曹颖老师

Review period 1. Students bring in what they have in mind about displacement so far.
Task 2-1: Imagine we all live at the same straight street, named Main Street, and we have different address number on this street for each individual’s home. Here is our school, also at this street. (Draw a straight line on the board and a shape of school building in the middle of the line.) Now choose a number for your imagined home at this street, and draw the displacement that represent you coming to this school from this home.
After they draw the displacement, have students share their responses with their neighbors and discuss about their work. The teacher can also ask several students to draw their imagined home on the board according the street and school already drawn, and explain to the class. Here there would not be too much argument.
When students are talking about displacement, teacher should pay attention whether they have clarified both the length of the displacement and the direction of the displacement. If some of them don’t, teacher may ask questions like “this way or that way?” and “how long?” I think by asking these questions, students may gradually realize that these two features of displacement are indispensible.
Task 2-2: Now try to think of a mathematical tool that can help us tell others about these displacements in a more accurate and concise way than using normal language.

At first, students may be confused by understanding this task. What does the teacher mean by “a mathematical tool”, and what does it mean be either accurateness or conciseness. It is good if some students ask for clarification, and other students are encouraged to respond with their understandings. By discussing over these points several rounds, students will be able to reach a certain agreement on the requirement of the task. And that is enough for them to move on.
It is possible that some students have already heard about the content or have read the textbook in advance and soon set up a Cartesian coordinates, very likely a 2-D coordinates, even though we are just talking about one dimensional movement. A 2-D coordinate system leaned in math class is what they understand a Cartesian coordinates should look like. They don’t understand Cartesian coordinates well although they think they do.
Certainly there are many other random (well, not really) thoughts. The teacher should walk around and suggest students to get into small groups and share their ideas.
At some point when almost every student has work out some ideas and has already discuss them with others, teacher may intervene by providing hints.
Hints:
Hint number one: this tool should be able to describe positions—original position and final position.
Hint number two: a displacement has distance and direction, as we have discussed before. How could your mathematical tool express them?
And then just keep their work going.
Small group discussions are encouraged.
Sharing ideas during the course of the class:
Ask students to speak out their ideas and the teacher should elicit several points, using students’ ideas they brought up (if they did):
Cartesian coordinates can be such a tool that satisfies the requirement of this task.
In a Cartesian framework, each position can be represented by a point with corresponding coordinates. (Before that we should stipulate an origin and a positive direction so that every coordinate can be expressed as a number.)
In a Cartesian framework, a displacement is a natural number. The absolute value represents the distance between the original place and the final place. The positive/negative sign represents the direction.
If the movement is just in a straight line, which is one dimensional, a one-axis coordinate is adequate to describe the motion, although two-dimensional coordinates definitely also work.
Note: if the teacher finds that students have not work enough to pull out these ideas, she should just keep patient. According to what the students have worked out already, pose questions to their ideas and get them back into their groups and discuss longer. And then bring them back to the whole class discussion on their own previous work, until they feel comfortable enough for the teacher to re-frame THEIR ideas about Cartesian coordinates as above.
Final task, Task 2-3: Using Cartesian framework, answer the last question in yesterday’s class: draw the displacement that you leave home, come to school and then go back home. And tell us about what you did and what your thinking is.
This is not easy, though. They would first set up a frame. Then determine the positions. And then figure out three ideas about the displacement: the placement of going to school, say n, the placement of coming back home, say –n, and the overall displacement of going to school and coming back home, which is zero, the sum of n and –n.

This will take time. Let them work and discuss and share. If two periods didn’t work, then extend to 3 periods. The content deserves a deep investigation and understanding. If they spend enough time and work out the concept of displacement on their own, the following discussion about velocity and acceleration in Cartesian coordinates will be much clearer to them than teaching displacement in a traditional way. They will catch up fast when the content moves on. All the “extra” time spent will be won back within a semester, and I believe even if still for standard tests, this way of learning physics will make students do better than the traditional teacher. And of course they will learn more than doing tests.

Lesson Plan: Displacement
Although I had been teaching high school physics, 10-12th grades, for years, I don’t like the traditional appearance of a lesson plan anymore. But I also don’t know what an innovated lesson plan should look like. In this work I try to describe what I am expecting the lesson should be going.
The words below are like a flow of events in a classroom with a physics teacher (I imagine that as me) and a group of students. The size of the class could vary. I have tried the similar, less radical innovated than in this plan, teaching in both a 30 students’ class and a 50 students’ class. The latter situation definitely worked less than the former. But I think it worked out enough. Since I have tried a mild version of teaching the content in this way, the students’ reactions described later are not totally speculations. Some of them are what I have repeatedly encountered in my experience.
An ideal role of a teacher in my mind is no longer a knowledgeable and eloquent authority, which had been my ideal for a while. Now she is a person that is patient and attentive to students. She is neither imposing nor judging. Sometimes students don’t even notice that she is teaching in the class. But she is absolutely deliberately consciously helping students doing science, in an unnoticed way .
Topic: Displacement
This is the topic of the very first class of physics in the first year of high school. In China, all high school students are required to take 1-2 years of physics before they split into two academic tracks: social study track and science/engineering track.

Students:
15-16 years old in 10th grade. In their native China, middle schools represent 7-9 grades, and high schools represent 10-12 grades.
Objectives (already incorporating the national standards):
Generate the concept of displacement.
Represent one dimensional movement displacement in Cartesian coordinates.
Time:
Two periods are on two successive school days.
Each period lasts 45 minutes.
With much flexibility and no strict division between the two periods, largely dependent on how the discussions are going.
Prior knowledge they might have:
Lots of everyday experience they have about motion.
They had two years of physics courses in 8-9 grades in middle school .

Cartesian coordinates has been covered in middle school math classes.

经历了今年暑假在心智家的一个月，我很想把这一个月中的经历和感受记录下来，开学后忙啊忙啊忙，不知不觉学期过半，如果再不写下来，估计就再也提不起笔来了，就从今天陆续地经常写一点吧。

话说路老师的“心智家”暑期体验营今年为了吸引生源，推出了“自编辅导教材”的亮点。我当时办着各种签证手续，又带着两份作业，原本是没有心思编什么辅导教材的。再说，教辅编来编去，已然大同小异：无非是知识点总结，重难点分析，例题详解，习题训练。书城里已经有那么多神一样的强大机构每年都有新品上市了，我这一己之力，又能编出什么新的来呢？

随着路老师那边不停地催债，我终于打开电脑，答应他们在限定日期之前，先写出一部分，然后在讲课的过程中边讲边继续往后写。之所以要先拿出一部分，是讲座时的招生宣传能拿出来展示一下，好让家长和学生们知道我们不是忽悠人的。

于是，我坐在桌前，打开电脑（又说一遍），想：写点什么呢？

既然我不愿意也不没那个实力去写一本惊艳亮相的传统模式的辅导材料（用传统模式我还真不知道咋能惊艳），那么，就让我试着写出来自己真正想写的吧：

写在前面的话：

这个小册子不是教材，你仍然需要手边有课本，而且非常必要。这个小册子是依据人教版高中物理教材来编写的，你在使用本书的时候需要同时使用这个课本。

这也不是一本教辅，这里面没有知识点总结和琳琅满目的习题。当你需要它们的时候，你仍需要一本比较传统的教辅书。

那么，这是什么？

也许，这会成为我们的交谈，是我和你一起写成的一本小书。书的内容是你的生活，和一点点物理。

（未完待续，敬请关注下一篇：《第一天》）

对人的认知过程研究是我的课业的重要甚至是全部的内容。这其中必然有众多学派，几百年来始终争论不休。建构主义是其中的一派，对人类认知科学知识、建立逻辑能力的过程有着很强的解释力。当然，在建构主义学派内部，也有各种小的分支，他们也在天天争论怎样才是对建构主义的最恰当的理解。学术界，就这样，不争不发展，不争不热闹。

建构主义总体上强调主体（人）在和客体（物体）之间的相互交流中建立起自己对客体的认识。知识和逻辑的来源在于建构，区别于知识的传递。换句通俗的说法，就是：“明白不明白”，没人能直接给你，别人替不了自己。而且，而且！！不同的人从相同的客体那里建构出来的知识是可以不同的。极端的建构主义观点甚至认为，没有一个所谓的”事实“ reality)。

比如，我经历了将近20年的学习后终于悟出了看书要内容结合目录，从目录看结构和逻辑联系，从内容看具体事例、描述和论证。然而我想站在讲台上告诉学生“你们要学会看书的目录”，用处不大。他们必然要在某一次学习过程中切身体验出这么做的作用，不可替代的奇妙的功效，他们才知道为什么要读书的目录。否则看也是个形式，必然不理解其中的关联。这就像绘画老师总跟孩子们讲，要先构图、勾出比例轮廓，然后填进细节，可拿起画笔的小朋友永远都是先把眼睛上的睫毛都画得自己很满意了才会去画鼻子。

小孩子认知始于细节而慢慢走向通识大成。这个过程谁也改变不了，你无法让他们跳过甚至也无法缩短它。学习需要时间，想省时间的办法，往往最后反而是浪费时间。

由此可以联系到很多。学科学知识是如此，学习生活知识也是如此：

“你现在上学多幸福，我想回去读书都没机会了”。小学生只会当耳旁风。

“你有条件学钢琴还不好好练，我们小的时候根本都没这条件”。他一样不愿意练。

“选男人不能只看他现在对你有多好，爱情不能当饭吃，你俩不合适，门当户对是千年古训屡屡应验”。这只会导致这一对栓得更紧一致对外。

。。。。。。

类似的例子太多了，举不完。这些孩子们长大了，走过来了，明白长辈的话说的对了，也同样会重复对自己的孩子们说，而他们的孩子也会以同样的抗拒而必须自己走过自己经历。

学习无人可以替代，谁也没法替你“明白”，谁也无法替你走过这个通往明白的过程。

这并不意味着父母长辈就只是放任自流袖手旁观，明白了建构的道理，父母教育孩子，老师教导学生，便要学习用巧劲儿，四两拨千斤，适时适度。这里面的学问可多了去了呀。这也要自己琢磨，别人列出的宝典绝招一二三四，没多大用。这也是建构。

身体认知（EMBODIED COGNITION)，这是我自己的翻译，不知道国内学术界咋称呼这个。其核心是认知过程不止在于大脑，也涉及身体。换句话说，认知不只是“想”，或者说，认知无法只是“想”，还必然同时要触碰感知外部世界。感官的体验对人对事物的认知有着重要的不可取代的作用。所以，这个理论强调不止要分析人类的大脑神经活动，还要分析人的举动。对学习科学概念而言，就要分析人们对一个物体的操作，身体的动作，和在表达自己意见的时候的手势什么的。没有身体的参与，认知过程不可能完成。我估摸着，”冥想“这玩意儿在身体认知的理论框架下，应该不怎么靠谱。

实际的研究过程中，我也的确发现，对同一个概念，你只是跟面前这个人对话，有问有答，和你们同时要写、要画、要摸要拿一些个具体的东西、要比比划划地讲，后者能带入更多维度的思考。经常的，身体参与带来的体验，和单纯的想和说，会产生认知上的冲突 。就是说，你本来想着就那么简单一个概念 （比如说质量），你自己肯定已经了解了，肯定是那么回事儿，根本不用去写去画去操作了。可是等你写过画过操作过之后 （当然，这个过程中，采访者的提问也很关键），却发现了不曾预料的困惑和矛盾。一个本来自己觉得非常明白的事儿，忽然发现自己一点都不明白。而认知的过程，在这个时候才刚刚启动。

这其实还是建构主义的大思路。有人把建构主义和身体认知联合在一起叫做个动作主义 （ENACTIVISM，也是我自己翻译的）。不过叫什么名字都无所谓，关键是要领悟这些理论的精神。

都说医生做久了看美女也都是骨骼肌肉神经，像我们这行的，跟人聊天说话中，没准就把人家给分析了。吼吼~

很多人，国内的同事朋友和美国这边的教授同学朋友，问我毕业后的去向。我来的时候是这么想的，经过了将近两年，我越来越坚定我当初的想法：我还是想回国，还回到中学，基本上也就是回到一中，不做领导，不做专家，不指点江山，不统领全局，你们就让我，还做个普普通通的老师，让我的价值，还在课堂上、自习辅导中，一点点展现。这样，我做一点，是一点。把自己架得很高，以为能发挥很大的作用，但是往往，反而发挥不了什么作用。

我并不认为拿个美国博士回去，我的课堂就要有天翻地覆的变化，与别的老师会有特别明显的不同。还是那些知识，还是相似的节奏，可能还是传统的教案，保证学生们在中国这个应试的大环境下安全地跋涉。

可能，变化更多发生在细节上。可能是对一个概念的解释，可能是对学生的一个问题的一句回答，可能是和学生在课下的一次交谈。有些可能是我有意识的，有些甚至可能是我无意识的。

我真的，只想做个好老师。海归博士做官员做学者的很多很多，不缺我这一个。但是回去还在中学一线工作的，恐怕不多。我更愿意这样来实现自己的价值。我觉得这很酷。

附：

有这么一个故事。
在暴风雨后的一个早晨，一个男人来到海边散步。他一边沿海边走着，一边注意到，在沙滩的浅水洼里，有许多被昨夜的暴风雨卷上岸来的小鱼。它们被困在浅水洼里，回不了大海了，虽然近在咫尺。被困的小鱼，也许有几百条，甚至几千条。用不了多久，浅水洼里的水就会被沙粒吸干，被太阳蒸干，这些小鱼都会干死的。
男人继续朝前走着。他忽然看见前面有一个小男孩，走得很慢，而且不停地在每一个水洼旁弯下腰去–他在捡起水洼里的小鱼，并且用力把它们扔回大海。这个男人停下来，注视着这个小男孩，看他拯救着小鱼们的生命。
终于，这个男人忍不住走过去：”孩子，这水洼里有几百几千条小鱼，你救不过来的。”
“我知道。”小男孩头也不抬地回答。
“哦？你为什么还在扔？谁在乎呢？”
“这条小鱼在乎！”男孩儿一边回答，一边拾起一条鱼扔进大海。”这条在乎，这条也在乎！还有这一条、这一条、这一条……”

这学期有门课，上得特别有意思。

这个教授只是有一个很初步的想法，写了个不长的立题申请，为了6月去加州参加一个学术会议，还要在会议上做报告。可是，他自己除了这个很粗很初步的想法之外，基本上什么都还没有做。我们选课的这5个人，就是和他一起准备出他去开会交流做报告的内容。

所以，这个课第一没有分数压力，老师说只要认真做事，都是A。第二没有个特别具体的大纲。起初的课上，经常是一节课下来大家越说越晕，几节课之后发现比刚开始的时候还要晕。老师有时候也说他有点晕了。

但是，我有一种从原始状态做起，做一个学术任务的感觉。那种从混沌中提取图形，从噪声中分辨出信号的感觉。听着大家的那些说完后自己都直摇头，不知道自己都说了些什么，看过的书和文章很多，但是不知道线索在哪里，我总觉得，这样的话最后做出成果的愉快感会更大。而其实，至少从我的观察，大家都觉得自己相对于刚开始，在每一节课中都或多或少理出一些头绪。

我在这门课中的任务相对比较简单。因为启发这个教授产生他的那个想法的一本书，是皮亚杰生前的最后一本。写的是科学史与人的认知发展之间的相似性的。有点像生物学上说一个个体的胚胎发育过程就是一个快进版的生物进化史。这本书是说，一个个体认知科学概念、建构科学理论的过程，就像一个快进版的科学发展史，按照目前为止我的理解。

由于那本书非常细节地在讨论和分析从亚里士多德到伽利略到牛顿的力学，以及几何学、代数学、和经典力学的概念和理论，我们这个教授看不大懂。我们全班的人都看不大懂。教授一直都是搞儿童发展的，其他的人都是学艺术的、学戏剧的，只有一个好像是沾点工程的边儿，但是也不是理科。所以，就只有我一个人比较可能多读懂一些这本书的各种物理概念的细节。所以我的任务就简化成了：把这本书读懂，并且讲出来让其他人能听懂。

其他的同学分别在研究计算机科学、芭蕾、和科学课程的学科发展 （可以只是其中某一个阶段的发展），并试图从中寻找发展过程中的特征。不是简单陈列发展的过程。我的工作有点像帮大家呈现一个模板，虽然其他人的工作内容都不同，不可能直接采用这个模板。但是希望可以从中得到一些启发。