左右互搏――老顽童

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左右互搏――老顽童 关于人生、社会、世界的思考。尤其是组合数学、数学教育、思考问题的方法的讨论。 首页 Why The Professor Can (16) 方法 (28) 妙文拾趣 (33) 网站日志 (5) 影视音乐 (8) 数学 (3) 经典欣赏 (11) 小说连载 (34) 评论 (8) 2004 年 5 月 Sun Mon Tue Wen Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 最后更新 沙僧日记――秀逗前年9月30日 此间的少年――乔峰（Ｉ）：一次篮球赛 沙僧日记――秀逗前年9月28日 此间的少年――乔峰（Ｉ）：关系铁 沙僧日记――秀逗前年9月27日 此间的少年――郭靖（Ｉ）：图书馆 沙僧日记――秀逗前年9月14日 此间的少年――郭靖（Ｉ）：朋友 窃喜即偷欢 风雨再访金文明 最新评论 冷峻散势 : 左右互搏就是自己. 金庸 : 多少风情， . 涓涓流水 : 这篇文章不长，但. darkevan : 搞个链接不就行了. ivy : that is a good o. mojaves : 用了我最喜欢的海. isgaryzhu : 你是纪晓岚剧组的. 存档 内人 E-Mail to 老顽童 我的链接 分页: 第一页 [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] 最后页 星爷的经典台词――大话西游精彩对白 - 2003-06-02 03:56 星爷的经典台词 大话西游精彩对白： 你妈贵姓？ 你又在吓我！ 小心啊！打雷喽！下雨收衣服啊！ 跟我说话吗？不是跟我说的吧？认错人啦！ 悟空，你怎么可以这样跟观音姐姐讲话呢？ 唉，文也不行武也不行，你不做山贼，你想做状元啊？ 喔－－！熟归熟，你这样乱讲话，我一样可以告你毁谤，哈！ 省省吧你！改变什么形象，好好地做你山贼这份很有前途的职业去吧！ 我怎么说也是个夕阳武士，你叫我亲我就亲，那我的形象不是全毁了！ 老弟，象我这么有理性的人，我怎么可能会接受这种无稽的事情呢？ 你把胡子剃光干什么？你知不知道你少了胡子一点性格都没有了？ 长夜漫漫无心睡眠，我以为只有我睡不着觉，原来晶晶姑娘你也睡不着啊！ 少罗嗦！你追了我三天三夜，因为你是女人我才不杀你，不要以为我怕了你了！ 看看你这副德性，鬼鬼祟祟丢人现眼披头散发人模狗样，怎么跟我出来闯荡江湖，啊？ 以前陪我看月亮的时候叫人家小甜甜，现在新人胜旧人了，叫人家牛夫人！ 我刚刚睡醒，经过外面无所事事，就顺便进来拜师学艺的。 你突然跟我提到成亲的事......我牙齿还没刷呢！ 谁说我斗鸡眼？我只是把视线集中在一点以改变我以往对事物的看法，干吗？造谣我不行了，想抢我的位子？ 紫霞在你心目中是不是一个惊叹号，还是一个句号，你脑袋里是不是充满了问号？ 爱一个人需要理由吗？不需要吗？需要吗？哎，我是跟你研究研究嘛，干嘛那么认真呢？ 你有多少兄弟姐妹？你父母尚在吗？你说句话啊，我只是想在临死之前多交一个朋友而已。 人和妖精都是妈生的，不同的人是人的'>的'>他的，妖是妖的'>的'>他的...... 所以说做妖就象做人一样，要有仁慈的心，有了仁慈的心，就不再是妖，是人妖。 我受不了你呀！你长得这么丑，帮个忙，大家都是神仙，不要再性骚扰我了行不行？ 论智慧跟武功呢，我一直比他高一点点，可是现在多了个紫霞仙子，他恐怕比我高一点点了。就是因为多了你这个累赘他才会高我一点点！ 悟空他要吃我，只不过是一个构思，还没有成为事实，你又没有证据，他又何罪之有呢？不如等他吃了我之后，你有凭有据，再定他的罪也不迟啊！ 悟空，你尽管捅死我吧，生又何哀，死又何苦，等你明白了舍生取义，你自然会回来跟我唱这首歌的！喃呒阿弥陀佛、喃呒阿弥陀佛、喃呒阿弥陀佛...... 一定要交代！所以我一定要拿回那个月光宝盒带你一起回去跟他们说清楚。我不管别人怎么说我，我也不怕后世会有千千万万的人对我唾骂，我要一个人承担下来。 大家看到啦？这个家伙没事就长篇大论婆婆妈妈叽叽歪歪，就好象整天有一只苍蝇，嗡……对不起，不是一只，是一堆苍蝇围着你，嗡…嗡…嗡…嗡…飞到你的耳朵里面，救命啊！ 所以呢我就抓住苍蝇挤破它的肚皮把它的肠子扯出来再用它的肠子勒住他的脖子用力一拉，呵－－！整条舌头都伸出来啦！我再手起刀落哗－－！整个世界清净了。现在大家明白，为什么我要杀他！ 哇！大哥，你化这个妆就说自己是孙悟空喽？给点儿专业精神好不好？你看，那些毛通通都开叉了，头上象戴了两块年糕似的，出来混饭吃得花点本钱嘛！看什么看，你的妆是恶心嘛！生我气我也这么说！ 你想要啊？悟空，你要是想要的话你就说话嘛，你不说我怎么知道你想要呢，虽然你很有诚意地看着我，可是你还是要跟我说你想要的。你真的想要吗？那你就拿去吧！你不是真的想要吧？难道你真的想要吗？ 喂喂喂！大家不要生气，生气会犯了嗔戒的！悟空你也太调皮了，我跟你说过叫你不要乱扔东西，你怎么又…你看我还没说完你又把棍子给扔掉了！月光宝盒是宝物，你把他扔掉会污染环境，要是砸到小朋友怎么办？就算砸不到小朋友砸到那些花花草草也是不对的！ 唉，那个金刚圈尺寸太差，前重后轻左宽右窄，他带上之后很不舒服，整晚失眠，会连累我嘛！他虽然是个猴子，可是你也不能这样对他，官府知道了会说我虐待动物的！说起那个金刚圈，去年我在陈家村认识了一位铁匠，他手工精美、价钱又公道、童叟无欺，干脆我介绍你再定做一个吧！ 你应该这么做，我也应该死。曾经有一份真诚的爱情放在我面前，我没有珍惜，等我失去的时候我才后悔莫及，人世间最痛苦的事莫过于此。你的剑在我的咽喉上割下去吧！ 不用再犹豫了！如果上天能够给我一个再来一次的机会，我会对那个女孩子说三个字：我爱你。如果非要在这份爱上加上一个期限，我希望是......一万年！ C&O 发表于 03:56 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――其他类 - 2003-06-02 03:54 星爷的经典台词 其他类： 对不起，我是卧底。 你看不见我你看不见我你看不见我...... 意不意外？高不高兴？开不开心？ 对不起啊，导演。嗯...... 根据角色的背景性格呢，等一下演的时候，在节奏上我想再调皮一点，但是又带点矛盾，你看怎么样？ 拿痛来说呢，根据俄国戏剧理论大师史坦尼斯拉夫斯基的说法呢。应该从外到内，再由内反映出来的。来，你现在再试着做一次看看。 不可能的，大傻的妹子的老**的'>*的大哥的儿子说是有的啊。 谈钱伤感情嘛！但是陈兄，我们几个兄弟跟你没什么感情可言，还是谈钱直接一点。 有没有钱没关系，但起码要做一个受人尊重的人！（话锋一转）――我宁愿有钱...... 你们大家都是女人，何苦自相残杀呢？就算是鸡，都有爱国的。 你快点回火星吧，地球是很危险地。 你想吓我是吓不倒地，我什么都怕就不怕鬼！ C&O 发表于 03:54 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――对话类 - 2003-06-02 03:52 星爷的经典台词 对话类： A： 十年了，已经十年了，我还以为国家已经把我忘记了。 B： 怎会呢，就算是一条底裤，一张厕纸，都有它的用处。 A：真的，如果我骗你，保证我生儿子没屁眼 B：看你这个样子，生儿子肯定没屁眼，就算是有，也是畸形屁眼！ A： 你究竟是何方神圣？ B： 江湖险恶，我从来都不轻易留下我的姓名。 A： 你既然不肯留下姓名，就只有留下你的人头！ B： 我一生孤独，唯一相依为命的就只有这个人头，你要拿走它，恐怕不是那么容易！ A： 好！是你迫我出手的，我要用你的鲜血染红这片大海。 B： 我一生漂泊，就仿如汪洋里面一页孤舟，早将生死置之度外。 C&O 发表于 03:52 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――短句类 - 2003-06-02 03:49 星爷的经典台词 短句类： 禀夫人，小人本住在苏州的城边，家中有屋又有田，生活乐无边。谁知那唐伯虎，他蛮横不留情，勾结官俯目无天，占我大屋夺我田。我爷爷跟他来翻脸，惨被他一棍来打扁，我奶奶骂他欺骗善民，反被他捉进了唐府，强奸了一百遍，一百遍，最后她悬梁自尽遗恨人间。他还将我父子，逐出了家园，流落到江边。我为求养老爹，只有独自行乞在庙前。谁知那唐伯虎，他实在太阴险。知道此情形，竟派人来暗算，把我父子狂殴在市前，小人身壮健，残命得留存，可怜老父他魂归天！此恨更难填。为求葬老爹，唯有卖身为奴自作贱，一面勤赚钱，一面读书篇，发誓把功名显，手刃仇人意志坚！从此唐寅诗集伴身边，我铭记此仇不共戴天！！！ 在一个月黑风高阴森恐怖的晚上，我是至尊宝你是白晶晶，奇妙的爱情就从桥头上这一点火开始的。我才一转身你就突如其来地向我一指，我整只手就著火了。你还要冲过来向我拚命地打拚命地打拚命地打，不是不是不是这样打，是这样这样这样，是了就是这样打的，你看到了吗？以后的发展我可以用一句峰回路转来形容，因为突然之间杀出了个牛魔王。当时你手拿一条骨大战牛魔王之后，就把我抓回了盘丝洞里。所谓光阴似箭，真的一点也不错，因为才一眨眼就到重头戏了。在断岩上就是感情爆发的时候，我不顾一切地摸你你也不顾一切地摸我，并立下了永不分离的誓言。可惜快乐永远是短暂的，换来的只是无限的痛苦跟长叹，为什么你会死呢？我只有利用月光宝盒使时光倒流查出真相，终于被我知道原来你是自杀的！在最后关头我於于能把你救活！可是最后一次时光倒流月光宝盒发生故障我"啾"的一下就回到了五百年前……就这样。 C&O 发表于 03:49 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――自述旁白类 - 2003-06-02 03:47 星爷的经典台词 自述旁白类： 你先走吧，我等我的腿没那么颤抖，心跳没那么乱的时候，我再走好了。 三十多年前，我上中学的时候，我真的时时刻刻都会想着她，有时候撒尿都会突然间停一下，然后想起她，心里甜甜的，跟着那半泡尿就忘了尿了。 子弹射入了我的大腿骨，压住了我的大动脉，挡住我的三叉神经，现在我左边脑部缺氧麻痹，右半身开始瘫痪，（撕开裤子）一定要用刀割开伤口把子弹取出来。 我是说我的这个方法，是古代神医华佗所用的分心可爱的家乡。古代有关云长全神贯注下象棋刮骨疗毒，今日有我007聚精会神看A片挖骨取弹头，开始－－ 当头一刀，就由额头砍到鼻子那，那（指档口），就在他的档口跟前，尾龙骨砍了好几刀，断了两条筋，压住了三叉神经，影响了大脑的中枢系统，连牙都窜出来了。 斩过鸡头，烧过黄纸，歃血为盟之后，韦小宝你就是我天地会的兄弟，暂时编入青木堂。我们有十大会规，二十大守则，三十大戒条，八十小戒条，如果犯了其中一条的话，就算你是我的徒弟，也要身受九九八十一刀而死。 不过这样，我是一个感情很复杂的人，一个感情很复杂的人如果只爱你一个人的话，就会变得感情有缺陷，一个感情有缺陷的人，你就算永远地拥有他，也是没用的。 (哭)旺财...... 旺财...... 旺财你不能死啊，旺财，你跟了我这么多年，对我有情有义，肝胆相照，但是到了现在我连一顿饱饭都没让你吃过，我对不起你啊，旺财！ 小强！小强你怎么了小强？小强，你不能死啊！我跟你相依为命，同甘共苦了这么多年，一直把你当亲生骨肉一样教你养你，想不到今天，白发人送黑发人。 C&O 发表于 03:47 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――羞辱求饶类 - 2003-06-02 03:43 星爷的经典台词 羞辱求饶类： 凭你的智慧，我很难跟你解释！ 屎，你是一滩屎。命比蚁便宜。我开奔驰，你挖鼻屎。吃饭！？吃屎吧你！ 碱水面没过过冷水，所以面里面全是碱水味。 鱼丸也没有鱼味，但是你为了掩饰，特别加上了咖喱汁，想把它做成咖喱鱼丸。但这么做太天真了，因为你煮的时间不够，咖喱的味道只在表面上，完全没有进到里面去，放进汤里面鱼丸就被冲淡了。好好的一颗咖喱鱼丸，让你做得是既没有鱼味又没有咖喱味，失败！萝卜没挑过，筋太多，失败！ 猪皮煮得太烂，没咬头，失败！ 猪血又烂稀稀的，一夹就散，失败中的失败！ 最惨的就是大肠了，里面根本没洗干净，还有一坨屎，你有没有搞错？哎，有坨屎哎，哎，有坨屎你看到了没有？哎，有坨屎！ 荒谬！我敢大胆的说一句，在我的面前，还没有人敢装模做样，你给我安静一点！ 剪头发不应该看别人怎么剪就发神经跟流行，要配合啊！你看你的发型，完全不配合你的脸型脸型又不配合身型，身型又和发型完全不搭，而且极度不配合啊！！欢哥！你究竟要怎么样啊？ 你说什么？你这种谎话也说的出口？你对不对的起自己的良心？对不对的起你的父母？对不对得起这个国家？你赶快召开记者会澄清，否则我就扒你的皮，拆你的骨，喝你的血！ 大姐，你也不怕别人笑话你，小心就连狗都会晕倒。 你完全没问题，是你爸妈有问题，把你生成这个样子。 你想？什么时候轮到我想？！ 不要怪我太坦白！就凭这你们这几个滥番薯，臭鸟蛋，想取我的性命，未免太过儿戏了吧！！！！ 实在令人太失望。听到你的声音，我还以为你是一个很有感性，很有电影幻想的人。看你这一身造型，就知道你太没有内涵了。 老板娘：你生儿子没屁眼，老爸卖屁眼，你自己烂屁眼，爱吃鸡屁眼。大屁股，你自己没生意，还跑来闹我？ 老板娘：不用你闹，我自揭身世。我三岁死了爹，四岁死了爹，五，六，七八岁都死过爹，十岁勾引男人，十一岁勾引男人，你的男人也被我勾了。 包龙星：你是柠檬头，老鼠眼，鹰勾鼻，八字眉，招风耳，大翻嘴，老羌牙，灯芯脖子，高低膊，长短手，鸡胸，狗肚，饭桶腰，我要是你，我早就自尽了 伯虎啊，不要这么绝好不好？大不了我发个毒誓，如果以后我再赌钱的话，就让天下最丑的女人夜夜轮奸，直到体无完肤，摇摇欲坠为止，这样可以了吧？ 两位姑娘，可怜可怜我吧，我一家六口一晚上全死光了。我身染十级肺痨，半卖半送，你就买了我吧。 命运真是不公平，为什么我这么帅却要掉头发，你们长的那么丑却不掉头发。 你怎么把我当猪啊，一看到我就让我睡觉。 C&O 发表于 03:43 | 阅读全文 | 评论(0) | 引用(trackback0) 星爷的经典台词――介绍吹捧类 - 2003-06-02 03:38 星爷的经典台词 介绍吹捧类： 其实我就是改变社会风气，风魔万千少女，刺激电影市道，提高年轻人内涵，玉树临风，风度翩翩的整蛊专家，我名叫古晶，英文名叫Jing Koo！ 介绍Pizzad的男朋友给你认识，他的发型又衰又难看，又没什么钱，也没读过书，性能力又马马虎虎，不过都算一表人才啦。哈哈...... 阿水出了名的泡妞无数，是我们所有男人的眼中钉。他优雅的体态散发出诱人的魅力，让所有的少女都难以抗拒。他那双叫人心碎的眼睛，不管多么冷傲的女性，都会被他温柔的眼神所融化，他是众所公认的街坊情圣，行运茶餐厅的灵魂，谁都认识的――蛋塔王子。 他高傲，但是宅心仁厚；他低调，但是受万人景仰。他可以把神赐给人类的火，运用的出神入化，烧出堪称火之艺术的超级菜式，他究竟是神仙的化身？还是地狱的使者？没人知道，但是可以肯定，每个人都给他一个称号――食~~神！ 此话当真？！说过的话不能不算数哦！不错！我就是美貌与智慧并重，英雄与侠义的化身唐伯虎！ 扫地只不过是我地表面工作，我真正地身份是一位研究僧。 先生：我左青龙，右白虎，老牛在腰间，龙头在胸口，人挡杀人，佛挡杀佛！ 贫僧乃少林寺方丈，法号梦遗。阿弥陀佛，我随风而来，随风而去...... 哇呀呀呀呀~~~，好！实不相瞒，小弟我就是人称玉树临风胜潘安，一支李花压海棠的小淫虫周伯通！ 凭你的智慧，我唬得了你吗？ 不怕告诉你，我从BB仔的时候就已经见过飞碟，即世人所说的UFO，不明飞行物体你懂不懂？4岁那年我又见过传说中的尼斯湖水怪，又同喜玛拉雅山的大脚怪聊过天猜过泉，再加上我从小到大天天早上都玩过山车，晚上呢就玩海盗船，也都会早上玩海盗船，晚上玩过山车，黄昏再玩多次海盗船都试过呀我告诉你。 先生，你额头有朝天骨， 眼里有灵光，仙人转世，神仙下凡，我终于等到你了。别动，虽然我泄露了天机，灾劫难免，可这是我命中注定，就算我要冒天大的危险，也要给你看个全相。 啊！师父的思维，果然天马行空仿如逆水行舟，厉害不愧以点子称王。 好！他想也不想就塞进去，不愧为一条荡~~~气回肠的汉子。我爱你！！！ 你以为躲起来就找不到你了吗？没有用的！象你这样出色的男人，无论在什么地方，都像漆黑中的萤火虫一样，那样的鲜明，那样的出众。你那忧郁的眼神，稀嘘的胡喳子，神乎其神的刀法，和那杯Dry Martine，都深深地迷住了我。不过，虽然这是这样的出色，但是行有行规，无论怎样你要付清昨晚的过夜费呀，叫女人不用给钱吗？ 除暴安良是我们做市民的责任，而行善积德也是我本身的兴趣，所以扶老太太过马路我每星期都做一次，星期天和公众假期也有做三四次的。 错！这并不是个普通的箱子，它是箱中之神，简称箱神！ 善有善因，恶有恶报，天理循环，天公地道，我曾误抓龙鸡，今日皇上抓我，实在抓得有教育意义，我对皇上的景仰之心，有如滔滔江水绵绵不绝，又有如黄河泛滥，一发不可收拾。 他武功的名堂呢，称之为九天十地，菩萨摇头怕怕，劈雳金光雷电掌！一掌打出，方圆百里之内，不论人畜、虾蟹、跳蚤，全部都化成了飞灰！ 我告诉你们，对付这种女人，一定要用居高临下的眼神，和一只强而有力的臂膀，把她从欲海当中解救出来。 C&O 发表于 03:38 | 阅读全文 | 评论(0) | 引用(trackback0) 大宋新闻联播 - 2003-06-02 03:27 大宋新闻联播 嘀铛嘀铛，嘀铛铛嘀铛……一阵随着熟悉的音乐，DSTV新闻联播，几个粗壮有力的大字从屏幕上滚过，每天19：00的大宋皇家电视台黄金时段的新闻节目又开始了。 一男一女两位播音员又出现在电视屏幕上，男的一身青衣，头插玉簪，背背三枝小箭，相貌英俊，正是浪子燕青，女的身着素服，淡扫蛾眉鬓戴一朵珠花，不是汴京第一美女李师师是谁？ 只见二人，神态端庄，面对镜头。“各位观众晚上好，今天是嘉佑元年农历二月二十丁未日，欢迎收看大宋皇家电视台新闻联播节目，我们先介绍一下这次节目的主要内容。”燕青中气十足的念道，“吾皇万岁会见大理国镇南王世子段誉率领的青年代表团；” 当念到吾皇万岁几个字时，神色肃穆地一抱拳，对空一揖，“王安石会见西夏大宋旅夏同胞联谊会总商会访问团，范仲淹考察安徽省税费改革工作；辽国边防军公然占领我燕云十六州，我外交部发言人公开表示抗议；民间抗辽团体丐帮举行集会，声讨前帮主乔峰的卖国行径……下面请看详细内容”画面出现壮丽的宫墙，镜头推移到大殿，一个戴束发金冠的青年，向坐在龙椅上的皇帝跪拜行礼，皇帝也站了起来，走下宝座，上前拉起青年，两人亲切交谈，并在旁边的偏殿落座叙话，皇帝是当今年青的天子赵哲，那戴束发金冠的青年，自然是大理国镇南王世子段誉，旁边跟随的朱丞相状态儒雅，武将军也相貌威武。 （李师师温婉的画外音响起：万岁在文华殿亲切会见大理国镇南王世子段誉率领的青年代表团一行，宾主在热烈的气氛中，就贸易与合作、科技与交流、和平与发展等问题进行诚挚友好地会谈，段誉世子表示，大理坚持一个大宋的原则，燕云十六州自古以来就是大宋的领土，是大宋不可分割的一部分，青年是民族希望和未来，大理将加强两国青年的交流与互访，两国将世世代代友好下去，……吾皇万岁也表示尊重和理解大理国的宗教信仰和民族习惯，非常钦佩大理段氏领导的民族解放运动和独立斗争，两国还将签订一系列的合资与合作协议……） 接着画面转到一个繁华的都市，高墙大瓦，飞檐斗拱，路上行人熙熙攘攘，甚是热闹，骑马的，坐轿的人人脸上喜气洋洋，连抬轿似乎也显得颇为轻松…… （燕青混厚的男中音响起：旧貌换新颜，曾经惨遭洪水袭击的陈州府，在包勉知府的亲自领导和指挥下，全州军民同心同德通过生产自救，不但彻底恢复生产，而且已基本建设成为商贸中心，配合国家中部大开发的政策，将成为一颗耀眼的明珠……）同时出现皇家电视台记者采访行人的镜头，一个坐轿的人探出头来接受采访，对着镜头用乡音表达感想，画面打出字幕：“火车跑得快全靠车头带，我们全靠知府大人的领导，才有了今天，全靠万岁爷开恩哪！”说着向天作揖。 画面再变，面容青癯的王安石在宰相府的西花厅中微微欠身，接见西夏代表团，代表团为首一人，头戴毡帽，塌鼻阔口招风耳，竟然是虚竹，自他与西夏公主成婚后，也不再做和尚，理所当然地成了在西夏的大宋侨领，这次率团归来一是想开展民间商贸往来，二是想回河南投资，也算是报答少林寺的栽培之恩。王安石面带微笑和他交谈，他一脸虔诚地听着。 （画面外李师师的声音响起：……王安石大人说：虚竹先生历尽千辛万苦，终于事业有成，但他们成功不忘报国，幸福不忘他人，毅然联络广大侨胞回来投资，支援家乡建设，我们地方各级府衙，一定要给予支持，在政策上要给予优惠……旅外宋人秉承炎黄子孙的优良传统，在域外孤身奋斗，非常地不容易，你们回来，我们一定要给予大家庭的温暖……） 画面换到安徽的市镇，头戴乌纱，身穿红袍的范仲淹在大小官员的簇拥下，穿行在街道上，视察了繁华的商业街，走访了几家徽菜馆和典当铺后，又来到了两大文化用品生产基地，徽墨和宣纸生产厂。在参观完宣纸的全套工艺流程之后，应纸厂的要求，欣然命笔，挥毫泼墨，写下了“先天下纸忧而忧，后天下纸乐而乐”的千古名句。 （燕青的声音解说道：范仲淹副枢密使在听取当地知府的汇报后作出指示，当前的税费改革工作责任重大，各级府衙一定要严格执行中央政策，“交子”作为我朝首次流通的纸币，在历史上是绝无仅有的，由于它的出现，我们节约了大量的贵重金属，这在货币流通史上具有划时代的意义，我们从事的是前无古人的事业，我们一定要打起十二分精神继续下去，不管前面是万丈深渊，还是地雷阵，我们一定要将改革进行下去。） 画面上随行人员均将双手提至胸前，上下相对，间距半尺，当他讲话一完，便长时间热烈鼓掌。 屏幕上出现一群蒙古、契丹、西夏、女真、波斯等异族装饰的人，在几个大宋官员的带领下，在汴梁城内游荡，…… （画外音响起：国际鞠联评估团听取我国申办世界首届鞠蹴联赛委员会的陈述，评估团在汴京参观视察，评估鞠蹴联赛的准备情况……） 画面上，燕青神色严肃地念道：“民间抗辽团体丐帮举行集会，声讨前帮主乔峰的卖国行径，……请看本台记者发回的详细报道。”杏子林中，开满枝头的杏花落了满地，还有些折断的树枝和损坏的武器也扔在一旁，一群破衣烂衫的乞丐围坐在一起，许多人都垂头丧气，看情形似乎刚刚经历了一场大战，但却没有发现血迹。皇家电视台的记者手持带小金龙标志的话筒正在一一进行采访。一个头戴方巾，眉目清秀的中年乞丐（打出字幕：丐帮长老全冠清），对着话筒义正词严：“本帮前任帮主乔峰，其实是一个暗藏的契丹特务，他阴谋杀害马副帮主，企图支持契丹，分裂丐帮。我们是可忍，孰不可忍！”镜头转向一白发老者（字幕：丐帮执法长老白世镜），他沉着脸说道：“乔峰本姓萧，乃契丹人之后，非我族类其心必异，为保持革命队伍的纯洁，本帮已将他开除。”一手持钢杖的矮个子来道镜头前（字幕：丐帮奚长老），涨红着脸说：“乔峰虽然救过我的命，但他要做契丹狗我第一个不放过他！”…… 镜头回到演播室，李师师语调低沉：“作江湖第一大帮派，民间最具规模的抗辽组织的首领，乔峰是怎样从一个英雄模范蜕化成一个叛徒的呢？请在新闻联播之后收看本台的焦点访谈。”一个国字脸，紫袍金带的官员出现屏幕上，在他身后悬挂着大宋的龙旗，面前一张黄绫缎包裹的桌案上摆满了各种标记的话筒，他面对镜头侃侃而谈…… （燕青义正词严地解说道：“辽国边防军公然占领我燕云十六州，我外交部发言人文彦博大学士公开表示抗议，燕云十六州自古以来就是大宋的领土，是大宋不可分割的一部分，我先皇太祖、太宗皇帝在世时，曾与辽国有过协议，现在他们却趁我新皇登基，国内进行经济改革之机，悍然发动侵略战争，占我领土，伤我边民，掠我财富，我们提出最强烈的抗议，我们敦促辽国政府耶律内阁，尽快停止错误行径，回到和平谈判的轨道上来，如若一意孤行，必将为所产生的后果承担全部责任。”） “下面播送国际要闻，”李师师念道。“西夏国农业科技人员研究出农作物栽培技术，从此西夏将结束不懂种植的历史；大理举行狂欢节，当地人民载歌载舞，热烈庆祝自己的传统节日；女真猎手阿古打活捉幼虎一头，现已饲养至3岁；……”画面随着她的解说不断地变化着图像……最后又会到了节目开始时的画面，两位主持人抬眼望着电视机前的观众，燕青平静地说：“各位观众，这次节目的全部内容播送完了，谢谢收看，请大家在明天同一时候继续收看我们的新闻联播节目，再见！”灯光渐渐暗淡，镜头也逐渐后退，出现演播厅的全景，灯光、布景等工作人员的名字逐行出现，最后出现一行字： 本节目主持人服装由王婆裁缝店提供。 C&O 发表于 03:27 | 阅读全文 | 评论(0) | 引用(trackback0) 几个让你终身受用的寓言 - 2003-06-02 03:20 １．当老婆刚刚冲完早出来老公正要开始淋浴时门铃响了，在几秒争吵谁该去应门之后老婆放弃了，裹了条毛巾急忙下去开门。她打开门看见Bob，他的邻居。在她还没开口之前，Bob就说：“如果你把那条毛巾拿下我就给你$800。” 老婆想了想，就脱下毛巾处裸站在Bob面前，过了几秒Bob给了钱就走了。 老婆困惑又兴奋她的好运的裹上毛巾上楼。当她回到浴室老公问她：“刚刚是谁呀？” “隔壁的Bob啦”她回答。 “很好”老公说，“那他有没有拿他欠我的$800还我吗？” 故事的寓意 在未了解事情的真相之前，永远不要轻易自行判断而造成错误，而且还不知道自己有多难堪。 ２．有个牧师开车在路上见到路旁有个修女，便停车主动载她一程。她进车后便翘起脚来，让她可爱的美腿从长袍中露了出来。牧师看了一眼高兴的差点让车子出了意外。在控制车子后，他偷偷摸摸的将她的手往美腿上移动。修女看了看他便说”神父，记得圣诗129吗？” 神父脸红连忙道歉，他被迫移开他的手，但是他的视线却离不开他的美腿。在几次换档之后，他的手又再次滑向美腿。修女又说”神父，记得圣诗129吗？”神父又在一次道歉”对不起，姊妹，肉体是虚弱的。” 到达修道院后，修女下车给了他一个寓意深长一眼就走了。当神父回到教堂他急忙拿出圣经想找出圣诗129是什么。 圣诗129节：“走向前并寻求，再更深入一点，你会找到荣耀的。” 故事的寓意 永远对你的工作保持熟悉，不然你会错过很多机会的。 ３．业务代表，行政职员，经理一起走在路上去吃午餐意外发现一个古董油灯，他们摩擦油灯一个精灵从一团烟雾中碰了出来。 精灵说”我通常都给每个人3个愿望，所以给你们每个人一人一个。” “我先！我先！”职员抢着说”我要到巴哈马，开着游艇，自在逍遥”噗！她消失了。 惊吓之后，“换我！换我！”业务代表说”我要在夏威夷，和女按摩师躺在沙滩上，还有喝不完的pina coladas(凤椰汁)，和生命之爱。”噗！他消失了。 “好了现在该你了。”精灵对经理说。 经理说：“我只希望他们两个吃完午餐后回到办公室。” 故事的寓意 永远让你老板先说话。 C&O 发表于 03:20 | 阅读全文 | 评论(0) | 引用(trackback0) Why The Professor Can't Teach――第十章　市场的嘲弄：帐篷的讽刺 - 2003-06-02 03:03 Why The Professor Can't Teach. CHAPTER 10: Follies of the Marketplace: A Tirade on Tents Four species of idols beset the human mind: to which (for distinction's sake) we have asssigned names.. . the third, idols of the market... Francis Bacon Curriculum and teachers are the most important factors in education. But there are also texts from which students might learn and which, at the very least, can reinforce the teachers' contribution. Unfortunately, concern for exposition is not one of the hallowed traditions of the mathematical world and the quality of texts at all levels is very low. The blame for this state of affairs must be laid on the professors. College texts are, of course, written solely by professors. The secondary and elementary school texts are often supposedly cooperative efforts between knowledgeable professors and experienced teachers, but the professors, "obviously" the authorities, dominate the projects. What should we expect of professors insofar as texts are concerned? Many professors are indifferent to pedagogy and others are totally ignorant of it. They receive no training in writing - even of research papers, let alone texts. On the basis of their backgrounds and major concerns one should no more expect effective writing from mathematics professors than good mathematics in mathematical research papers were they written by English professors. Our expectations are more than fulfilled. Explanations of mathematical steps are usually inadequate - in fact, enigmatic. Because mathematicians do not take the trouble to find out what students should know at any particular level, they do not know how much explanation is called for. But the decision is readily made. It is easier to say less. This decision is reinforced by the mathematician's preference for sparse writing. If challenged, he replies, "Are the facts there?" This is all one should ask. Correctness is the only criterion and any request for more explanation is met by a supercilious stare. Surely one must be stupid to require more explanation. Though brevity proves to be the soul of obscurity, it seems that the one precept about writing that mathematicians take seriously is that brevity is preferable above everything, even comprehensibility. The professor may understand what he writes but to the student he seems to be saying, "I have learned this material and now I defy you to learn it." Some of the great masters of mathematics did write enigmatically. The most notorious in this respect was Pierre-Simon Laplace. His assistant Jean-Baptiste Biot, who helped Laplace to prepare for the press the latter's masterpiece, the Mécanique céleste, reported that Laplace was frequently unable to reproduce the steps by which he had reached a conclusion and so inserted in the manuscript, "It is easy to see that.. ." Evidently modern textbook writers have taken seriously the precept that one should emulate the masters. Even if one does not become a master thereby, one can at least appear to be one. There are textbook writers who believe that a mathematical presentation that is logically sound explains itself to the reader who faithfully follows the author step by step. Presumably the meaning need not be stated by the author explicitly but can be grasped by the reader from the details he ploughs through. The authors do not see the need to take the readers into their confidence, to explain where the road is going, why this one is better than another, and what is really achieved. They give no inkling of how a proof was arrived at, why anyone sought the result to begin with, or why anyone should want it now. In effect, the texts are challenges to clairvoyance. Some textbook writers, unwilling or unprepared to do research, display their "talent" in their texts. They deliberately omit steps that they could not have supplied as students and that they know belong. By pretending that the omitted steps are readily supplied, they seek to put themselves in the position of great masters who have omitted only the trivial. If this condemnation appears too strong, let us remember that with respect to character, mathematicians, whether researchers or teachers, are just a cross section of humanity and, with respect to egotism, a rather disagreeable portion of humanity. In any case, their texts are too often unintelligible. Surprisingly, many professors object to the few texts that give full explanations and discuss the significance of the ideas being presented. They often complain that such texts are too wordy. Too wordy for whom? These professors prefer to see an enigmatic presentation that leaves the student baffled. Then they, the teachers, can display their brilliance by explaining the text. This preference is well known, but one can also find evidence for it in print. A professor at a good college had the following to say in his review of a text: "So much is here written that is normally spoken by the teacher that the teacher in using the book as a text may find it hard to break away from the book not only in his formal presentation but also in his asides." But if the professor were really teaching ideas and creative thinking he would have so much to do in raising questions, guiding the students' thinking, and improving their suggestions that no book, however helpful, could replace him. Much poor mathematical writing is due to sheer laziness. There are mathematicians who fail to clarify their own thinking and attempt to conceal their vagueness by such remarks as, "It is obvious that ...," "Clearly it follows that.. . ," and the like. If a conclusion is really evident, it is rarely necessary to say so; and when most authors do say so, it is surely not evident. Often what is asserted as obvious is not quite correct, and the unfortunate reader is obliged to spend endless time trying to establish what does trujy follow. In some cases the difficulty is the writers' sheer ignorance. Even matters that are well understood by reasonably good mathematicians are not understood by numerous authors of high school and college texts. They put out books mainly by assembling passages and chapters from other books, and where the sources are inadequate so is the pirated material. In their books one finds inaccurate statements of theorems, assertions that are not at all true, incomplete proofs, failure to consider all cases of a proof, the use of concepts that are not defined, reliance upon prior results that were not proved or are proved only subsequently, the use of hypotheses that are not stated, two nonequivalent definitions of the same concept, extraneous definitions, assertions of a theorem and its converse with proof of only one part, and actual errors of logical reasoning. A glaring deficiency of mathematics texts is the absence of motivation. The authors plunge into their subjects as though pursued by hungry lions. A typical introduction to a book or a chapter might read, "We shall now study linear vector spaces. A linear vector space is one which satisfies the following conditions. . ." The conditions are then stated and are followed almost immediately by theorems. Why anyone should study linear vector spaces and where the conditions come from are not discussed. The student, hurled into this strange space, is lost and cannot find his way. Some introductions are not quite so abrupt. One finds the enlightening statement, "It might be well at this point to discuss. . ." Perhaps it is well enough for the author, but the student doesn't usually feel well about the ensuing discussion. A common variation of this opening states, "It is natural to ask. . . ," and this is followed by a question that even the most curious person would not think to ask. One need not always precede the treatment of a mathematical theme with the major reason for studying it. The introduction could be the historical reason the topic was studied. But if this is not the reason for its importance today, applications of current importance should immediately follow the treatment. Unfortunately for the authors, most applications involve physical science, with which few mathematicians and high school teachers are familiar. The best that many authors can do is simply to state that there are important practical applications of the subject treated. Some actually promise they will discuss applications but fail to do so. Problems of science need not be the sole motivation. The mathematics to be taught might be related to the students' world. Perseverance would reveal what excites student interest, but this effort is far more than authors are willing to undertake. The consequence is bare bones and no meat. Even the prettiest woman seeks to enhance her appearance with dress and cosmetics. Similarly, mathematics should be made more attractive by relating it to the interests of neophytes. The lack of motivation has been criticized by Richard Courant, whom we have cited in other connections: It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon to the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives.... To begin a text with a statement of the axioms is to write a work that omits the first chapter and that demands of the reader an understanding without which he cannot comprehend the text before his eyes. Mathematicians wreak additional hardships on the students by indulging their own tastes. As mathematicians they recognize the advantages of generality and abstraction. Surely a general result covers many special cases. Hence, they conclude, it is more efficient to present the general result at once. Logically this is correct; pedagogically it is false. The recklessness with which authors of texts plunge into generalities indicts their judgment. For example, before students have worked with concrete functions such as y = 2x, y = 2x+3, y = x2 and the like, they are asked to learn a general definition of function in terms of mappings. A mapping from a set A to a set B is a set of ordered pairs with each first component from set A and each second component from set B. Mappings are "wonderfully" broad. The relationship of a set of fathers to a set of sons is a mapping, and knowledge of this fact "clearly" improves the relationship between parents and children. To be sure, the definition of a mapping includes the concrete functions just mentioned; but it also includes relationships that students will never encounter or that are certainly not illuminated by the mathematical definition. Moreover, the vagueness of a general definition leaves students uneasy. Whereas a generalization extends to a wider class of objects a result known only for a special class - for example, one may prove for all triangles a theorem known previously only for isosceles triangles - abstraction selects from different classes of objects properties common to the classes and studies the implication of these properties. No one would question the value of abstractions for mathematics, but one must question the abstract approach to the concrete. Children do not learn about dogs by starting with a study of quadrupeds. This elementary principle does not seem to have been learned by mathematicians. They love abstractions and indulge in them freely, of course at the expense of the student. Many other faults already cited apropos of teaching methods are repeated in the texts. Rigorous presentations addressed to beginners in a particular subject are common. From a conceptual standpoint the most difficult mathematical subject is calculus. The concepts can be far more readily understood intuitively, and this is how mathematicians grasped the subject until, after two hundred years of effort, they managed to erect the proper logical foundations (Chapter 7). But many modern authors courageously risk the students' necks. They start their calculus texts with the rigorous formulations of the concepts and at the outset succeed in destroying the students' confidence in their ability to master the subject. Some authors choose the rigorous approach because they are insecure. They are fearful that if they compromise in order to help the student they will appear ignorant to their colleagues. To justify their stand they argue that texts at least must be precise and complete, and often they insist that understanding can best be obtained through the rigorous formulation. The result is elementary mathematics from a complicated standpoint. Most authors profited as little from their study of English as their readers then profit from the study of mathematics. The writing in mathematics texts is not only laconic to a fault; it is cold, monotonous, dry, dull, and even ungrammatical. The author seeks to remain impersonal and objective. As one reviewer said of the writing in a particular text. "The book is mathematically masterful, grammatically grim, literarily limp, and pedantically pompous. It tells the undergraduate more than he wants to know, presuming, at the same time, that he knows more than he does." Of course good texts should have a lively style, arouse interest, and keep the readers? background in mind. But few do. The books are not only printed by machines; they are written by machines. One ingredient of style is humor. A relevant story or joke does revive a sagging spirit. But the professors object. They use the same text a number of times and to them the humor becomes stale or the joke palls. But for whom is the book written? What would these professors say about an actor who must repeat for the thousandth time a most dramatic line or a joke as though it were the first time he ever said it? Beyond their sheer incapacity or unwillingness to write interesting mathematics, authors splurge in terminology that baffles the reader. In addition to using many technical words unnecessarily, mathematicians love to introduce new vocabulary. Thus they have long used the words homomorphism and isomorphism, which at least preserve the etymological meanings of similar structure and same structure, respectively. Instead of saying that a certain homomorphism is an isomorphism, the practice is to say that the homomorphism is faithful - a statement that does nothing to convey its meaning in mathematics, though it may have the merit of suggesting a steadfast, if illicit, romance. Of course, the appearance of a new term gives the impression that a new concept has been introduced. The terms greatest lower bound and least upper bound of, say, a set of numbers were used for years and do describe what they stand for; now, presumably in the interest of brevity and certainly in the direction of making comprehension more difficult, the terms infimum and supremum are used. Single-valued functions and multiple-valued functions are now functions and relations. Further, one no longer speaks of the values of x that satisfy x2 = x + 7 but of "truth values." Apparently, truths can now be obtained readily and we need no longer ponder the mysteries of the universe. New terms to replace old ones appear constantly. This practice disturbed even Cauchy, who shared with Gauss leadership in mathematics in the first half of the nineteenth century, and he felt obliged to complain of the strange terminology introduced in his day: "One should enable science to make a great advance if one is to burden it with many new terms and to require that readers follow you in research that offers so much that is strange." Instead of introducing new, meaningless terminology in place of suitable words, mathematicians would do well to replace the old terminology that has misled students. Terms such as irrational, negative, imaginary, and complex, which were historically terms of rejection, remain in the lexicon of mathematics to disturb students. Even the great mathematicians of the past were frustrated by such terms. The resistance to imaginary numbers persisted for three hundred years after their introduction, partly because the word imaginary suggested something unacceptable. As Gauss remarked, if the units 1, -1, and had not been given the names positive, negative, and imaginary units but were called direct, inverse, and lateral units, people would not have gotten the impression that there was some dark mystery in them. Meaningless terminology is only one evil of the language used. Mathematicians believe in brevity so much that they invent shortened terms. A partially ordered set is now a poset. Still more brevity is achieved by using acronyms a.e. (almost everywhere). This atrocity, added to already barbarically poor writing, makes it almost impossible to read the text, let alone understand it. The l.q.m.w. (low quality of mathematical writing) has no bottom. The evils of terminology are compounded by the excessive use of symbols. No one would deny that mathematical thinking and processes are expedited by the use of symbols, and one of the great features in the progress of mathematics was the introduction of better and better symbolism. But mathematicians have turned a virtue into a vice. They sprawl symbols over all the pages of their texts just as some modern painters splash paint on canvas. Page after page, almost devoid of exposition, is filled with Greek, German, and English letters, and various other symbols. Some books use as many as a few hundred symbols, presumably in the interest of brevity but more likely to conceal shallowness. Even a gain in brevity hardly compensates for the burden on the reader's memory. What is worse is that a symbol introduced on page 50 is not used again until page 350, with no reminder to the reader of what the symbol stands for. A few authors, somewhat conscious of this problem, include in their texts a glossary of the symbols employed. However, the reader stuck on page 350 must interrupt his reading to find the meaning of the symbol among the several hundred in the list. The natural reaction is exasperation. In modern texts symbols do not facilitate communication; they hinder it. Many authors seem to believe that symbols express ideas that words cannot. But the symbolism is invented by human beings to express their thoughts. The symbols cannot transcend the thoughts. Hence, the thoughts should first be stated and then the symbolic version might be introduced where symbols are really expeditious. Instead, one finds masses of symbols and little verbal expression of the underlying thought. As in the case of terminology, much could be done to improve older symbolism. Perhaps the most imperative need is to replace the symbol dy/dx of calculus. The most important idea to be transmitted in calculus is that the derivative is not a quotient but the limit of a quotient. However, the symbol dy/dx, though intended to be taken as a whole, looks like a quotient of dy by dx. (In fact, this is what it was for Leibniz, who failed to formulate the precise concept.) Hence, the notation seems to refute what the teacher must attempt to convey. Superior notations have been proposed, but professors resist change in this area as zealously and perversely as they promote it where the traditional symbolism is altogether adequate. A mathematician of the sixteenth or seventeenth century often presented his discoveries in the form of an anagram that was intended as evidence to his rivals that he had solved a problem but that was also intended to be undecipherable to the rivals so that they could not claim they, too, had solved the problem. When challenged, the composer of the anagram could then reveal what the anagram stood for and establish his claim. This practice continues today, except that the anagram is called a textbook. Mathematicians claim to teach thinking, and this can be promoted by getting students to help discover theorems and proofs. But the texts do no such thing. Definitions, axioms, theorems, proofs, and obscurity are the style and content, the sum and substance. This type of presentation has the advantage - for the author - of facilitating the writing. One does not have to think about what to say because the theorems and proofs of the usual undergraduate textbook are well known. However, as we have previously noted (Chapter 6), most theorems of any consequence have been reproven many times; each time some refinement or modification is achieved that makes the theorem more general or the proof shorter. Often an ingenious trick will do the latter. Since even the original proof may have been the product of weeks, months, and perhaps years of thought, to which a succession of mathematicians may have contributed, a modern proof is almost sure to be sophisticated and highly artificial, though mathematicians would describe it as elegant. These refined proofs, presented in a page or so, stun and humble the students. They cannot help imagining themselves being called upon to make such proofs and readily realize that the task would be inordinate for them. The inevitable consequence is that they lose confidence in their ability. To pass examinations they memorize the proofs. Good writing, like good teaching, calls for letting the students in on the struggles mathematicians have undergone to arrive at the proofs. Students should be told how long and hard the best mathematicians worked to obtain the proofs, and how many false proofs were often published in the belief that they were correct. This history not only would avert discouragement and loss of confidence but also would dispose students to the kind of effort they must be prepared to make when attempting a proof on their own. But authors are reluctant to level with the students. By presenting proof after proof with no mention of how these were obtained, the authors seem to suggest that the clever proofs are due to them and, very likely, this is the impression some wish to give. Authors do not recognize the psychological damage of a bare logical presentation. *Texts do present historical material, usually to the effect that Descartes was born in 1596, died in 1650, and had one illegitimate child. Why can't texts be more informal, almost conversational? Suppose an author is about to present the theorem that the three altitudes of a triangle go through the same point. This fact should surprise anyone. Should not the author remark on this, perhaps state that it is not an expected fact, and first give some intuitive reason that it should be so before proving it? Calculus texts treat the derivative of the product of two functions. Students expect that the result should be the product of the derivatives and are surprised to find that it is not so. Even Leibniz stumbled on this point and spent a whole month getting the correct result. The authors could state what superficial argument suggests and then point out why it is not correct. The fact that Leibniz struggled to understand this matter might also be mentioned and would reassure students that they are not so far below the Leibnizes in intellectual capacity. Such discussions should precede the formal presentation. To rebut the charge that the texts proper do not call for student participation and thinking, the authors point to the exercises. Good exercises could be some redress for the dogmatic text. However, the texts usually work out half a dozen typical problems in each section and then assign exercises of the same type. The students, called upon to do an exercise, look among the illustrative examples to find one that fits the exercise. They then repeat the steps made in the illustrative example without necessarily understanding them and certainly without having to do any thinking for themselves. Thus, the students do the homework successfully and feel satisfied. The professors, in turn, congratulate themselves on their successful pedagogy. Of course, some illustrative examples are needed. Students cannot be expected to acquire techniques without guidance. But the examples should be accompanied by a discussion of how the theory is involved, why the solution should take one course rather than another, and any other pertinent comments. In fact, rather than being set out as examples, these illustrations are best incorporated in the text proper to oblige the students to read the text - something that students often shirk if not compelled to do it. Moreover, some of the exercises could raise questions about the examples. Alternative methods might be proposed that may or may not work, and the student might be asked to evaluate them. Mere repetition of a process that is illustrated will teach technique, but it will not inculcate understanding or foster thinking. The usual exercises are intellectual slavery rather than intellectual challenges. Many textbook authors boast of the number of illustrative examples their texts contain. What they are really saying is that the students do not have to read the texts or do any thinking. These texts are rightly called cookbooks. Actual cookbooks usually offer recipes: pour a half cup of flour into a bowl, add one quarter cup yeast, sprinkle with vinegar and bake for one hour. Lo and behold, a cake appears. But the cookbook gives the cook no idea why such a mixture produces a cake. The illustrative examples are likewise recipes for getting answers. If the recipes were changed and produced absurd answers, the students would not have the insight to recognize this fact and would be content as long as their answers agreed with those given by the text. Clearly, the valuable role that texts could play in the educational world is nullified by the various defects we have cited. The students certainly do not read the texts, because the texts are unreadable. Surprisingly, when choosing texts for their classes many professors have said openly that they do not care about text exposition. They look only at the illustrative examples and the exercises. But in our civilization, learning to think and learning to use books are surely some of the objectives of higher education. Apparently these objectives have been abandoned. Since the texts are so bad, one is impelled to ask, why are such texts chosen? The reasons are numerous. The poor exposition is not recognized by most professors because they themselves are not trained in writing. Lack of motivation and application in textbooks is even welcomed by professors. Such material must usually draw on subject matter that lies outside mathematics proper, and to teach it would require that the professors know and feel secure about, for example, a bit of science. But the professors do not know science, and they are not willing to learn it just to do a better teaching job. In fact, many professors fear any book that would make them deal with the history of mathematics, science, or cultural influences. Hence, they choose one that takes the straight and narrow path of mechanical, technical mathematics and routine exercises. Terminology, symbolism, rigor -these are dear to the hearts of mathematicians. From their point of view one could not possibly overdo such features. A major reason for the choice of poor college texts is that the bulk of the undergraduate courses is taught by graduate students. For such teachers, stock material and routine presentations are musts. Any felicitous or unusual approach, especially if it calls for pedagogical skill, would be ignored or bungled. Many professors choose a text because the topics treated are what they want to teach. But they do not care about the text's presentation. They give their own. The student is then faced with the task of reconciling what the teacher says and what the book says. This is difficult to do in mathematics. And since the book is most likely to be poor, the difficulty is compounded. If the professor really has a better presentation than what is available in an existing text, he should write up his material and distribute it so that students will not have to spend the class time in copying. In many cases the professor's presentation is not better, but he considers it demeaning to follow someone else's. There are even university professors who deliberately adopt a difficult book because it bolsters their ego to be able to say that they are using it. They hope that others will judge them and their students favorably, because presumably both can master such a book. Actually, many of the professors who choose such books are hard put to understand them, but the students are so much more bewildered that the professors can get away with almost any kind of explanation. Professors at four-year colleges often feel inferior to those at the prestigious universities. To overcome the feeling of inferiority many four-year college professors try to "outdo" the university professors by adopting texts that are far too difficult for the students. When asked at a professional society meeting what texts they are using, they can name them and imply that they are really doing wonders with their students and, of course, have no trouble themselves in teaching on the advanced and sophisticated levels that these texts bespeak. Teachers at the two-year community and junior colleges, which, on the whole, have the weakest students, also use difficult texts just to be able to boast that they are teaching on a high level. They claim they must use these books to prepare students who will transfer to a four-year college. But they kill off the students and so make transfer impossible. Only about 25 percent go on to a four-year college, and most of these students do not take any more mathematics. The phenomenon of low-level institutions using high-level texts is especially prevalent in areas dominated by a major university. Many texts are chosen by a committee. If a book contains any applications, some professors who are unfamiliar with them will object. Other professors may rightly or wrongly object to the level of presentation. Still others may object to the "wordiness." The consequence is a compromise that almost necessarily is a dull, meaningless, inept book. Even where a text is chosen for departmental use by a single professor, he may, like so many others, lack insight, conviction, and determination, and pick a "safe" book - which usually means a mediocre one that will satisfy most of the professors. Quite often a department decides to change the text in use because some members complain that it is not satisfactory; or it may be going out of print. One would think it might be replaced by a good text, but that rarely happens. Most of the staff prefer a text that is old hat, so they do not have to read it and do new exercises. Hence, the replacement is usually a "copy" of the previous text. After all, change is sufficient evidence of progress in our society. There are many other reasons that a professor will pick a poor text. Professors are most likely to be narrow specialists. An algebraist who is called upon to teach differential equations is not interested in how to teach that subject. He wants a book that is easy to teach from, and this means one that presents either a series of techniques or a canned sequence of theorems and proofs that need only be repeated. Even if all or a majority of the texts were good, the students in many institutions would still suffer. Some professors choose texts that interest them and from which they can learn new ideas or new proofs, whether or not these texts are right for the students. Thus, an algebraist might pick an advanced text for an elementary course not because the students can learn from it, but because he can. At one respectable institution the professors used a text that was two or three levels higher than the course, and a large percentage of good students failed. Others, also highly qualified, became discouraged and abandoned mathematics. When the professors were asked why they used such an unsuitable text they replied that they were conducting an experiment. They might just as well have said that they had fired six bullets into a man's heart to see if he would die. Why are so many poor texts written? The main reason is obvious - greed. Texts bring in royalties, and money does interest some people. To make money, one must write a text that sells well. But the poor texts sell best, and the money-minded author caters to the market. Most professors write with more than one eye on the market. They rivet their attention on it. What happens is well illustrated by the history of calculus texts. For years only mechanical or cookbook treatments of calculus were used. Authors, accordingly, wrote cookbooks. As American professors became better educated, they decided that students should receive the benefit of professorial enlightenment and that calculus should be taught with a full background of theory. A spate of rigorous calculus books soon appeared on the market. When this pedagogical blunder became apparent and the intuitive approach became popular, professors showed their open-mindedness and flexibility by turning to an intuitive approach. It did not take long before the very authors of rigorous texts wrote intuitively oriented texts and even boasted that they offered this approach. Professors do learn remarkably fast - what the market wants. Because most authors aim for the largest possible market, they repeat endlessly books that sell well. All that is required is a minimum of knowledge, shoddy writing, standard exercises, and reasonable caution against outright plagiarism. One need only vary the order of the topics to make a book seem different, and since there are about twenty-five topics in the usual text, the possible permutations are large enough to allow for many thousands of "different" college algebra, trigonometry, calculus, and other texts to be written. The fact that the sources may be incorrect or poorly written is a minor concern compared to the expected gain. To hide obvious repetition of existing texts, some authors introduce a few variations, such as contrived proofs even though more natural ones are available, sophisticated definitions, new terminology, and their own brand of symbolism. When accused of plagiarism the professors can always retort that the truth never changes. One must of course have a different title. But then one can use College Algebra, Elementary College Algebra, College Algebra: A Full Course, College Algebra: A Short Course, and College Algebra: A Seven-Eighths Course. The possibilities are clearly infinite. In fact, since there are irrational numbers, one could use Algebra: An Irrational Course. The outright imitation of successful texts - successful financially though usually not at all pedagogically - is a fact. Many authors do not hesitate to admit this. They speak proudly of their books as being in the mainstream of mathematics education, as though this fact is an assurance of quality. Actually, in view of what books sell best, a book in the mainstream is sure to be dull, unoriginal, and pedagogically disastrous. Are all texts repetitious of each other? No. Another spate of bad texts comes from professors who have achieved a reputation for research in their specialty or whose name is well known in the mathematical world, perhaps because they have held high office in a professional society. These authors, most of whom have never or only rarely taught the courses for which the books are intended and are unconversant with how college students think and what backgrounds the students have, nevertheless decide to cash in on their names and plunge unhesitatingly into the writing of texts. "Genius" transcends mediocrity; so these texts contain innovations in concepts and proofs that students cannot possibly grasp. The exposition of the topics is shoddy and the writing is shameful. The books are hastily written and often contain numerous errors. Chapters or sections begin with one objective and end up with another. Within the same section authors shift from one topic to a totally unrelated one. They ask the students to do exercises that are not workable on the basis of the material in the text or, if related to the text, require a Newton. To make a token gesture to that sector of the market that wants some applications, these researchers include some brief mention of relativity or quantum mechanics, topics that mean nothing to undergraduates at the levels for which the texts are written. It is clear that these professors dash off the books as fast as they can just to get them out and "earn" royalties. Were these authors judged by their texts they would not be admitted as graduate students to any decent graduate school. Nevertheless, many schools adopt such texts on the basis of name alone. Usually the texts are so bad that they are dropped after one year's use. About all one can say of them is that they are flops d'estime. Ironically, these prestigious professors, who rush to write texts for low-level courses, would disdain teaching them or, if obliged to do so, would be ashamed to admit that they were teaching such lowly work. Sometimes these prestigious professors resort to second and third editions and, having learned by this time how to meet the market on its terms, sell more books. The venality of such professors and their crass commercialism are disgraceful. In these later editions they may succeed in selling more books, but they also succeed in sacrificing students and vitiating educational goals. Cheap fiction, potboilers, are far more excusable because the authors make no pretense to ethical principles and are not under any obligation to develop young minds. If these professors are really capable research men or seek to exert beneficial influence through office-holding in professional societies, why do they lower themselves by writing the hundredth facsimile of cheap, commercial texts? Or are the supposedly intelligent professors as badly confused about their role and goals in life as any adolescent? The problem of writing for financial gain does call for keeping up with the market. As we have already observed (Chapter 7), mathematical teaching as well as mathematical research is swept by fads. Analytic geometry, formerly taught as an independent course preceding calculus, is now submerged in calculus. The successful author must yield to this fad or his book will not sell. If the fad is to incorporate linear algebra in the calculus or the differential equations text, whether or not there is any point to doing so, one must incorporate the linear algebra. To keep up with fads one must put out new editions every few years. But professors do not object because this eliminates the secondhand market for the older edition and students are obliged to buy the new one. The determination of what the market wants is made rather scientifically. The publishers canvass the colleges for what they would like to see in the texts, and then the authors willingly set about supplying the common denominator of those wants. The author's own convictions, if he has any, as to what a text should contain are irrelevant. The normal market can be enlarged by special devices. One such device is to offer applications but to crowd them all into the last chapter. There is method in this madness. Applications are desired by some professors but frighten off others. If they are placed at the end, professors who do not want to teach them manage to end the semester before reaching the last chapter, thereby omitting them with least embarrassment. Applications placed at the end of a text serve little purpose in any case, because whatever value these applications might have as motivation and meaning for the mathematics proper comes too late. To enlarge their market many authors employ ruses that are deliberately fraudulent. When the New Mathematics became popular these authors took traditional books, inserted a few pages of New Mathematics material here and there, changed terminology in spots, and sprinkled words such as sets, commutative law, inverse, and the like throughout; they then proclaimed that they were presenting the New Mathematics. Many teachers aided in~ this fraud because they could convince their superiors that they were teaching the New Mathematics, while actually continuing to teach the material they either preferred or knew better. Calculus texts often contain a facade of rigor to please those professors who wish to include some theory but the rigor, usually in the first chapter, is thereafter never utilized. There are other types of deception. One would expect that a text entitled Mathematics for Biologists would contain not only the mathematics that biologists use but also some indication of how biologists use it. But the contents are the same as any traditional text that covers the same level of mathematics. Many authors know that students come to college disliking mathematics. However, some colleges still require a course in mathematics as a degree requirement. Even if they don't, the professors wish to attract students to a mathematics elective so there will be more jobs. Hence, many authors write texts that purportedly offer an appreciation of the role of mathematics in our civilization. The titles are inviting: Mathematics, An Intellectual Endeavor; Mathematics, the Science of Reasoning; An Appreciation of Mathematics; Mathematics, the Creative Art; Mathematics, Art and Science. But the texts teach axiomatics, symbolic logic, set theory, topics of the theory of numbers such as congruences, the binary number system, finite geometries, matrices, groups, and fields and so do not really live up to their promise (Chapter 6). Clearly, one can't judge a book by its title. Since a course in mathematics proper does not attract liberal arts students and has little value for them, some professors have taken another tack. For their books they gather together curiosities, trivia, puzzles, and bits and pieces of standard topics that never get to any serious level and do not require any thinking on the part of the student. The chapters are deliberately unrelated to each other so that the student will not have to carry an extended train of thought and so that the teacher can pick and choose what pleases him. Since these measures rarely succeed in interesting students, some professors have resorted to the ingenious device of including cartoons. There are even calculus texts "enlivened" by cartoons. Why not? After all, isn't mathematics supposed to be fun? Perhaps pointed, truly humorous cartoons can be admitted as a pedagogical device on the college level, but shallow sequences of drawings that would hardly elicit a smile from six-year-olds make no contribution. Something can be said for cartoons: They do enlighten us as to the intellectual level of the authors. Mathematical texts do not as yet resort to pornography, though this means of attracting students would be more acceptable because it would not be mistaken for a pretense to education in mathematics. These puerile "liberal arts" texts also sell well. Students, deceived or not as to the worth of the material, can earn credit for the course without really being pressed into thinking. The professors can teach such material without any effort and thereby "solve" the problem of what to teach the liberal arts student. Many professors express concern that the lowering of standards for admission to college and automatic admission of any high school graduate will result in the lowering of the educational level for all students. But by publishing the liberal arts and cookbook texts we have described, which are used in hundreds of colleges, these professors have reduced standards to about the lowest level possible. The financial gain to be derived from textbook writing has corrupted many professors. Some authors ask publishers for guarantees up to $100,000. Apparently the authors have no confidence in their works and seek to ensure profit by a guarantee. The argument is sometimes made by authors that a publisher will work harder to push a book on which it has given a guarantee. But this is hardly a justification. The investment of the publisher can range from $50,000 to $100,000. Surely no publisher will invest such a sum and then fail to promote the book. If the author is asking for sales promotion beyond the merits of the book, he is certainly culpable. There are two possible controls over the quality of texts. The first is reviews. Most texts are reviewed in one or more of the professional journals. However, some reviewers are apparently too polite to write the condemnation that most texts should receive. Instead, they merely describe the contents or compare the book with similar ones and often end with the "compliment" that it is good because it is just like the others on the market. Other reviewers respect the principle of honor among malefactors. What we need is honest, damning reviews of books that impose unnecessary hardships on students and fail to teach the values that the course in question should offer. Though critical reviews of texts are rare, one does find some. One reviewer of a new calculus text said that the "exercises are presented with less imagination than" - and here he mentioned a best-selling calculus book - "if that is possible." One might look to the publishers to control the quality of texts. But this is not fair. Publishers do have manuscripts reviewed before they accept them; but generally the reviewers are men who teach at the same level as the proposed book, and they are no more critical and no more demanding about pedagogy than the authors. If they see material they are able to teach, they approve the manuscripts. Moreover, publishers are in business to make money. This is their avowed purpose, and they cannot alter the market. If they do not yield to it, they will fail. They certainly cannot exist on the rewards of virtue. No doubt many exaggerate the qualities of what they publish. Often, too, they seek to anticipate a trend and accelerate it by promoting books that further it and give the impression that such texts are already in wide demand. They did this when the New Mathematics was in the offing and are now hastening to break from the New Math because they foresee its doom. Publishers are often criticized because they publish books just like dozens of others already on the market. But if a publisher is to stay in business he must have saleable books in each of the subjects and perforce must duplicate existing books. The better publishers do compensate somewhat for publishing junk by putting out high-quality monographs and treatises on which they lose money though they may gain prestige. The responsibility for good texts definitely rests with the professors, who, unfortunately, regard their station as practically a license to publish. In these times the only concession they must make to secure the full imprimatur is to have an opening chapter on set theory, whether or not it is relevant to the body of the book or referred to in later chapters. Good texts, so sorely needed, would raise the educational level immeasurably. Not only students would benefit. Young teachers, older ones when called upon to teach a course in an area unfamiliar to them, and even knowledgeable and competent teachers can learn much from a good text because the author would have devoted months and years to the selection and presentation of the material, whereas the teacher could not hope to do that in more than one area. The low quality of the texts is the severest indictment of the professors. Those who deliberately cater to the market even when capable of doing a better job besmirch their character. Those who write texts for courses they have never or only rarely taught impugn their integrity. And experienced teachers who sincerely attempt to write well demonstrate that the arts of pedagogy and writing are rare gifts. This derogation of the quality of American mathematics texts may seem overdrawn or grossly exaggerated. It is not. The low quality is as much a consequence of the development of the nation?s educational efforts as are the poor content and pedagogy of the courses and curricula. The principle of universal education from the elementary school to the highest levels students can attain certainly was and is desirable. But the constant immigration of mainly poor and uneducated people has placed a burden on the country that would be difficult to carry under any conditions. To make matters worse, the emphasis on research in the last thirty or forty years has diverted manpower from teaching and so has cut off the flow into the fountain of all our educational efforts, the teaching in the colleges. Perhaps rather belatedly we shall develop sincere and capable cultivators of mathematics - a science and an art - who will recognize that exposition is as vital in their medium as it is in painting, music, and literature. Why The Professor Can't Teach. C&O 发表于 03:03 | 阅读全文 | 评论(0) | 引用(trackback0) 10.589369058609