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DanMeyer_2010X-_数学课需要改革_
Can I ask you to please recall a time when you really loved something -- a movie, an album, a song or a book -- and you recommended it wholeheartedly to someone you also really liked, 我想请你回忆过去, 当你真的热爱过一些东西, 一部电影,一张专辑,一首歌曲或一本书, 并且你全心全意地推荐它 给你很喜欢的某个人,
recall:v.记起;回想起;使想到;勾起;召回;n.记忆力;记性;回归请求;回收令; recommended:v.推荐;举荐;介绍;劝告;建议;(recommend的过去分词和过去式) wholeheartedly:adv.全心全意地,全神贯注地;
and you anticipated that reaction , you waited for it, and it came back, and the person hated it? 你期望他的反应,你一直等待着, 但反馈回来的却是他很讨厌它。
anticipated:adj.预期的; v.预期; (anticipate的过去式和过去分词) reaction:n.反应,感应;反动,复古;反作用;
So, by way of introduction, that is the exact same state in which I spent every working day of the last six years. (Laughter) 因此,以这种方式介绍, 在这种完全相同的状态下, 我度过了在过去六年工作中的每一天。
by way of:经由;当作; working day:n.一天中的工作时间;工作日;
I teach high school math. 我教授高中数学。
I sell a product to a market that doesn't want it, but is forced by law to buy it. 我是将一种产品卖到一个 不受欢迎的市场,但是依据法律强制购买它。
I mean, it's just a losing proposition . 我的意思是,这是一种 - 它只是一个亏本生意。
proposition:n.提议;待处理的问题;任务;(美国)法律修正议案;见解;命题;v.向...提议;
So there's a useful stereotype about students that I see, a useful stereotype about you all. 因此,关于学数学的学生和你们所有人,我看到一个很形象的 刻板印象。
stereotype:vt.使用铅版;套用老套,使一成不变;n.陈腔滥调,老套;铅版;
I could give you guys an algebra-two final exam, and I would expect no higher than a 25 percent pass rate. 我可以给你们 一个代数Ⅱ的期末考试, 我不会期望 超过百分之25的合格率。
And both of these facts say less about you or my students than they do about what we call math education in the U.S. today. 这两个事实并不表示你们的问题或是我学生的问题, 它表现的是在当今的美国,我们所谓的数学教育 所面临的问题。
To start with, I'd like to break math down into two categories . 首先,我想把数学分成两类。
categories:n.(人或事物的)类别,种类(category的复数)
One is computation; this is the stuff you've forgotten. 一个是计算。这是你们已经忘记的东西。
stuff:n.东西:物品:基本特征:v.填满:装满:标本:
For example, factoring quadratics with leading coefficients greater than one. 例如,首项系数大于1的 保理二次方程式。
factoring:n.[数]因子分解,[数]因式分解; v.把…因素包括进去(factor的现在分词); quadratics:n.二次方程式论(quadratic的复数形式); coefficients:n.[数]系数(coefficient的复数形式);
This stuff is also really easy to relearn , provided you have a really strong grounding in reasoning. Math reasoning -- we'll call it the application of math processes to the world around us -- this is hard to teach. 这东西也很容易重新学习, 只要你有一个关于推理,数学推理真正过硬 的基础。 我们将这称之为 我们周围世界里的数学程序应用。 这点是很难教授的。
relearn:vt.重学;再学习; provided:conj.假如; v.提供; (provide的过去分词和过去式) application:n.应用;申请;应用程序;敷用; processes:n.过程; v.处理(process的第三人称单数形式);
This is what we would love students to retain , even if they don't go into mathematical fields. 这也是我们希望学生能够掌握并应用, 即使他们不进入数学领域。
retain:v.保留;保持;持有;继续拥有; mathematical:adj.数学的,数学上的;精确的;
This is also something that, the way we teach it in the U.S. 这也是在美国,由于我们教授它的方式
all but ensures they won't retain it. 以致于学生不会应用它。
ensures:v.保证,确定(原形为ensure);
So, I'd like to talk about why that is, why that's such a calamity for society, what we can do about it and, to close with, why this is an amazing time to be a math teacher. 所以,我要谈谈这是为什么, 为什么这是当今社会的灾难,我们可以为此做什么, 而且,更进一步,为什么现在成为一名数学老师, 这正是一个千载难逢的好时代。
calamity:n.灾难;不幸事件;
So first, five symptoms that you're doing math reasoning wrong in your classroom. 首先,你在数学课堂上 做的五个征兆 是在数学推理上错误的。
symptoms:n.症状;征候;征兆;(symptom的复数)
One is a lack of initiative; your students don't self-start. 一个是缺乏主动性,你的学生没有自我行动。
You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks. 你完成你的演讲, 然后马上,你就会看到五个人举手 要求你到他们课桌前重新解释整件事。
lecture:n.演讲;讲座;讲课;谴责;v.开讲座;讲授;讲课;指责;告诫
Students lack perseverance . 二学生缺乏坚持不懈。
perseverance:n.坚持不懈;不屈不挠;n.耐性;毅力;
They lack retention; you find yourself re-explaining concepts three months later, wholesale . 三他们缺少持续记忆力,你会发现自己 在3个月后需要完完全全的重新解释这些概念。
wholesale:n.批发; v.大量地,大批地; v.批发; adj.批发的;
There's an aversion to word problems, which describes 99 percent of my students. 四还存在着一种对文字题的反感, 这占了我学生中的99%。
aversion:n.厌恶;讨厌的人; describes:v.描述;形容;把…称为;画出…图形;(describe的第三人称单数)
And then the other one percent is eagerly looking for the formula to apply in that situation. 五这种情况下,剩下的百分之一 正在急切地寻找公式 来解决问题。
eagerly:adv.急切地;渴望地;热心地; formula:n.公式; adj.(赛车)方程式的(指赛车要符合规定的体积,重量及汽缸容量等); apply:v.申请;涂,敷;应用;适用;请求;
This is really destructive . 这实在是毁灭性的。
destructive:adj.破坏的;毁灭性的;有害的,消极的;
David Milch , creator of " Deadwood " and other amazing TV shows, has a really good description for this. 大卫·米尔希是“死木”美剧以及其他的精彩电视节目的创造者, 对此他有一个很好的描述。
Milch:adj.生乳的;产奶的; Deadwood:n.枯枝;朽木;碎屑; description:n.说明;形容;描写(文字);类型;
He swore off creating contemporary drama , shows set in the present day , because he saw that when people fill their mind with four hours a day of, for example, "Two and a Half Men," no disrespect , it shapes the neural pathways , he said, in such a way that they expect simple problems. 他发誓要停止创造 当代戏剧, 及当今的单元连续剧, 因为他意识到,当人们的脑中 一天四小时想到,例如,“两个半男人”,没有冒犯的意思, 这就形成了神经传导通路,他说, 以这样一种方式,人们期望简单的问题。
contemporary:n.同时代的人;同时期的东西;adj.当代的;同时代的;属于同一时期的; drama:n.戏剧;戏剧艺术;戏剧文学;戏剧性事件; present day:adj.现代的;当今的;现在的;现时的; disrespect:n.无礼,失礼,不敬; neural:adj.神经的;神经系统的;背的;神经中枢的; pathways:n.小路;小径(pathway的复数);
He called it, "an impatience with irresolution." 他称这是“一种无法做决定的焦虑。”
impatience:n.急躁;无耐心;
You're impatient with things that don't resolve quickly. 人们对不能快速解决的事情不耐烦。
impatient:adj.焦躁的;不耐心的; resolve:vt.决定; vi.解决; n.坚决;
You expect sitcom-sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track . 人们期望情景喜剧一般可以在22分中结束, 3个广告中断和一个笑声背景。
wrap:v.缠绕;隐藏;掩护;包起来;缠绕;穿外衣;n.外套;围巾; commercial:adj.贸易的;商业的;赢利的;以获利为目的的;n.(电台或电视播放的)广告; track:n.小道;足迹;车辙;轨道;v.追踪;跟踪;
And I'll put it to all of you, what you already know, that no problem worth solving is that simple. 我告诉你们所有人, 如大家知道的,解决任何问题都不是那样简单。
I am very concerned about this because I'm going to retire in a world that my students will run. 我对此很担忧, 因为我将要在我的学生主宰的世界中退休。
concerned:adj.有关的;关心的;v.关心;与…有关;(concern的过去时和过去分词)
I'm doing bad things to my own future and well-being when I teach this way. 当我以这种方式教学,我正在做 对我自己的将来和幸福感 不利的事情。
well-being:n.幸福;康乐;
I'm here to tell you that the way our textbooks -- particularly mass-adopted textbooks -- teach math reasoning and patient problem solving, it's functionally equivalent to turning on "Two and a Half Men" and calling it a day. 我在这里告诉大家,我们的教科书,特别是 大众常用的教科书,它们教授数学理论 和耐心解决的数学问题, 功能上和打开“好汉两个半”电视系列剧一样,然后这就结束了（消磨时间）。
particularly:adv.特别地,独特地;详细地,具体地;明确地,细致地; functionally:adv.功能地;函数地;职务上地; equivalent:adj.等价的,相等的;同意义的;n.等价物,相等物;
(Laughter) （笑声）
In all seriousness . Here's an example from a physics textbook. 非常严肃地说,这是物理教科书上的一个例子,
seriousness:n.严重性;严肃;认真;
It applies equally to math. 它同样适用于数学。
applies:v.适用;申请;运用;专心;(apply的第三人称单数)
Notice, first of all here, that you have exactly three pieces of information there, each of which will figure into a formula somewhere, eventually , which the student will then compute . 首先注意到这里 大家有正好3个信息, 每一个都可以表示成某个公式, 最终, 学生可以以此计算。
first of all:adv.首先; eventually:adv.最后,终于; compute:vt.计算;估算;用计算机计算;vi.计算;估算;推断;n.计算;估计;推断;
I believe in real life. 我相信在真实生活中。
And ask yourself, what problem have you solved, ever, that was worth solving where you knew all of the given information in advance; where you didn't have a surplus of information and you had to filter it out, or you didn't have sufficient information and had to go find some. 问问自己,什么问题你们解决过的, 值得解决的, 在此问题中,你提前知道所有信息, 或者你没有多余信息,然后你需要过滤信息, 或是你没有足够的信息, 你需要去查找些信息。
surplus:n.剩余;[贸易]顺差;盈余;过剩;adj.剩余的;过剩的; filter:n.滤波器;过滤器;滤光器;滤声器;v.过滤;渗入;(用程序)筛选;缓行; sufficient:adj.足够的;充分的;
I'm sure we all agree that no problem worth solving is like that. 我肯定大家都同意解决问题都不是如上所述那么简单。
And the textbook, I think, knows how it's hamstringing students because, watch this, this is the practice problem set. 我认为,教科书实在是误人子弟。 因为,看看这个,这是一个练习题,
hamstringing:n.腘绳肌腱;大肌腱;v.妨碍;使不能正常工作(或行动);
When it comes time to do the actual problem set, we have problems like this right here where we're just swapping out numbers and tweaking the context a little bit. 当要解决实际问题时, 我们在这就有类似问题, 我们只是在交换数字和稍稍调整内容。
swapping:v.交换(东西);交换(工作);用…替换;(swap的现在分词) tweaking:v.捏,扭,拧;对…稍作调整(tweak的现在分词); context:n.环境;上下文;来龙去脉;
And if the student still doesn't recognize the stamp this was molded from, it helpfully explains to you what sample problem you can return to to find the formula. 如果学生们不知道这类数学题模式, 而它会帮助向你解释例题, 什么样题你可以返回去找出公式。
recognize:v.认识;认出;辨别出;承认;意识到; molded:adj.模塑的;造形的; helpfully:adv.有益地;有用地;
You could literally , I mean this, pass this particular unit without knowing any physics, just knowing how to decode a textbook. That's a shame. 你确实可以,我很认真的说, 通过这个测试,没有任何物理知识, 仅仅知道如何解译教科书。那是一种耻辱。
literally:adv.按字面:字面上:确实地: decode:vt.[计][通信]译码,解码;vi.从事破译工作;
So I can diagnose the problem a little more specifically in math. 我能在数学中更准确得解决这个问题。
diagnose:vt.诊断;断定;vi.诊断;判断; specifically:adv.特别地;明确地;
Here's a really cool problem. I like this. 这是一个很酷的问题。我喜欢这个。
It's about defining steepness and slope using a ski lift . 它是关于确定陡度和坡度 在一个滑雪缆车上.
defining:v.解释(词语)的含义;给(词语)下定义;阐明;界定;(define的现在分词) slope:n.斜坡;坡度;坡地;山坡;v.倾斜;有坡度;悄悄地走;潜行; ski lift:n.(运送滑雪者上坡的)上山吊椅;
But what you have here is actually four separate layers , and I'm curious which of you can see the four separate layers and, particularly, how when they're compressed together and presented to the student all at once, how that creates this impatient problem solving. 但在这里有四个不同层面。 我很好奇你们哪个可以看到这四个不同层面的, 特别是,它们如何压缩在一起, 一次性的展现给学生, 又如何轻易地解决了问题。
layers:n.层;表层;层次;阶层;v.把…分层堆放;(layer的第三人称单数和复数) curious:adj.好奇的,有求知欲的;古怪的;爱挑剔的; compressed:adj.(空气或气体)压缩的; v.(被)压紧; (compress的过去式和过去分词)
I'll define them here: You have the visual . 我将在这里详细说明它们。你有图像。
define:v.定义;使明确;规定; visual:adj.视觉的,视力的;栩栩如生的;
You also have the mathematical structure , talking about grids , measurements , labels , points, axes , that sort of thing. 你也有数学结构, 谈到格子,测量,标注, 点,轴,诸如此类。
structure:n.结构;构造;建筑物;vt.组织;构成;建造; grids:n.[数]网格(grid的复数形式);栅格; measurements:n.测量值,尺寸(measurement的复数); labels:n.标签;分类(label的复数形式);v.贴标签于;把…称为(label的三单形式); axes:n.轴线;轴心;坐标轴;斧头(axe的复数);
You have substeps, which all lead to what we really want to talk about: which section is the steepest . 你有子步骤,它们都引到我们真正想谈论的问题, 哪段是最陡的？
steepest:adj.陡峭的;不合理的;夸大的;急剧升降的(steep的变形);
So I hope you can see. 我希望你们能看到。
I really hope you can see how what we're doing here is taking a compelling question, a compelling answer, but we're paving a smooth, straight path from one to the other and congratulating our students for how well they can step over the small cracks in the way . 我真的希望你们能看到,我们在这里 是在谈一个激发兴趣的问题,一个有意思的答案, 但我们在开拓一个平整的,简单明了的路径, 从一点到另一点, 然后祝贺我们的学生,为他们 能够很好的沿路踏过小缝隙。
compelling:adj.引人入胜的; v.强迫; (compel的现在分词) paving:n.[建]铺砌;铺路材料;块石面路;v.铺设;为…做准备(pave的现在分词); cracks:n.裂纹; v.破裂; (crack的第三人称单数和复数) in the way:妨碍;挡道;
That's all we're doing here. 这就是我们做的。
So I want put to you, if we can separate these in a different way and build them up with students, we can have everything we're looking for in terms of patient problem solving. 所以我想展示给你们的是,如果我们能以不同方式分开这些, 和学生们一起建造它们, 我们可以迎刃处理所有需耐心解决的问题。
So right here I start with the visual, and I immediately ask the question: 就在这里,我以图像开始, 我马上问个问题:
Which section is the steepest? 哪个部分最陡？
And this starts conversation because the visual is created in such a way where you can defend two answers. 这会引起交谈, 因为这个图像创造的方式使你可以用两个答案辩解。
So you get people arguing against each other, friend versus friend, in pairs, journaling , whatever. 这样你可以促进人们互相争论, 朋友对朋友的争论, 一对对,日志式,随便怎样。
versus:prep.对;与...相对;对抗; journaling:n.日志;注册;登记;
And then eventually we realize it's getting annoying to talk about the skier in the lower left-hand side of the screen or the skier just above the mid line. 然后我们最终认识到 谈到 在屏幕左手边滑雪的人 或是刚上中线的滑雪的人,这是挺讨厌的。
annoying:adj.烦人的;使生气的;使烦恼的;v.使生气;打扰;骚扰;(annoy的现在分词) skier:n.滑雪的人; left-hand:adj.左手的;左侧的;
And we realize how great would it be if we just had some A, B, C and D labels to talk about them more easily. 我们认识到如果 我们更简单地谈论带有一些a,b,c,d的标志, 这该是多么好。
And then as we start to define what does steepness mean, we realize it would be nice to have some measurements to really narrow it down, specifically what that means. 然后我们确定陡峭程度是指什么, 我们认识到这是一个好主意,如果有一些测量 来真的缩小范围,特别是那意味着什么。
narrow:adj.狭窄的; v.使窄小; n.峡谷; (场所,物品等的)狭窄部分;
And then and only then, we throw down that mathematical structure. 然后,在此之后, 我们放下那个数学架构。
The math serves the conversation, the conversation doesn't serve the math. 数学服务于对话, 对话却不为数学服务。
And at that point, I'll put it to you that nine out of 10 classes are good to go on the whole slope, steepness thing. 在这一点,我将展示给你们,10个班里有9个班 能很好的继续解决整个坡度,陡度的问题。
on the whole:基本上,大体上;就全体而论;
But if you need to, your students can then develop those substeps together. 如果你需要 你的学生可以在一起展开那些子步骤。
Do you guys see how this, right here, compared to that -- which one creates that patient problem solving, that math reasoning? 你们可以比较这边这个和那个－－ 哪个班处理了耐心解决的问题,以及数学推理呢？
compared:adj.比较的,对照的; v.相比; (compare的过去式和过去分词)
It's been obvious in my practice, to me. 在我的实践中,我一目了然。
obvious:adj.明显的;显著的;平淡无奇的;
And I'll yield the floor here for a second to Einstein, who, I believe, has paid his dues. 我这就要谈谈爱因斯坦, 我认为他做了应有的贡献。
yield:n.产量;产出;利润;v.屈服;让步;放弃;提供;
He talked about the formulation of a problem being so incredibly important, and yet in my practice, in the U.S. here, we just give problems to students; we don't involve them in the formulation of the problem. 他谈到规划问题的能力是如此重要, 但在我的实践中, 在美国这儿, 我们仅仅把问题交给学生; 我们不把他们参与到问题的形成和规划过程中。
formulation:n.构想,规划;公式化;简洁陈述; incredibly:adv.难以置信地;非常地; involve:v.包含;需要;牵涉;牵连;影响;(使)参加;
So 90 percent of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math reasoning and patient problem solving. 所以我做的90％的事 和我每周5小时的准备时间 是拿问题中非常吸引人的元素, 像在我的教科书里的这些问题, 把它们重组成能支持数学推理和耐心解决问题的方法。
prep:n.预备;预习;准备功课;v.上预备学校;作好准备; fairly:adv.相当地;公平地;简直; elements:n.要素;基本部分;少量;一群;(element的复数)
And here's how it works. 这里是它如何运作的。
I like this question. It's about a water tank. 我喜欢这个问题,这是关于一个水桶。
The question is: How long will it take you to fill it up? 问题是:多长时间可以装满这个水桶呢？
First things first , we eliminate all the substeps. 第一件事,我们简化子步骤。
First things first:要紧的事情先做;英语初阶;凡事有轻重缓急; eliminate:v.消除;排除;
Students have to develop those, they have to formulate those. 学生们必须得展开这些子步骤, 用公式化表达它们。
formulate:v.制订;规划;准备;确切表达;
And then notice that all the information written on there is stuff you'll need. 然后认识到写在那里的东西是他们所需要的所有信息。
None of it's a distractor , so we lose that. 没有一个是多余信息,用不着删除。
distractor:n.错误选择;诱导答案;
Students need to decide, "All right, well, does the height matter? Does the side of it matter? 学生们需要决定,好了, 高度重要吗？它的尺码重要吗？
Does the color of the valve matter? What matters here?" 开关的颜色重要吗？这里什么是重要的？
valve:n.阀;[解剖]瓣膜;真空管;活门;v.装阀于;以活门调节;
Such an underrepresented question in math curriculum . 这在数学课里是不具代表性的问题。
underrepresented:adj.代表名额不足的;未被充分代表的; curriculum:n.课程;总课程;
So now we have a water tank. 这样在这里我们有了一个水桶。
How long will it take you to fill it up? And that's it. 多长时间会把它装满,就是这样。
And because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks, we go out and we take a picture of it. 因为这是21世纪, 我们喜欢以真实世界的表达方式来谈论真实的世界, 不是以你常在教科书上看到的线条艺术 或是插图艺术来表达。 我们出去应用,并给它照个相。
clip:v.剪辑;修剪;削减;固定;n.夹;夹子;速度;钳;
So now we have the real deal. 现在我们有了真实的东西。
How long will it take it to fill it up? 它要多长时间装满？
And then even better is we take a video, a video of someone filling it up. 更好的,我们录像, 一个人在装满它的录像。
And it's filling up slowly, agonizingly slowly. 它在慢慢的装满,令人不耐烦的等待。
agonizingly:adv.使人烦恼地;苦闷地;
It's tedious . 这很乏味。
tedious:adj.沉闷的;冗长乏味的;
Students are looking at their watches, rolling their eyes, and they're all wondering at some point or another, "Man, how long is it going to take to fill up?" 学生们在看他们的表,翻白眼, 他们时不时地想, “伙计,这个要多长时间装满呐？”
(Laughter) （笑声）
That's how you know you've baited the hook , right? 这就是你想要引起关注的地方,好。
baited:vt.引诱;在…中放诱饵;折磨;n.饵;诱饵;vi.中途休息; hook:n.钩;挂钩;鱼钩;钓钩;v.挂住;箍住;钓(鱼);打曲线球;
And that question, off this right here, is really fun for me because, like the intro , 这个问题,就在这里,对我来说很有趣。 因为,像个引言,
intro:n.介绍;简介;
I teach kids -- because of my inexperience -- 我教小孩子,因为我的经验,
inexperience:n.缺乏经验;无经验;不熟练;
I teach the kids that are the most remedial , all right? 我教那些需要辅导的孩子。
remedial:adj.治疗的;补救的;矫正的;
And I've got kids who will not join a conversation about math because someone else has the formula; someone else knows how to work the formula better than me, so I won't talk about it. 我不教那些不参与数学对话的孩子, 因为他们懂公式, 也知道如何更好地运用公式,甚至比我好。 所以我不讨论这个。
But here, every student is on a level playing field of intuition . 但在这里,每个人都在同一个水平上运用直觉。
level playing field:公平竞争环境;公平竞争的环境;公平赛场; intuition:n.直觉;直觉力;直觉的知识;
Everyone's filled something up with water before, so I get kids answering the question, "How long will it take?" 每个人都装过水, 所以我让孩子们自己回答这个问题:多长时间装满水。
I've got kids who are mathematically and conversationally intimidated joining the conversation. 我让这些在数学上和交谈上感到恐惧的孩子们 也加入谈论。
mathematically:adv.算术地,数学上地; conversationally:adv.会话地; intimidated:adj.害怕的;受到恐吓的;v.威胁,恐吓;(intimidate的过去式和过去分词)
We put names on the board , attach them to guesses, and kids have bought in here. 我们把名字写到黑板上,把它们连到猜测的答案上, 孩子们把答案带到这里。
on the board:在董事会,将在会上讨论;在那块木板上; attach:v.贴上;重视;把…固定,把…附(在…上);参加;与…有联系;
And then we follow the process I've described . 然后孩子们遵照我描述的过程。
described:v.描述;形容;把…称为;做…运动;(describe的过去分词和过去式)
And the best part here, or one of the better parts is that we don't get our answer from the answer key in the back of the teacher's edition. 最好的部分,或者说,一个更好的部分 是我们没有从 教师版教科书的后面得到答案。
We, instead, just watch the end of the movie. 我们却看到了录像的结尾。
(Laughter) （笑声）
And that's terrifying , because the theoretical models that always work out in the answer key in the back of a teacher's edition, that's great, but it's scary to talk about sources of error when the theoretical does not match up with the practical . 这很有意思,对吧。 因为理论模型总是得出 和教师版后面的答案一样的答案, 这很好, 但谈到错误的来源, 当理论不符合实际的时候,就让人害怕。
terrifying:adj.令人恐惧的;骇人的;极大的;v.使害怕,使恐怖;(terrify的现在分词) theoretical:adj.理论的;理论上的;假设的;推理的; sources:n.来源;出处;起源;根源;原因;v.(从…)获得(source的第三人称单数和复数) practical:adj.实际的;真实的;客观存在的;n.实习课;实践课;
But those conversations have been so valuable , among the most valuable. 但那些谈论是如此珍贵, 是最有价值的。
valuable:adj.有价值的;贵重的;可估价的;n.贵重物品;
So I'm here to report some really fun games with students who come pre-installed with these viruses day one of the class. 所以我在这里报导一些很有趣的收获, 关于在数学课程刚开始的时候,学生带有这些预置的 错误征兆。
pre-installed:预装;
These are the kids who now, one semester in, 这些孩子现在已经学了一个学期,
semester:n.学期;半年;
I can put something on the board, totally new, totally foreign, and they'll have a conversation about it for three or four minutes more than they would have at the start of the year, which is just so fun. 我能在黑板上写下一些 全新的,完全陌生的问题, 他们能就此展开讨论, 这比他们在学年开始的时候长3,4分钟, 这真有意思。
We're no longer averse to word problems, because we've redefined what a word problem is. 孩子们不再反感数学问答题, 因为他们从新定义数学问答题。
averse:adj.反对的;不愿意的; redefined:adj.重新定义的;vt.对…再加以解说;再给…下定义(redefine的过去分词);
We're no longer intimidated by math, because we're slowly redefining what math is. 孩子们不再恐惧数学, 因为他们在慢慢从新定义数学。
redefining:v.改变…的本质(或界限);重新定义;使重新考虑;(redefine的现在分词)
This has been a lot of fun. 这个过程很有意思。
I encourage math teachers I talk to to use multimedia , because it brings the real world into your classroom in high resolution and full color; to encourage student intuition for that level playing field; to ask the shortest question you possibly can 我鼓励数学教师多多应用多媒体, 因为它把真实世界以高清晰度的图片和全色彩图像带到 你的教室, 来鼓励学生对那个场景的直觉, 来问你可能问的最短的问题,
multimedia:n.多媒体;adj.多媒体的; resolution:n.解决;分辨;解析;决议;
and let those more specific questions come out in conversation; to let students build the problem, because Einstein said so; and to finally , in total, just be less helpful, 让那些更细,更具体的问题随着交谈显露出来, 让学生们着手解决问题, 正如爱因斯坦所说, 总而言之,就是给予更少的帮助,
finally:adv.终于;最终;(用于列举)最后;彻底地;
because the textbook is helping you in all the wrong ways: 因为教科书在以非常错误的方式帮助大家。
It's buying you out of your obligation , for patient problem solving and math reasoning, to be less helpful. 它在免去大家 对耐心问题的解决和数学推理的责任,更没有帮助性。
obligation:n.义务;责任;职责;(已承诺的或法律等规定的)义务;
And why this is an amazing time to be a math teacher right now is because we have the tools to create this high-quality curriculum in our front pocket. 那为什么现在是作为一个数学教师的绝好时候, 这是因为我们有工具来创造 这个高质量的数学课程,就在我们的口袋里的工具手机等等。
high-quality:adj.高质量的;
It's ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous. 它无所不在,非常便宜。 还有自由散播它的工具, 在公开授权下, 从没有比现在更便宜或更普遍的社交互联网工具。
ubiquitous:adj.普遍存在的;无所不在的; distribute:v.分发;分配;分销;分散; licenses:n.许可(license的复数);授权;v.允许(license的三单形式);
I put a video series on my blog not so long ago and it got 6,000 views in two weeks. 不久之前,我把一系列的录像放在我的博客里, 在两周之内它得到6000的观看率。
series:n.系列,连续;[电]串联;级数;丛书; blog:n.博客;部落格;网络日志;
I get emails still from teachers in countries I've never visited saying, "Wow, yeah. We had a good conversation about that. 我还收到很多我从来没有去过的国家的邮件,有的教师写邮件说: “哦,是的。我们就此展开了很好的讨论。
Oh, and by the way , here's how I made your stuff better," 哦,顺便说一下,这是我如何改善你教学材料的例子。”
by the way:顺便说一下;
which, wow. 这么多,喔。
I put this problem on my blog recently : 我最近在我的博客上提出这个问题。
recently:adv.最近;新近;
In a grocery store, which line do you get into, the one that has one cart and 19 items or the line with four carts and three, five, two and one items. 在一个杂物店,你排那个队, 一个是有一个手推车和19个商品 或是另一个有4个手推车和3,5,2 和1个商品。
grocery:n.食品杂货店;食品杂货; items:n.项目;一件商品(或物品);一则,一条(新闻)(item的复数) carts:n.运货马车; v.用马车运送; (cart的第三人称单数和复数)
And the linear modeling involved in that was some good stuff for my classroom, but it eventually got me on "Good Morning America" a few weeks later, which is just bizarre , right? 这里牵涉到的线性模型,它成为了我的教学中很好的材料, 但它最后让我上了在几周之前“早安,美国”的节目, 这的确是不可思议,对吧。
linear:adj.线的,线型的;直线的,线状的;长度的; involved:adj.有关的; v.涉及; (involve的过去式和过去分词) bizarre:adj.奇异的(指态度,容貌,款式等);
And from all of this, I can only conclude that people, not just students, are really hungry for this. 从所有这些,我只能下此结论 人们,不仅仅是学生, 都非常渴望这个。
conclude:v.断定:得出结论:终止:达成:缔结(协定)
Math makes sense of the world. 数学解读世界。
Math is the vocabulary for your own intuition. 数学也是描述人们 直觉的词汇。
So I just really encourage you, whatever your stake is in education -- whether you're a student, parent, teacher, policy maker, whatever -- insist on better math curriculum. 所以我只是鼓励大家,无论你们是什么教育程度, 无论你们是学生,还是家长,老师,决策者,不论是什么, 请坚持更好地应用数学教程。
stake:n.桩,棍子;赌注;火刑;奖金;v.资助,支持;系…于桩上;把…押下打赌; policy:n.政策,方针;保险单;
We need more patient problem solvers . Thank you. (Applause) 我们需要更多耐心的问题解决者。谢谢。
solvers:n.解决者(solver的复数形式);