you say what you’re going to write as you write it down, and then repeat it once it’s already written down. You don’t have to do this to a completely mechanical extent, but if you practice this, it should start to become fairly natural.

3. Don’t just write down the equations, write down the words between equations. This is especially true in a proof class, where the words between the equations and symbols (“for every”, “there exists”) are almost more important than the equations and symbols themselves.

4. If you are presenting definitions, theorems, and proofs, clearly indicate which is which. It’s especially important to separate theorem from proof, and to indicate what you’re assuming and what you want to conclude in your proof.

5. Structure your lecture from the top down, like any other kind of oral or written communication. In other words, start with an outline on the highest/broadest level, and then fill in the details.

6. When writing on the board, go from top to bottom, left to right. Don’t skip around or proceed in a nonlinear fashion.

7. Avoid large-scale erasing of mistakes if you can, as erasing makes it hard to take notes. Instead, cross things out, or if you do erase, pause for a moment to let people catch up.

8. If you follow all of the above tips, you may start to feel as if you are speaking at an incredibly slow pace and that you are going to grow old and die at the board. If so, you’re going at the correct speed to be understood! In fact, slowing yourself down is yet another reason to write everything down.

How to give a math lecture的更多相关文章

  1. [C2P3] Andrew Ng - Machine Learning

    ##Advice for Applying Machine Learning Applying machine learning in practice is not always straightf ...

  2. 机器学习、NLP、Python和Math最好的150余个教程(建议收藏)

    编辑 | MingMing 尽管机器学习的历史可以追溯到1959年,但目前,这个领域正以前所未有的速度发展.最近,我一直在网上寻找关于机器学习和NLP各方面的好资源,为了帮助到和我有相同需求的人,我整 ...

  3. TPO-19 C1 Discussing A Point Raised In A Lecture

    TPO-19 C1 Discussing A Point Raised In A Lecture 第 1 段 1.Listen to a conversation between a student ...

  4. Randy Pausch’s Last Lecture

          he University of Virginia American Studies Program 2002-2003.                     Randy Pausch ...

  5. JavaScript中Math对象的方法介绍

    1.比较最值方法 比较最值有两种方法,max() 和 min() 方法. 1.1 max() 方法,比较一组数值中的最大值,返回最大值. var maxnum = Math.max(12,6,43,5 ...

  6. JavaScript Math和Number对象

    目录 1. Math 对象:数学对象,提供对数据的数学计算.如:获取绝对值.向上取整等.无构造函数,无法被初始化,只提供静态属性和方法. 2. Number 对象 :Js中提供数字的对象.包含整数.浮 ...

  7. Chrome V8引擎系列随笔 (1):Math.Random()函数概览

    先让大家来看一幅图,这幅图是V8引擎4.7版本和4.9版本Math.Random()函数的值的分布图,我可以这么理解 .从下图中,也许你会认为这是个二维码?其实这幅图告诉我们一个道理,第二张图的点的分 ...

  8. Math.random()

    Math.random() 日期时间函数(需要用变量调用):var b = new Date(); //获取当前时间b.getTime() //获取时间戳b.getFullYear() //获取年份b ...

  9. Math.abs()方法 取绝对值

    定义和用法 abs() 方法可返回数的绝对值. 语法 Math.abs(x) 参数 描述 x 必需.必须是一个数值. 返回值 x 的绝对值. 实例 在本例中,我将取得正数和负数的绝对值: <sc ...

随机推荐

  1. 04. pt-deadlock-logger

    死锁:是指两个或则多个事务在同一个资源上相互占用,并请求锁定对方占用的资源,而导致恶性循环的现象:当产生死锁的时候,MySQL会回滚一个小事务的SQL,确保另一个完成.上面是死锁的概念,而在MySQL ...

  2. Python之路(第二十四篇) 面向对象初级:多态、封装

    一.多态 多态 多态:一类事物有多种形态,同一种事物的多种形态,动物分为鸡类,猪类.狗类 例子 import abc class H2o(metaclass=abc.ABCMeta): ​ def _ ...

  3. list,set等集合遍历时,不能remove集合中的元素。需要new一个Object或者list,set,里面add需要删除的元素,等集合遍历完了进行remove(Object)或者removeAll(list/set)操作

    list,set等集合遍历时,不能remove集合中的元素.需要new一个Object或者list,set,里面add需要删除的元素,等集合遍历完了进行remove(Object)或者removeAl ...

  4. Vim on Mac Terminal

    2018-04-15 在Python 里面加标注, 发现Vim强大的两种用法, 比如要在1-5行加标注: 1. 用寻找和替代(basic search and replace),:1, 5s/^/# ...

  5. java script入门之知识

    1.注释 /*              */ 多行 //单行 2.常见形式 <!DOCTYPE html><html><head><title>My ...

  6. [C#.net]Connection Timeout和Command Timeout

    每次对数据库连接时,我们有时候会碰到连接超时或者命令超时,这两个超时是不一样的.以ADO.NET为例,当客户端和服务器端连接时,碰到的超时情况主要有下面几种: 当从连接池获取一个连接时,碰到超时. 当 ...

  7. MySQL中使用SHOW PROFILE命令分析性能的用法整理

    show profile是由Jeremy Cole捐献给MySQL社区版本的.默认的是关闭的,但是会话级别可以开启这个功能.开启它可以让MySQL收集在执行语句的时候所使用的资源.为了统计报表,把pr ...

  8. transform.forward和vector3.forward

    Vector3.forward的值永远是(0,0,1)(这里的(0,0,1)是世界坐标的(0,0,1)),而transform.forward我们可以理解为其对应物体的z轴方向,是一个向量,而不是一个 ...

  9. Maven手动将jar包放入本地仓库

    mvn install:install-file -Dfile=jar包的位置 -DgroupId=上面的groupId -DartifactId=上面的artifactId -Dversion=上面 ...

  10. 通过http.client解析url返回的数据时为什么中文变成了unicode码

    今天在解析json数据的时候得到了一堆这样的数据:{"errNum":0,"errMsg":"success","retData& ...