Title:Why it's so hard to help with your kid's math homework

Two years ago I walked into a car rental return center in Charlotte and interrupted Adrianette Felix mid-rant.

两年前，我走进了夏洛特的一个汽车租金回收中心，打断阿德里安内特·费利克斯·里坦特。

"I can't even help my own child do her homework, it's so frustrating, and I feel so stupid," she said. "What kind of mother can't understand first-grade math?"

“我甚至连自己的孩子都帮不上做家庭作业，这太令人沮丧了，我觉得这么愚蠢，”她说，“什么妈妈不能理解一年级的数学？”

Felix and I spent the next half-hour engaged in a spirited discussion about the state of math education in America; how we got here, why it's changed; and where experts on math education hope it's taking us.

费利克斯和我花了半小时，对美国数学教育状况进行了热烈的讨论；我们为什么来这里，为什么会改变；数学专家希望它带着我们。

The simple answer to why math education has changed, "Common Core State Standards," is only part of the story. Math teacher Christopher Danielson outlines the rest of the story in his book, "Common Core Math for Parents for Dummies," and it goes something like this: Math education in America has evolved in response to concerns about our international competitiveness, first with Europe, and later, with Russia and its space program. Consequently, American math education prioritized the education of professional scientists and mathematicians who could get satellites in orbit and send men to the moon.

简单回答为什么数学教育改变了“共同核心国家标准”，这只是故事的一部分。马特老师克里斯托弗·丹尼尔森在他的书《父母为杜米做父母的共同核心数学》中概括了其他故事。美国的数学教育已经演变为回应人们对国际竞争力的担忧，首先是欧洲，然后是俄罗斯及其空间方案。因此，美国的数学教育优先教育专业科学家和数学家，他们可以把卫星送入轨道并送人登月。

While we were busy chasing those lofty goals, we failed to educate most students in the basic foundations of math. To rectify this, the education pendulum swung back in the other direction, toward rote memorization. Cue the era of multiplication-table work sheets and timed math facts, tasks that still make up the bulk of elementary school math homework assignments.

当我们在追求这些崇高目标时，我们没能教育大多数学生数学的基本基础，为了矫正，教育钟摆向另一个方向，转向死记硬背。缩短乘法表工作表和时间计算的事实，这些任务仍然构成小学数学作业的大部分。

Between 1989 and 2009, in large part because of the advent of No Child Left Behind, state standards and the testing necessary to measure states' progress, math education became what Danielson refers to as a "mile-wide, inch-deep curriculum." We teach many topics in each grade but at a superficial level. Math education became a series of skills served up in bits and pieces but never as part of a unified, mathematical whole.

1989年至2009年，主要是由于没有儿童落伍、国家标准和衡量州进步所必需的测试，数学教育成了Danielson所称的"全哩深渊课程"。我们在每个年级都教授很多课题，但浅显。数学教育变成了一系列技能拼凑而成的，但却从未成为统一数学整体的一部分。

Notably, we failed to give American children math sense, a natural and instinctive dexterity with numbers.

值得注意的是，我们没能给美国孩子们数学感觉，一个天生的和本能的熟练程度和数字。

I was one of those children, despite having been educated in the top-ranked public school district in Massachusetts (Dover-Sherborn Regional High School). My mathematical education was characterized by drills memorization and instructions to accept abstract axioms and mathematical order of operations as "simply how it's done," concepts, my teachers promised, I would understand later. I dutifully followed their directions, memorized the steps and regurgitated on demand, but the understanding I had been promised never materialized. What I got instead was a raging case of math anxiety and the belief that I am not a math person.

我是其中一名儿童，尽管在马萨诸塞州名列前茅的公共学校（多弗-谢尔本地区高中）接受过教育。我的数学教育的特点是记忆训练和指示接受抽象公理和操作的数学秩序，就像“干得怎样”的概念，我的老师答应，我以后会理解。我恪守他们的指示，记住步骤，按要求重新入伍，但是我所承诺的理解从未兑现，相反，我得到的是激怒了数学焦虑，坚信我不是数学家。

It wasn't until my mid-40s, when I retook Algebra with my middle school students and a gifted educator, that I discovered the truth: I had not failed at math; my math education had failed me.

直到我40年代中期，当我和我的中学生和天才教育家反驳阿尔代布雷纳时，我才发现了真相：我数学没有失败；我的数学教育使我失败。

With rare exception, most American children still receive a similarly counterproductive math education, one that produces adults who can recite multiplication tables but can't make change when the cash register isn't working, let alone view math as poetry.

除了极少的例外，大多数美国儿童仍然接受同样适得其反的数学教育，这种教育产生能够背诵乘法表的成年人，但在现金登记册失职时，却不能改变。更不用说数学是诗歌了.

"The highest achieving kids in the world are the ones who see math as a big web of interconnected ideas, and the lowest achieving students in the world are the kids who take a memorization approach to math. The United States, you won't be surprised to hear, has more memorizers than any country in the world," said Jo Boaler, professor of mathematics education at Stanford University, in a phone interview.

"世界上成绩最高的孩子是那些认为数学是一张充满相互关联思想的大网站，而世界上成绩最差的是采用记忆方法计算数学的孩子们。斯坦福大学数学教育教授乔·博阿勒(Jo Boaller)在电话采访中说：“你听到的美国并不奇怪，他们的记忆比世界上任何一个国家都多。

This chopping up of mathematical concepts, asserts Boaler, is where American math education fails children, and why Felix gets frustrated by her daughter's math homework. Felix learned how to memorize, while her daughter is learning something much more valuable and useful: Number sense, relevance and mental flexibility.

波勒说，数学概念被破坏了，这是美国数学教育失败的地方，为什么费利克斯被女儿的数学作业所挫败。费利克斯学会了如何记忆，而女儿正在学习一些更有价值和更有用的东西：数量意义、相关性和精神灵活性。

When the average teacher has about 200 separate math concepts or skills to teach in a given year, the connections between each piece disappear. "The kids don't get to see them, and most teachers don't know about them, either," Boaler says. "When teachers are armed with the research about brain growth and [the reality that] everybody can learn math, it changes what they do. Teachers that are empowered with this research are doing amazing things. Really amazing things."

当普通老师在一个特定年份内有200个单独的数学概念或教学技能时，每篇文章之间的连接就消失了。“孩子们看不到他们，大多数老师也不知道这些概念，”博勒说。当老师们对大脑发育的研究以及每个人都可以学习数学的现实进行研究时，这就改变了他们的工作，通过这项研究获得授权的教师正在做令人赞叹的事情，真的是件了不起的事。

Math coach Tracy Zager agrees. "It's a phenomenal time to be a math teacher. We are in a time of great revolution and excitement, moving away from rote memorization and toward an understanding of process. It doesn't mean that answers don't matter, and it doesn't mean that skills and memorization don't matter, but when a student does something wrong, we want them to understand why," she said in a phone interview.

玛特教练崔西·扎格也同意：“现在是一个了不起的体育老师的时候。我们正处在一场大革命和激动的时代，从死记硬背走向对过程的理解。这并不意味着答案无关紧要，也不意味着技能和记忆没有关系，但当一名学生做错事时，我们要他们明白为什么，"她在电话采访中说。

In her book, "Becoming the Math Teacher You Wish You'd Had," Zager writes, "Math is not about following directions, it's about making new directions." So I emailed her to ask about the direction she would take math education.

扎格写到：“成为数学老师‘你希望拥有它’，”玛莎在书中写道，“数学并不是关于方向的，而是关于新方向”，所以我给她发电子邮件问她接受数学教育的方向。

"We have to undertake the real work: High-quality, sustained, classroom-based professional development," she said. "Doing it systematically would take money and time and belief in teachers as professionals."

她说：“我们必须从事真正的工作：高质量、持续、基于课堂的专业发展。

While teachers, administrators and education policymakers do battle over Zager's question, Felix and her daughter need help today, with tonight's homework assignment.

当教师、管理者和教育决策者对扎格的问题展开斗争时，费利克斯和她的女儿今天需要帮助，完成今晚的作业。

For that kind of practical advice, I returned to Danielson and his book, "Common Core for Math for Parents for Dummies." Danielson suggests that parents stop giving kids easy answers and instead focus on asking these five essential questions:

为了得到这种实际的建议，我回到丹尼尔森和他的书《家长数学的共同核心》中，丹尼尔森建议父母停止给孩子简单的答案，而是专注于询问这五个关键问题：

"Why?" and "How do you know?"

"为什么"和"你怎么知道？"

"What if?"

"如果可以，怎么办？"

"Is it good enough?"

"它够好吗？"

"Does this make sense?"

"这有用吗？"

"What's going on here?"

"这里发生什么事了？"

The questions, "Why?" and "How do you know?" require children to construct arguments, to justify their answers and to think about the reasons their answer may be correct. It's not enough to know that 8 + 4 = 12, as Danielson writes, students must be able to articulate how they might figure out the sum of 8 and 4 if they do not automatically know the answer.

"为什么"和"你怎么知道?"的问题要求儿童提出论据，为其回答辩解，并思考他们的回答可能正确的原因。正如Danielson所写的那样，仅仅知道8+4=12，学生如果不能自动知道答案，必须能够说明他们如何计算8、4。

"What if" is a fantastic question to ask in any context, but in math, it's particularly important. "What if" is at the root of play, experimentation, innovation and exploration. "What if" allows us to push students to contemplate questions beyond their immediate understanding and can fuel curiosity, deeper learning and intellectual breakthroughs.

“如果”是一个很美妙的问题，无论从什么角度来说，但在数学上，它尤为重要，“如果”是游戏、试验、创新和探索的根源。“如果”能让我们让学生超越他们眼前的了解，思考问题，从而激发好奇心、更深层次的学习和知识突破。

The question "Is it good enough" gets at the concepts of estimation and precision. Is it good enough to say that .99 repeating is close enough to 1 to say that they are equal? Asking this question requires that students pay attention to units and attend to precision both numerically and linguistically.

“这还不够好”从估计和精度的概念上来看。说99个重复已经足够接近1说它们是平等的说法是否足够好？问这个问题需要学生注意单元并注意在数字和语言上的精确性。

"Does this make sense?" is a great question to ask at every step of the process, from choosing a path forward ("Does it make sense to add here?") to the final answer ("Does that answer make sense?") and gives kids the opportunity to pause, take stock and exercise judgment. Sometimes, of course, the answer to this question is going to be, "No," and wrong answers can be just as useful as the right ones, Danielson argues, because, "A classroom climate that only values right answers is less likely to encourage students to persevere."

"这有用吗？"这是一个重大问题，需要问及从选择前进的道路（"在这里增加是有道理的?"）到最后答案（"回答是有道理的?"），让孩子有机会停下来，做总结和做判断。当然，这个问题的答案将是"不"，错误的答案可能与正确的答案同样有用，达尼埃森说，因为，"一个只重视正确答案的教室氛围不太可能鼓励学生坚持下去。

Finally, the question, "What's going on here?" helps kids look for the underlying structure of a problem. For example, "If you know that n is a whole number, then 2n is an even number and 2n + 1 is an odd number. What's more, the expression 2n + 1 represents all odd numbers. This is the power of looking for and making use of structure - representing infinitely many things in a single short expression."

最后，问题是"这里发生了什么?"，帮助孩子寻找问题的基本结构，例如，"如果你知道n是一个整数，那么2n是一个偶数，2n+1是一个奇数。再者，2n+1表示所有的奇数数，这就是寻找和利用结构的能力，这代表了一个简短的表达中的无穷多事物。

I had given Felix a copy of Danielson's book after we first met, so I called her to find out how she and her daughter are faring in math.

我第一次见面之后给费利克斯写了一本Danielson的书，所以我打电话让她了解她和她的女儿在数学方面是如何活动的。

"Oh, honey, we are doing fantastic. That book was fantastic," she said. "My daughter is doing great in math, and I can help her when she needs it. Plus, I get to feel smarter than a third-grader."

“哦，亲爱的，我们做得很了不起。那本书太棒了，”她说，“我的女儿在数学方面做得很好，我可以帮助她度过她需要的时候。而且，我比一个三年级的学生更聪明。

This is where successful math education starts - with adults who know what questions to ask and who have the skills to help children discover their own solutions.

这是成功的数学教育开始-成人，他们知道要问哪些问题，以及谁具备帮助儿童找到自己解决办法的技能。

Lahey is a teacher and the author of "The Gift of Failure: How the Best Parents Learn to Let Go So Their Children Can Succeed" and a forthcoming book on preventing addiction in children.

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