小孩子应该记住乘法口诀表吗？ [美国媒体]

-------------译者：yearning-审核者：糯米团子------------



if yes kindly provide the upper limit .

如果答案是“应该”，那么背到多少乘多少合适呢？


-------------译者：地瓜1994-审核者：糯米团子------------

Pablo Solis Math PhD and friend of algebra and geometry
Written Jul 26 2014
Multiplying numbers in an efficient way will form the basis of higher reasoning and problem solving skills for children and such skills will undoubtedly serve them well in the future.  Many other answers have expressed similar ideas and I largely agree with them.
I mainly wanted to point out that some memorization is unavoidable but Keith Devlin points out in his book the math instinct that learning multiplication for numbers from 1 to 10  (potentially 100 different multiplication problems) can be reduced to a few rules and just 10 multiplication problems:
1) you can multiply numbers in either order e.g. 3 x 5 = 5 x 3
2) the answer to 1 x n is n and the answer to 10 x n is n0 (that is add a 0 to the end of n e.g. 10 x 7 = 70)
3) 2 x n can be handled by your knowledge of even numbers 
4) 4 x n can be handled by applying 3) twice
5) 3 is small enough to answer 3 x n by performing the sum n + n + n
6) 5 x n follows a simple pattern 510 15 20 25 ..
this leaves the following multiplication problems for strict memorization
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
7 x 7 = 49
7 x 8 = 56
7 x 9 = 63
8 x 8 = 64
8 x 9 = 72
9 x 9 = 81
actually with a somewhat creative rule you could in principle reduce this to just the squares 6 x 6 7 x7 8 x8 9 x 9 but that's probably over kill.
The point is memorizing everything is of marginal use later on in life and it misses an opportunity to leverage one's knowledge of counting and addition. 
Said another way I think the real pay off to learning (notice I said learning and not memorizing) multiplication is that it can be a stepping stone towards useful high powered thinking.  Such thinking doesn't come from having memorized a large database of unrelated facts. It comes from having a small collection of facts together with different skill sets that you can use to decompose a problem.

巴勃罗·索利斯（Pablo Solis）擅长于代数和几何的数学博士
写于2014年7月26日
将数字相乘是一种有效的方式来使儿童形成更高的推理思维和解决问题的能力，而这些技能在未来无疑将很好地为他们服务。其他答案很大程度上表达了类似的想法，并且我同意他们的观点。
我主要是想指出一些记忆是不可避免的但基思·德夫林在他的书中指出学习从1到10乘法形成的数学直觉(可能存在100种不同的乘法问题)标点符号啊亲，这么长读完要死人的”可以简化10以内乘法问题的运算规则。
1)如您可以用数字顺序。3 x 5 = 5 x 3
2)答案1 x n = n和10 x n的答案是n0(也就是说添加一个0到n例如10 x 7 = 70)
3)2 x n可以处理你偶数的知识
4)4 x n可以通过应用3的方法两次简单处理
5)3是足够小到回答3乘与x等于执行总和n + n + n
6)5 x n遵循一个简单的模式5、10、15、20、25，..
这使得剩下的乘法问题需要严格的记忆
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
7 x 7 = 49
7 x 8 = 56
7 x 9 = 63
8 x 8 = 64
8 x 9 = 72
9 x 9 = 81
实际上有些有创造性规则原则上可以减少这种平方6 x 6，7 x7，8×8，9 x 9，这可能有点过了。（过度处理）。
重点是，记住了这些，在以后生活中可以随时使用，而不必采用计数法或者复杂的加法手段“
从另一种方面来说我认为真正的回报(注意我说的学习而不是记忆)乘法学习它可以是一个跳板去做一些高效率的思考。这种想法不是来自有于记忆了一个不相关的事实数据库。它源自于一个采用不同技巧且真实有效的小集合，你可以用它拆分问题。

 -------------译者：s555555555-审核者：糯米团子------------

Carter McClung High School Teacher
Written Apr 16 2014 R26; Upvoted by Anne W Zahra M.Ed. Language Teaching
Yes. Yes. Yes. As a teacher I can't emphasize this enough.

对对对。作为一名老师我对这强调的不能再强调了。

I am typically anti-memorization. In the calculator/Google age if you can look it up it's usually not worth memorizing. Math is not about memorization. It is more important for them to understand the pattern behind the multiplication table than to memorize it.

我是一向反对死记硬背的。在计算机网络时代，如果你动动手指就能计算好，那记下来就不怎么值当了。我想说的是数学并不以记忆为主，它更多的是要你领会你记下的这些公式表格背后所包含的规律。

S。o why memorize? if students don't have basic multiplication facts memorized it becomes difficult for them to find patterns and understand otherwise simple concepts down the line because they're chained to a calculator bogged down on the simplest examples. It also makes doing basic division and fractions a real pain.

所所所以问为什么要去记忆呢？假如学生们连最基本的乘法例子都记不住而沉溺于计算器的话，那靠什么领导他们去理解这些基本的概念，更别说除法分数这些更进一步的概念了。

Students should memorize addition 0 through 10 and multiplication 0 through 10. (Later students should memorize the squares 0 through 10.) Beyond this is pretty worthless in the calculator age.

学生们应要记住0-10的加法和乘法就够。（这样他们自然就记住了0-10的平方。）再多就不合时宜了。

You don't have to drill and kill. There are apps for that. There are games. There are fun ways to do it... but they have to learn it.

你也不用去死读书，现在有很多软件很多游戏很多种方法帮你背下来，只要你肯学。

Yes you need to build intuition. Yes you need to give application. Don't kill the joy but please please for the love of all that is good teach your children their multiplication tables.

要建立对数学的感觉、要去试着运用数学、要保持兴趣，最最重要的是爱上数学。去教你们的孩子乘法表吧。

-------------译者：鹤。-审核者：龙腾翻译总管------------

Joel V Benjamin I'm still learning more than I'm forgetting ... I hope.
Written May 10 2015
No.
They should learn a method to compute it by understanding the relationship between numbers.
They should realize that 6*7 is 7 more than 5*7 and twice as much as 3*7.
After repeatedly computing simple products they'll learn them by heart.
They'll end up hsving memorized the multiplication table but would have done it in such a way that they will retain their appreciation of the relationship of numbers to each other.

不。
他们应该通过理解数字之间的关系来学会一种计算的方法。
他们应该明白6*7比5*7多，是3*7的两倍。
在重复地计算出简单的乘积后，他们会熟记这些。
最终他们会记住乘法口诀表，但是是通过记忆数字之间奇妙的关系而记住的。

-------------译者：s555555555-审核者：糯米团子------------

Kristina Kučanda PhD student in (nano)chemistry; welcoming suggestions for a better name/surname
Written Jul 24 2014
They should learn them (up to 10×10). But preferably not by rote memorization but through being explained and shown what multiplication is (in relation to addition) through games and with various approaches so there's something for each child's learning style.

他们应该学的(10×10以内就好。不要只死记硬背，要去解释和举例乘法到底是什么（比如阐明和加法的联系，通过游戏和其他各种各样的方法让孩子们学好概念。

I couldn't memorize them as tables but I did mental addition and subtraction more and more quickly until it gradually transitioned into recalling the values right away. So at that stage I was initially testing among the bottom of the class but perfectly by the end of it; and stayed top of the class in maths til the end of primary school "even" doing well in maths competitions. A quite successful graduate student in chemistry now although I admit I would never be able to be a mathematician (but my friends maths students tell me that I deal with numbers more than they do).

我没去背乘法表，不过随着我的心算加法和减法越来越快，乘法表上的东西算的越多自己自然就记下来了。 所以在那个时候，我的数学一开始很渣在班里排倒数， 但到了小学毕业时我的数学却已经名列前茅，“甚至”能在数学竞赛中表现尚佳。 现在的我是一名化学研究生，虽然我承认我永远不会成为一名数学家（但我数学系的朋友告诉我，我处理数字的能力比他们还好）。

-------------译者：gretino-审核者：糯米团子------------

Emily Czinege Bioinformathematician
Written Sep 24 2013
Yes.
I know maths isn't about memorizing rules and tables. I like maths and I'm fairly good at it but I never did my best at them in school and I'm still really bad at multiplication and addition. Maths is hard enough that you don't want to be worrying about simple calculations too. Especially if the kids will be dealing with linear algebra later they will lose 90% of their time with simple calculations.

Emily Czinege 生物信息学数学家
于 2013年九月二十四日发表
应该。
我知道数学不在于记住规则和表格。我喜欢数学，而且对它还算拿手，但是当我在学校的时候我的数学成绩并不是非常好，而且即使现在我也仍然不擅长于加减乘除。数学本身就已经非常难了，你也不可能想被简单的计算麻烦到。特别是那些小孩将来会要面对代数等等困难学科，（如果他们不记住乘法表）他们会在简单计算上浪费百分之九十的时间。

-------------译者：兔子无敌-审核者：糯米团子------------

Gavin Sinclair Mathematics teacher
Written Apr 5 2014
Having addition and multiplication facts in your head helps you to understand those processes. If you're no good at processing whole numbers you're disadvantaged when you learn about fractions and then algebra.

在头脑中拥有加法和乘法的事实会帮助你理解这些计算。如果你不善于计算整数，你就会在学习分数时处于劣势地位，然后是代数。

Learning mathematics is a process of building layers of knowledge and understanding. Those layers have to start somewhere and it should be a solid foundation. Number facts are a solid foundation. 

学习数学是一个建立知识和理解层次的过程。这些层次必须要在某处开始，它应该是一个坚实的基础。数字表就是坚实的基础。

That is my opinion as a mathematics teacher.

这是我作为一名数学老师的看法。

 -------------译者：magicqueen99-审核者：糯米团子------------

Jon Ziegler sent my home schooled math kid to Cambridge
Written Jul 28 2014
There are many children who cannot memorize the multiplication tables for various reasons.  Should they learn to multiply easily and quickly at some point?  Yes!  If they like math and are good at understanding mathematical concepts should they be prevented from going any further until they've memorized the multiplication tables?  No!

很多孩子因为各种原因记不住乘法口诀表。他们应该在某个时候学会轻松快速地做乘法吗？对!如果他们喜欢数学，并且善于理解数学概念，那么在他们记住乘法口诀之前就不应该继续学习数学了吗？不!

So learning is good.  Memorization works for some but understanding and use leads to remembering which is better.  Moving on to more complex math also motivates becoming quick at arithmetic something that's important for some students.  Picking the one and only true way and making all students conform is just bad teaching.

所以，学会方法很重要。死记硬背有时候管用，但是理解了以后再去记忆就更好。这样的话，在学习更复杂的数学时，也会激励学生算得更快，这对有些学生来说很重要。拘泥于一种而且是唯一一种正宗的方法，然后让所有学生仿效，这种教学很糟糕。

-------------译者：Linsanity2018-审核者：糯米团子------------

Paul Briercheck
Written Jul 23 2014
Without basic 'math facts' memorized future success in mathematics is improbable. Fractions factoring distributive multiplication division etc. become frustrating and discourage effort in any further endeavors. Calculator use is acceptable AFTER fundamental understanding is ensured.

如果没记住那些基本的“数学事实”，将来就不太可能在数学方面取得成功。
以后要进一步学习分数、因式分解、乘法分配律和除法等内容时就会感到灰心丧气。
使用计算器是可以的，但应该是在对数学的基本理解得到保证之后。

-------------译者：bla123-审核者：糯米团子------------

Matthew Van Buskirk Software Engineer
Written Jul 23 2014
I didn't see a lot of no's so figured I'd weigh in. As an engineering major in college I took a lot of math. I found that the higher math classes were just as easy for me if not easier than lower ones. As a kid I was forced to sit out in a hall because I could not memorize the multiplication tables. Still can't. Doing the problems over and over again gave the ability to break down math problems. I couldn't memorize all of them so I memorized a few which was agony. If you talked to my teacher at the time she would have said I was struggling with math. Talk to my mom and she would have told you that I had a better grasp on math than my older brother 4 years older. The focus on memorization at that age is bad. Teaches the wrong thing. 

我没有看到什么反对意见所以我想说出一些自己的意见。我大学念的是工科，所以学了很多数学知识。我发现高等数学对我来说不难，但对其他等级较低的人来说是个大问题。当我是个小孩的时候，我曾因无法记住乘法表被罚坐走廊。即使这样我还是没办法记住。一遍遍处理问题给了我去攻克数学难题的能力。我无法记住全部，但我还是尽力去记住了一部分。如果你那时问问我老师，她可能会说我不擅长数学。但我妈会说我的数学理解能力比我那个大4岁的哥哥要好。。在孩子小时候就着重让他们记忆不太好，那是一种错误的教学方法。

It doesn't help with higher math. I'm living proof of that. A kid needs some way to come up with those numbers but memorization is not the only answer. Speed test for how quickly they can answer is ridiculous. Some can memorize it fine but the idea it is need is just not true. You should be focusing on the ability to manipulate numbers at that age not memorization. By the time they get to higher math it's too late for some kids.

记忆乘除表对高等数学又没什么用。我就是一个活生生的例子。孩子需要一些方法帮助他们去联想数字，死记不是唯一的方法。测试他们多快能说出答案是愚蠢的。虽说一些孩子可以记住，但这种方法是不对的。应该着重让孩子去运用数字而不是单纯的记忆。这种方法来教孩子数学，等到他们长大了学高等数学的时候早就晚了（错过培养数学能力的最佳年龄）。

-------------译者：Linsanity2018-审核者：糯米团子------------

Vasant Prabhu Software Engineer chess lover
Written Jul 21 2014
Yes and the earlier the better. My school math teacher (Mrs Gazala Shaikh)made me learn tables upto 25 by heart by 4th standard (grade) age 10 roughly. She used to make me (and my whole class ) recite the tables once a day. And I am grateful to my teacher for this.
I am 28 today and I still remember the tables perfectly upto 25(and somehow manage till 30 too). I am not a brainy IITian or a scientist so I  believe anyone can do it.
Memorizing tables have helped me a lot making faster calculations in competitive exams and always given me a edge over competition.

是的，而且越早越好。
在我四年级（大约十岁）的时候，我的学校数学老师（加扎拉·沙伊克女士）让我用心记忆25以内的乘法口诀表。
她曾经让我和我们全班同学每日背诵一遍乘法口诀表。我为此对她心怀感激。
现在我28岁了，依然还完好地记得25以内的（甚至是30以内的）乘法口诀表。
我并不是一个聪明绝顶的IT工作者或者科学家，所以我相信任何人都能做到这一点。
记住乘法口诀表让我获益良多，使我在竞争激烈的考试中有着更快的计算速度，常常在竞争中给我带来优势。