因材施教 yin_1 cai_2 shi_1 jiao_4

Teachers and Parents, when teaching, ought as far as possible to teach students according to their abilities. – Confucius

Dedicated to my dear daughter who made me re-learn math, view the stuff in a different perspective, made me realize that she has her own way to learn math, and made me know how to make her understand what I understand; while sometimes also made me be puzzled quite a bit of her mistakes.

Don’t give up! Just like an English teacher is always saying that you don’t like reading is because you have not found a kind of books that fit you. Same with math. You don’t like it because you have not found a way of dealing with it.

Parents, you need to learn math first and then learn how your child think second. Then put these two together, you can help them.

Parents, don’t be lazy! You might think there are enough tutorial stuff online out there. That is exactly the problem we have in this information era: too much information. You cannot count on a 10-year-old kid to sort out what he or she needs quickly, not mention about to grasp all the stuff s/he goes over.

My purpose is to help more American kids like my daughter in math. I’ve just started working on this project from tutoring my daughter. I will constantly add and edit my posts here and I welcome your comments and suggestions. English is not my first language and I would also highly appreciate it if you can point out my mistakes.

In addition, my elder daughter Grace who excels in math is happy to join this cause and offers math tutoring for students from 6th – 12th grade.

I use overleaf as math editor, a free online version of Latax.

**What math study does to our kids?** It makes them calm down, be patient, apply what they know, think harder, and figure out what they don’t know. Yes, it makes them struggle. But after this struggle, they will be able to handle more complicated issues and their hearts will be filled with solid happiness.

Math also includes a lot of methodological and philosophical ideas which can surely shed light in our life. For example, **the distributive property** tells you how to change a multiplication into an addition, downgrade a higher level problem into a lower level issue, therefore it is easy to understand and calculate. Reverse the problem, factoring is to change an addition into a multiplication. Hence, you speed up the calculation. This is really a life time lesson: how many times have you had such a situation where you need to simplify the issue at hand or you need to speed up to finish your task / to duplicate some factors to start up your business.

Have you noticed that your child try to figure out everything in his or her head without resorting to a pen to write down knowns and unknowns on a paper? Have you noticed that your child have got bombed with a bunch of new concepts all at once? This is the way of the US math teaching. I feel sad for our kids who study this abstract yet far-reaching subject in this way, feeling frustrated and having to drop off eventually in middle or high school level.

The US way of teaching is very different and sort of intimidating. I remember we started from linear, then quadratic, then exponent etc step by step in middle school in China. Then we went back to learn about domain and range. In the US, the teacher started from domain and range by throwing all kinds of functions onto kids. To understand domain and range of a quadratic function can be very confusing before kids know about the quadratic functions. The questions ask kids to figure out some patterns of each function family: the general graph of, the effects of coefficient and the constants by typing the functions into a website and looking at the graph shown up.

Somehow, I can see why many kids drop off their math track in middle school or high school. The stuff is given to you all at once, yet nobody spends time driving each concept home with you. I can feel our kids’ frustration: those graphs don’t make any sense to some of them and they do not know the meaning of knowing the patters.

Having said the above-mentioned problems in the US math teaching, I have to confess the math education in China has its fails as well. From my own experience, I feel the math education in China focus too much on logic in terms of why and overloaded practice in terms of how. Well, why and how are the most important parts, but these two focuses have made students miss the intuitions and imaginations. In short, it is like our philosophy Confucianism or Chinese chess trying to put our heads in a strictly ordered enclosed circuit. I still remember I resisted very much in learning number theory, set theory, and game theory when I was in Ph.D program. However, when I see my children have no difficulty in transferring numbers between digit and binary and other bases, I have to confess the US system is an open one with its own advantages.

Different ways of teaching have brought up different capabilities. In China, the math capability distribution is a normal distribution: majority fall in the middle and few people fall in bad and extraordinary ranges. In the US, a few students are extraordinary in math. Most people fall behind.

Confucius provided a solution for us: Teachers, when teaching, ought as far as possible to teach students according to their abilities. For majority, don’t give up and apply China’s way of teaching. For a few with math intuitions, apply the US way of teaching.

Yes, the US is pushing individualized education. But a teacher has to take care of several students at different levels. Parents, take on this responsibility, schools are only partners of your kids’ education. You are the main educator for your own children.

**a revolutionary idea passes through three phases:**