Tag Archives: education

Degrees and angles | 角度

Today in the fourth grade weekend lesson we learned about angles📐 and degrees. We explained what degrees was first🥇 because angles are classified using degrees📏. Degrees were discovered by Egyptians. They invented the degree symbol ° and also came up with the 360° circle⚪.  There is an interesting history of how they connect the movement of the Sun with time.   They first divided a year into 360 days, noting that the Sun moved in a circle. Around 1500 BC Egyptians divided 24 hours⏳, though the hours varied with the seasons originally. Then the Greek astronomers made the hours equal. About 300 to 100 BC the Babylonians subdivided the hour into base-60 factions: 60 minutes an hour and 60 seconds in a minute.

We use degrees to measure angles. An angle is a figure formed by two rays🛴 called sides of the angle. In geometry there are three types of angles: an acute angle between 0 and 90 degrees, right angle a 90 degree angle, and an obtuse angle between 90 and 180 degrees. In 1936 a clay tablet was found buried at Shush (Khuzestan region of Iran🌏) some 350km from the ancient city of Babylon on which was inscribed a script that was only translated as late as 1950. The text provided confirmation that the Babylonians measured angles using the figure of 360 to form a circle. The Babylonians knew that the perimeter of a hexagon was exactly equal to six times the radius of a circumscribed circle. This is why they chose to divide a circle in 360 parts⚪. If we did not discover degrees or angles we would not be able to build anything properly🧱. So if we tried building a house without degrees or angles the house would collapse🏚.

We will talk about triangles next time.

Welcome to our New Google Classroom!!😃

Hello everybody!😃 Welcome back to Magic Math Mandarin.  Since we are staying home because of covid-19, we brought our classes to google classroom so our students can keep on learning even during this pandemic👩‍🏫. Now we can all communicate with each other online💻. In this classroom we will be learning Chinese🈷, math➗, and programming👩‍💻. Our teachers will put new assignments everyday about each topic.  If you would also like to join our wonderful classrooms then here is the class code mtxl6j4

Remember to stay home and don’t get sick!😷 Please join our classroom today!👍💖


Ipython Shell Keyboard shortcuts 键盘快捷键 (Kuàijié jiàn)

In this past weekend’s coding class we practice keyboard ⌨ shortcuts in the interactive Python shell (Ipython).

Since most of the students are learning typing ⌨, practicing these keyboard shortcuts actually help them learn typing by reinforcing memory of where the keys are.

The keyboard shortcuts allows you to minimize finger movements on the keyboard, which means you don’t even have to lift your hand ✋ for the “Backspace”, ‘Home’, ‘End’ or arrow keys (most of the time).    Spend 15 minutes per day practicing these.  Pretty soon, you will be a fast coder.


keystroke Action
Ctrl-a Move cursor to the beginning of the line
Ctrl-e Move cursor to the end of the line
Ctrl-b or the left arrow key Move cursor back one character
Ctrl-f or the right arrow key Move cursor forward one character

👦Text Entry

Keystroke Action
Backspace key Delete previous character in line
Ctrl-d Delete next character in line
Ctrl-k Cut text from cursor to end of line
Ctrl-u Cut text from beginning of line to cursor
Ctrl-y Yank (i.e. paste) text that was previously cut
Ctrl-t Transpose (i.e., switch) previous two characters

🐞Command History

Keystroke Action
Ctrl-p (or the up arrow key) Access previous command in history
Ctrl-n (or the down arrow key) Access next command in history
Ctrl-r Reverse-search through command history


Keystroke Action
Ctrl-l Clear terminal screen
Ctrl-c Interrupt current Python command
Ctrl-d Exit IPython session

The shortcuts are referenced from  Python Data Science Handbook.   As its author Jake Vanderplas says, these shortcuts are not inherent in Ipython shell itself, but are based on GNU Readline library.

秋天好 | Autumn is good

Today in class we talked about autumn (qiū)(tiān) in this weekend’s Chinese lesson.

magic math mandarin

Fall is here.  Fall is good.
Blue sky and white clouds.
The baby looks up and laughs.

Besides 中文, we are also working with other organizations to help children with computer programming 编程.


zero, one and two | 零,一,二

It is not easy for a young child to comprehend multiplication by 1, as how they are taught in school is often the robotic multiplication table.   She or he can very quickly answer mutiplications by 2, or 3.    Because of this, questions like “what is the product of 1,2, 3, 4” (i.e. 4 factorial) can get a wide range of answers because the number “1” confuses the young mind.

Pychologist says that an infant learns the number 2 before the number 1.   And we can see why: with 2, there is something to compare against, like two fingers.  If there is only one finger, there is no variation, it is confusing.

When we teach multiplication, don’t forget to show that math is an integral part of the real world around us.   It is invented to simplify addition.  Multiply by 1 means just the thing itself.  Multiply by 2 means adding two of this thing together.  Multiply by 3 means adding three of the thing together.  The thing can be a bag of candies or the footage of a home.

Finally, we should show children how to use computers (not calculators) to do computations.   While a question like “give me the sum from 1 to 199” can be solved within seconds with math tricks, a slightly different question “give me the product from 1 to 199” won’t work with the same trick.  But if you know how to make the computer do the job, you can still answer it within seconds.


Parents and students in China – impressions from our summer trip | 中国家长和学生- 暑期中国行印象

We always knew that Chinese parents and teachers are dedicated to education.   Even so, we were still amazed by how Chinese teachers and parents are working hand-in-hand pushing the boundaries of education.

We don’t necessarily agree with everything they do, such as the bias towards solving test problems in classes.  But there are a great deal more things we agree or appreciate, such as relentless hard work and practice than ones we don’t appreciate.

Below is a snapshot of a first-day summer class for seven year old children.   Just look at how intently the parents are.   Some parents sat through the entire class to take notes, and some sat in the lounge in the corridor chatting about schools or doing various things while waiting for their kids.    The temperature was about 100 degrees outside.

Magic Math Mandarin

The level of dedication is astonishing. 

From time investment perspective, at least one family member, whether mother, father or a grandparent, spends as much as 20 hours and up each week on their children’s education.   

From the money side, summer/winter break, weekend, or after-hour schoolings are privately run, which aren’t cheap.   Some well-to-do ones have spent hundreds of thousands (measured in US dollars) before high school.  Some bold ones even send their kids, sometimes as young as eight or nine years old, to overseas private boarding schools in exclusive locations in Switzerland, the UK and other places.    Poorer families still pay for various lessons to make sure their kids are as nourished as possible in education.   For those very constraint in resources, such as those parents who must work 7 days a week, we saw their kids studying with video lessons on mobile phones in cram corners instead of hanging out loose.  

The primary motivation is the quality of survival for the next generation: to get into top middle schools, top high schools, top universities, great social network and ultimately great jobs in adulthood.   Parents start count down of the number of days till college entrance exam even at primary schools.   Kids routinely study until mid-night since third grade, and don’t get a day off until winter/summer break.

On the contrary, in United States, students and parents are heard asking for less homework and more free time to play.    Over the last two decades, the quality of education, as measured by test scores, have steadily declined in the US.   Less work is a key factor.  However, a deeper question is: why do American parents and kids want less work from schools?   These questions need to be answered by representative data, not ideaologies.

python numpy basics | 基础 python numpy 1

Tonight our class played together numpy basics and math.  We put together a numpy basics notebook:

Programming by trial and error is a great way for kids to learn not only programming but also math. — this should play a bigger and bigger role in children’s day to day learning.  玩编程也帮助学习算术。

Somehow I have a feeling that learning long division in this day and age is wrong.  在这个时代还学长除法那就不对了。

Go ahead and tinker with the code in the notebook. Nothing will break, we promise 🙂

To see a world in a grain of sand | 从沙粒看世界

Professor ShouCheng Zhang “passed away”. He is forever with us, seeing a world in a grain of sand, holding infinity in

这是张首晟所有视频里我们最喜欢的一个视频。 张教授深入浅出,循循善诱。尽管已经“离世”, 张教授永远和我们在一起从沙粒看世界,把永恒留在刹那时光。

We won’t quote any physics or mathematics from the video, except the title of the lecture, originally from William
Blake, and dedicate them to Professor Zhang:

To see a world in a grain of sand
And a heaven in a wild flower,
Hold infinity in the palm of your hand
And eternity in an hour.


Chinese style education & empty basketball courts |中国式教育和空荡荡的蓝球场

I was in China this November to conduct surveys on education.  I had a few chances of sitting in some after school education programs and cram school classes, including XDF新东方, and was shocked by the amount of work Chinese kids have to do and was saddened by the way they are learning.

Let’s talk about the amount of work first.   I saw very few kids out and about any time of day except commuting hours.   Basketball courts are empty, even on weekends.   Where are all the kids?  They are in endless cram school 补习班 classes.

A middle school child routinely gets up before 7 am and does not go to sleep until midnight or after.   Middle school students stay in school until 8 pm, and work on additional homework from 8 pm till midnight.   Younger students are often working similar hours.

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