如果把负担都放在原生家庭的教育水平和经济条件上，结果就是阶级固化，下层有一定天赋的人失去机会，出不了头。 公立教育本来应该是个equalizer, 好的学生被identify, support, help to grow, and realize their potential. 老师和学校应该起非常大的作用。中国小镇做题家，不管你怎么笑话看不起他们，学校起了一个改变命运，改变阶层的作用。而现在美国大多数学校和教学大纲的设置，使这样几乎不可能（少数stem school, special schools 除外，而且能进这些学校往往已经需要家庭的极力支持了）。
如果把负担都放在原生家庭的教育水平和经济条件上，结果就是阶级固化，下层有一定天赋的人失去机会，出不了头。 公立教育本来应该是个equalizer, 好的学生被identify, support, help to grow, and realize their potential. 老师和学校应该起非常大的作用。中国小镇做题家，不管你怎么笑话看不起他们，学校起了一个改变命运，改变阶层的作用。而现在美国大多数学校和教学大纲的设置，使这样几乎不可能（少数stem school, special schools 除外，而且能进这些学校往往已经需要家庭的极力支持了）。
2019: The U.S. team tied for first place with China at the 60th International Mathematical Olympiad (IMO), which was held in Bath, United Kingdom, July 11-22. The six U.S. team members, Vincent Huang (a returning member from 2017 and 2018), Luke Robitaille, Colin Tang, Edward Wan, Brandon Wang and Daniel Zhu also won gold medals for their individual high scores in the Olympiad, known as the world championship mathematics competition for high school students. poinciana 发表于 2021-12-15 14:40
这里是common core初中（6-8年级）数学课标里的统计与概率知识点（content） http://www.corestandards.org/Math/Content/SP/ 包含了复合概率、数据建模、线性拟合等我认为比较advanced的内容。具体学校里能教成什么样我不知道，跟班里学生总体水平和老师水平有关。 数学common core课标里还包含math skills，各位可以比对下，自家小孩达标没。 Statistics & Probability PRINT THIS PAGE Grade 6 Develop understanding of statistical variability. CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students'''''''''''''''' ages. CCSS.MATH.CONTENT.6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: CCSS.MATH.CONTENT.6.SP.B.5.A Reporting the number of observations. CCSS.MATH.CONTENT.6.SP.B.5.B Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. CCSS.MATH.CONTENT.6.SP.B.5.D Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Grade 7 Use random sampling to draw inferences about a population. CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. CCSS.MATH.CONTENT.7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. CCSS.MATH.CONTENT.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CCSS.MATH.CONTENT.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Investigate chance processes and develop, use, and evaluate probability models. CCSS.MATH.CONTENT.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. CCSS.MATH.CONTENT.7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. CCSS.MATH.CONTENT.7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. CCSS.MATH.CONTENT.7.SP.C.7.A Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. CCSS.MATH.CONTENT.7.SP.C.7.B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? CCSS.MATH.CONTENT.7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. CCSS.MATH.CONTENT.7.SP.C.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. CCSS.MATH.CONTENT.7.SP.C.8.B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. CCSS.MATH.CONTENT.7.SP.C.8.C Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Grade 8 Investigate patterns of association in bivariate data. CCSS.MATH.CONTENT.8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CCSS.MATH.CONTENT.8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. CCSS.MATH.CONTENT.8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. CCSS.MATH.CONTENT.8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
看看中小学教师的水平就知道教出什么样的学生了 高中有些stem老师还是很好的，清楚地知道学生的弱点，物理老师不得不cover大量algebra的练习 天才是无师可以自通的 大多数人还是需要在学校有效的学习的 看过一句话，美国中小学数学教育是mile wide and inch deep 溜溜哒哒 发表于 2021-12-15 15:32
等号就是天平，你把两边减同一个数，等号还成立。看起来就是移过去变号。
是的，我感觉现在虽然还在嘲讽nerd，但电视总的风向是nerd虽然小时候不受欢迎，但长大后工资还是挺高的。
公立教育本来应该是个equalizer, 好的学生被identify, support, help to grow, and realize their potential. 老师和学校应该起非常大的作用。中国小镇做题家，不管你怎么笑话看不起他们，学校起了一个改变命运，改变阶层的作用。而现在美国大多数学校和教学大纲的设置，使这样几乎不可能（少数stem school, special schools 除外，而且能进这些学校往往已经需要家庭的极力支持了）。
首先，美国数学教育水平方差很大的。教育高地顶尖私校或者公校，和教育洼地一般的公校，是没法相提并论的。是不是洼地，家长自己心里得有点数。去amc 10/12里扒个近两年排名靠前的数据，如果公校里人很多但没到10个，大概率学校学习数学氛围不太行，不能指望娃靠着peer pressure自己往前推。 其次，家长要搞清楚期望跟付出的关系。你不能又指望娃学好stem，又身在洼地啥也不管。lz女儿都初中了才开始抱怨，早干嘛去了。 最后，娃跟娃差异也很大。虽然父母这辈都是知识分子，基因都不差，但是娃行不行还是看运气。别人家啥也不管学的很好，不代表你家也如此。还是那句话，家长得有点数。在美国差，并一定换到国内就好，也可能高中都考不上。 如果一定跟国内比，美国数学在低龄阶段的资源很多，难度广泛各个等级都有。我理解美国的教育是，占你半天的时间，学到60分水平，剩下半天自由发挥，爱干嘛干嘛去。中国是占你一天，各科都得学到80分。如果是顶尖的，天生90分水平那种，显然在美国吃香，毕竟自由时间多，搞数学的没必要跟生物化学死磕。如果吊车尾的，50多分的，也是美国吃香，在国内可能早就淘汰了，在美国努把力还能混过去。中间那部分，70分上下的，国内学校管的严点，还能推上去，在美国就看家长了
有了娃之后看房最大的感触就是，学区真坑人。 国内穷人家学习好的孩子，好歹小升初还能去个好中学，改变下命运
神烦这种，拿个简单的概念，嘚瑟数学的意义。。就跟读了一遍c++教材以为自己学会编程了一样。。
你确定道德信仰能保持科技进步？你以为这是中餐馆打工？
这个我们都是自己推出来要变号，根本不需要老师讲
光看 last names, 呵呵，靠公校老师，没有自己课外下功夫，没门
是啊。这个就是很好的例子，靠父母提供的额外的资源，不是靠学校。 非要理解成我们abc的孩子比别人聪明，不是公立学校数学基础不好。。。🤷♀️
国内外很多重量级单位在RISC-V支持者名单上， 看来给予很大希望。但很难动摇ARM的地位。 https://riscv.org/members/
其实这些年来美国的竞赛成绩一直很好。当然有人非要说只有第一名有意义那也没法。
美国的最大问题就是没有集训。看过新美国的领队也是抱怨为啥只集训两周不是两个月。
其实想想没啥好抱怨的，游泳队一样是六月选拔出来的才有机会三周集训去奥运参赛的。游泳田径这是全民项目，数理化往后排了。
天才是无师可以自通的 大多数人还是需要在学校有效的学习的
看过一句话，美国中小学数学教育是mile wide and inch deep
这里是common core初中（6-8年级）数学课标里的统计与概率知识点（content） http://www.corestandards.org/Math/Content/SP/ 包含了复合概率、数据建模、线性拟合等我认为比较advanced的内容。具体学校里能教成什么样我不知道，跟班里学生总体水平和老师水平有关。 数学common core课标里还包含math skills，各位可以比对下，自家小孩达标没。
Statistics & Probability PRINT THIS PAGE Grade 6 Develop understanding of statistical variability. CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students'''''''''''''''' ages. CCSS.MATH.CONTENT.6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: CCSS.MATH.CONTENT.6.SP.B.5.A Reporting the number of observations. CCSS.MATH.CONTENT.6.SP.B.5.B Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. CCSS.MATH.CONTENT.6.SP.B.5.D Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Grade 7 Use random sampling to draw inferences about a population. CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. CCSS.MATH.CONTENT.7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. CCSS.MATH.CONTENT.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CCSS.MATH.CONTENT.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Investigate chance processes and develop, use, and evaluate probability models. CCSS.MATH.CONTENT.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. CCSS.MATH.CONTENT.7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. CCSS.MATH.CONTENT.7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. CCSS.MATH.CONTENT.7.SP.C.7.A Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. CCSS.MATH.CONTENT.7.SP.C.7.B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? CCSS.MATH.CONTENT.7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. CCSS.MATH.CONTENT.7.SP.C.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. CCSS.MATH.CONTENT.7.SP.C.8.B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. CCSS.MATH.CONTENT.7.SP.C.8.C Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Grade 8 Investigate patterns of association in bivariate data. CCSS.MATH.CONTENT.8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CCSS.MATH.CONTENT.8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. CCSS.MATH.CONTENT.8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. CCSS.MATH.CONTENT.8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
英国人觉得中国数学教育也不够深度，呵呵。
太搞笑了，小学老师肯定讲了为什么要变号，中国数学书也写了。 如果你觉得你是背下来的，那是你智商太低了，太低了，太低了。
你家小孩遇到的老师不适合你家的education needs，毫无疑问。如果有的选就跑路。没得选就课外补。
同意，所谓好坏就看你在哪个角度看。老有人和收银员比数学，这就是一叶障目了。
又想起我这的秘书， 看着网站上真人验证 56 / 8 = ? 的问题和我大眼瞪小眼。 我觉得他至少也是上过 college 的。
有这么多顶尖移民，还要走衰的话，你让别的国家怎么混。
我第一次听说ca公立很好，以前华人都说加州十分公立都烂透了，必须去私立
国内的学区房也很坑人的吧？
好歹有小升初择优录取好不好
这是什么烂校的engineering学生？算这么个破题需要5秒？lol
这是实话。。 就怕制度废了中产割狠了，那就啥都没了
穷人可以上charter。
again，取决于你在哪，有没有charter
你的孩子真的在美国好的公立学校读过书吗? 美国学校从小学开始就会分级了。数学好的孩子都是可以跳级的。 我们学校中西部。孩子们5年级开始数学分级考试。一个年级大概20%的孩子可以分到快班。快班比正常进度高俩个年级。八年级在学Geometry这种样子。然后5%数学会跳3级，八年级修algebra2, 大概一个年级2-3个数学特别好的孩子，可以跳4级，八年级修preculculas这种。后面俩种是直接去高中上课的。所有的亚裔孩子都是数学跳级的。 这种因材施教的模式我觉得很好。
很多学区不分级的。
那就是学校不够好。我们周围9-10分好学区的学校，数学都分级的。 我们还是中西部。加州更厉害。每次竞赛，加州的学生碾压我们这边的高中。
五年级才开始分级算什么好学校啊，从k到四年级整整五年时间孩子们就该浆糊着吗 我们学区是从k就可以分级的，隔壁学区比我们讲平等但是好歹3年级也开始了。不过虽然分了级，改变不了小学老师都是从不喜欢数学的学生成长起来的不喜欢数学老师这件事
呵呵。小学的数学算什么啊?高中数学好的孩子才是真的好。最重要的是兴趣。 另外一年级开始，你孩子如果数学特别好，老师会给challenging problems,也会给自学的数学软件。IXL和khan acedemy特别好用。我孩子低年级就是用这俩个软件长大的。可以无限制地往高年级做题。每个部分都有vedio演讲。 另外还有GT班。也可以学 advanced数学和英语。 美国学校资源非常多。你孩子真的聪明，数学好的话绝对不会被埋没的。
跳四级？what''s the point。真有那么天才么。除了十万里挑一的天才，大概率父母见识太短了
我觉得跟着国内的进度差不多就好了。不耽误将来做院士或者是大C
这种真的是井底之蛙,我9年级娃数学现在学geometry honor,我可以证实是我们高二学的东西,下学年要pre calculus的课,我看了下,基本上就是国内高一高二大学数学一部分的混合,有些题相当难和绕,不比中国的数学作业考试差.我高中数学还可以的,虽然没参加什么竞赛,现在还暂时能辅导9年级娃数学,明年开始,我就跟不上了,只能让娃自己拼了. 像你说小学移民过来的没学新内容的这种,不会高中毕业都只修了algenra1的课吧.....
那几个孩子是真的聪明。 另外高中课是会算GPA的。孩子跳级如果拿不到A是得不偿失的。所以跳级的孩子都是有那个天赋的。高中之后还可以修AP课乃至大学课程。
一般差区数学的正常进度是高中只要修完代数和几何就可以高中毕业了吧？好像不是required修微积分的。所以差不多是我们学校中国孩子9年级就能修完的内容了。那确实是简单。 但问题是美国好的高中开了各种ap课。各种难的课程。孩子们完全可以挑战自己的。爬藤的娃没有哪一个不修微积分的。 但是其实我们那时候在国内。微积分是大学的内容了。 就这还叫简单吗?不能理解。
Precalculus初中学honestly正常智力都可以，需要天赋么？？ 一个小小的precalculus需要啥天赋。我认为任何别人已经发明的东西只是学一下根本不需要啥天赋。
至少我不会让任何一个小孩这么搞。
美国系统确实还在小马过河，结果还要几十年后才知道。不过我们小时候超前四年的那一批都混的很一般。真的是一步步走下坡路。
有一个吧做了faculty但是paper也非常平庸。大部分普通打工人，赚个十几几十万。
应该弄深，比如竞赛如果真有天赋，广，比如博览群书，而不是超前。
加州一些学区把数学快班取消了。
大概是我孤陋寡闻，我没见过小学一团浆糊厌烦数学，到了中学反而喜欢上数学能学明白的孩子。小学时候觉得数学太easy粗心错，中学以后认真起来的孩子不属于这种情况 IXL就是大量基本运算，khan academy虽然基本概念讲解很清楚，但是内容还是很浅的。anyway看起来我对好的数学教育的理解跟你不太一样
那不了解。我们这边好学校都有。刚才问了几个其他州的朋友。也都有。就是honor math。 另外孩子还可以单科跳级。只要通过了考试就行。
我不觉得precalculus普通初中生都会。在国内也是高中的内容了。 我觉得美国学校教育最好的一点就是因材施教。不会一刀切。
哈哈看来你根本不了解这俩个数学软件。IXL绝对不是简单的运算。现在每个年级都是有很多知识点。比如说我老二的二年级，还有分数时间计量单位等等。各种知识点。 不过我倒是记错了要纠正一点。IXL是没有讲解录像的。只有solution。 Khan academy有讲解录像。知识面更全。 这些网站都是学校购买的。学生们可以随便用。
为之，难者亦易。不为，难者亦难。
中学的数学，正常智力初中想学都可以。
那是你牛啊。国内数学进度好像都没这么快吧?国内初中学三角函数了吗？好像是高中学的吧。
对呀。所以我说不需要初中学吧。高中搞搞就行了。文革以后，这个是大一的内容，那一代人，就是咱们父母一代了，不就是现在把火箭送上天的么
美国数学是有教材的。只是不会发给学生而已。 我老大上次暑假准备数学跳级考试。问学校老师借了geometry的教材。我看了一下。真的是编写得太好了!!当然一般老师不会把所有章节都讲完的。只讲部分章节。 美国的数学教材真的很好的。
khan是公益网站，不需要购买的，任何人都可以去看。ixl我们学区买了，我觉得就是重复刷题，真的一点不符合你前面说的兴趣最重要啊
这是我截图的ixl。二年级内容。我觉得知识面很全啊。可能我要求不高吧。
美国人的教育就是能吹。一堆词汇。但是不扎实，不深。
纽约是一刀切，任何人不得跳级。
各个学区选的教材不一样。小学的话，有套Everyday Math，也叫Chicago Math，被很多家长吐槽。但也有家长觉得拓宽思路挺好，小孩学着没什么问题。不少学区已经不用这套教材了，但还有学区用的。
你去查查近二十年的fields、nobel获奖者，看看有多少人是在美国接受的k-12教育。
教材不发，老师不讲完，光教材好，有啥用呢？没有课外补数学的孩子还是没学，基础可不就是打不好吗？
纽约的公立学校是不能跳级的。没听过例外。因为生日转学跳级的不算。纽约读几年级只看生日，Only
完全同意。我老板辅导孙子功课就跟我吐槽过这个。 说看起来他们学的那些概念一点都不落后，但是孩子们其实还没理解好呢就跳下一步了，最后等于没学。
我觉得挺多的呀。
看看五百强c level恨不得百分之八十。相信美国教育。我对美国教育相当欣赏。他们的数学的教法，讨论而不是习题，注重应用和创新。
下一代这批刷题的还是给老美打工的命
这个有何不妥么？我也是这么算的
基础都没打好，还谈什么“应用和和创新”？
纽约哪所Charter有跳级先例（这几年）,请举例 纽约就是Nobody left behind, 哪怕你homeschool,也不让你跳级。我朋友疫情期间问他Home school要跳级，教育局说没有政策 其余地方不清楚，说纽约教育好，我不认同 网上有人说在纽约高斯帕斯卡在纽约也不能跳级，我猜是实情。反正我没听过公立跳级的
我在说fields/nobel、不是五百强c level。 五百强c level，是因为美国公司在五百强占比最高。
fields从2002年到最近的2018，总共颁发了18个奖牌，只有一个人获奖时有美国国籍，并且此人是印度裔，加拿大长大。
作为对比，五个人有法国籍，四个人有俄罗斯籍。
这个“螺旋式上升”也是那套Everyday Math的特点和被吐槽的点之一。 不过我觉得现实工作里很多新东西就是没理解好就得用了，得多用反复iterate慢慢掌握的。
你想用这个比例说明什么？美国的人口可不到世界的1/18
是啊美国聪明人都去学经融了么。所以说他们教的是应用和创新。而不是算几道题么
手动点战。
逻辑思维很多就是在重复训练中巩固和培养的，我不是说刷题搞竞赛，而是数学做为抽象思维的学科，数学的思维就是要需要大量的、具体的、细节的练习中培养的。
三四岁小孩就是这么算的
没说跳级。为什么执着跳级这件事。有result-oriented charter school，其中有衡水型的，特别适合贫困儿童翻身。Outlier那本书里有讲这么一个学校。
美国世界第一是有原因的，但好像真不是因为K-12数学教育特别好。
是的，上了高中课程突然变深，孩子更不上很容易产生厌学情绪。
就是innovation和脸皮厚么。看看这次covid解药。别管前期谁有贡献，最后都是老美的。这还不是成功的教育？ 窃国者侯么
但是1962-1986年这二十几年间，每次fields必有至少一位美国人。
美国数学教育在退步，是很显然的。
当然，consequence是啥，谁也不好说。你觉得这能导致美国更好更强大，那也是可以的。
我们这里三年级就开始数学分班了
美国不需要更强大。老中烙印的娃长大后只要继续发扬他们这种死卷的风格。过那么几十年就会倒退几十年，完全不必担心。
就看咱论坛上都在死卷给人打工拿了多少package就可见微知著了
你觉得不卷就可以当Elon Musk，卷的那些小中小印就当大厂螺丝钉也行。
62-86年的时候，世界很需要数学。举个简单例子，那时候没有超算，飞船上天需要手算欧拉法。
现在其实已经不怎么需要数学了。不是ai都能hypothesis推公式了么。
在新兴，有应用的学科，美国教育出来的一直是世界第一，而且遥遥领先
别一说就是musk，介于musk和大厂打工之间，还有那么十个层次左右呢。
好的，AI解决一切，啥都不用干等机器人投喂就好。
现在的ai我觉得他们屁都解决不了。但是至少提出了这个概念和雏形。那将来的credit都是他们的。
这不就是创新么
哈哈，翻到过一本书，专门写爱因斯坦相对论里的数学错误。但是别人只记得爱因斯坦。
这个是真的，所以我就觉得美国小学教的很难，全靠孩子天赋。家里不辅助一下，肯定是跟不上的。但是班上孩子都很厉害，各种解法，孩子倒是能从别的孩子身上学到不少。但听不懂的孩子估计就倒霉了，但是学区好，估计80%孩子都很厉害。剩下20%也能跟上大纲。
基础打不完的。前人积累的知识是学不完的。你可以无限delay应用和创新。
不是执着跳级，这不是帖子里大家用有跳级说美国教育好吗？我说美国最大的城市的公立学校不允许跳级。高斯来了也跳不成。驳斥论据。跳级好 不好另说。当然也有从国内读了一年级在这里读三年级的，原因是生日在这里够上三年级。不是因材施教，是因生日施教。教的啥暂不知道
认同
对于脑子好使的娃，提前接触点知识，没有问题。 对于脑子一般的，也就是刚刚学懂现在的能力，提前讲了也听不懂，搞到最后，也不知道哪些该懂哪些不用一定懂，还以为都似是而非就行了
狗屁。fields 奖 发的 都是 坚深的证明，和计算毫无关系。fields 奖 那些 理论结果 200年内都派不上用场。
是啊，这个过程很快啊，而且reliable。
你这个conclusion给的很好。聪明的，怎么都可以。不聪明的也别费劲了。
不觉得努力能改变什么。最终，看身体，颜值和智商。
但是那时候数学在美国有群众基础么。那时候有一种职业叫做computer。就是专门做计算的。那时已经有小计算器，所以很重要的手算是高等数学，比如积分，常微分方程，解析几何，和矩阵等等。其payment堪比今日的马工。整个stem领域重视数学/计算。就是你前面说的，小学就学微积分，也是为什么我认为，中学数学到precalculus对于任何智力在正常范围的小孩，iq在80以上吧，在初中都可以完成。
后来对这个职业的需求越来越少了。现在就是零了么。有软件可以做。所以这方面的群众基础少了不少。
所以美国强大是因为疮粉 而不是移民