The Importance of Mathematics for AI Development

Hello everyone, I am Xiaoban’s dad.

The evolution of AI is happening too fast! Just over a month after Sora’s release, last weekend, “AI Composer” Suno made its debut.

I tried inputting Xu Zhimo’s poem “Farewell to Cambridge” as lyrics into Suno.

Quickly, the AI version of “Farewell to Cambridge” was freshly produced, and everyone can listen to it and feel the experience 👇

PS:

If you find it interesting, you can visit its experience website (https://app.suno.ai/) and play with it yourself.

AI is so interesting and powerful, what should children learn to prepare for the AI era?

This question reminds me of a piece of news we shared in our live stream not long ago.

Parents in the live stream felt that this news was significant and persuasive, and many left comments in the interaction area:

Your needs are the motivation for our work.

Thank you for your trust; today I am here to submit my homework

In the next three days, we have arranged “three sessions” to discuss elementary school mathematics.

The first session is today, my article will first outline the two main categories of learning content in elementary school mathematics: what is learned in school mathematics and what is learned in Olympiad mathematics.

Answering a question: Which children are suitable for learning Olympiad mathematics?

The second session is tomorrow, on Thursday’s main article, we will recommend a mathematics course“Hu Xiaoqun Teaches Mathematics”

Teacher Hu graduated from the Mathematics Department of Fudan University and has taught for many years at one of the “four prestigious high schools” in Shanghai, Fudan Affiliated High School. He has led experimental classes in high school and has also been a “question setter” for entrance exams at various stages from elementary to high school, making him a rare expert who understands both how to teach mathematics and how to test it.

The third session is the day after tomorrow, on Friday at 8:30 AM, I and Tiao Ma will hold a special session on mathematics planning for elementary school in the 【One Sentence East, One Sentence West】 live stream.

Everyone is welcome to click to make an appointment and participate at that time!

OK, let’s start the first session!

What is learned in elementary school mathematics?

Elementary school mathematics is mainly divided into four major sections: Numbers and Algebra, Shapes and Geometry, Probability and Statistics, and Comprehensive and Practical Applications.

Among these four modules, statistics and probability only involve basic applications, which are relatively simple and not heavily tested, so I will skip discussing them.

The other three modules are more important, and I will translate them into terms that everyone is more familiar with: Calculation, Geometry, and Word Problems.

Many children reach higher grades and may clearly know how to solve some problems, but due to calculation errors, they unfortunately lose points. Therefore, the importance of calculation in elementary school mathematics cannot be overstated.

First, it is the recognition of three types of numbers.

Secondly, it is mastering two major categories of four operations.

Calculation can easily lead to various errors, and the root cause is insufficient mastery of integer calculations.

To master integer calculations well, one must grasp two cornerstones:

One is the decomposition of numbers within 10.

This is the foundation for addition and subtraction within 20, as it involves using the ten-complement method and ten-breaking method. Decomposition must be very proficient, to the extent of being able to recite it with eyes closed. After that, all integer addition and subtraction, as well as multiplication and division, will require this foundational skill.

The other is the multiplication table, especially the multiplication part.

We group multiplication and division together because they are merely different representations of a quantity relationship.

Addition and subtraction, multiplication and division are inverse operations of each other; the proficiency of one operation directly relates to the mastery of the other operation.

The key point for decimal calculations is just one: moving the decimal point.

The key point for fraction calculations is a basic property: if the numerator and denominator of a fraction are both multiplied or divided by a non-zero natural number, the size of the fraction remains unchanged.

The simplification and common denominator in fraction calculations are both based on this property.

The geometry learning in elementary school can be roughly divided into the following parts.

Due to the developmental bottleneck of students’ logical abilities, elementary school geometry is mainly a preparation for the plane geometry section of middle school mathematics. It may seem broad, but most of it consists of knowledge points—basic elements of plane and solid geometry, which are neither deep nor difficult.

The key to learning is to clarify basic concepts and make proper distinctions, similar to the mind map below, which is very helpful.

Most of the challenging questions in elementary school mathematics are word problems. There are many types of word problems, and combined with Olympiad mathematics, there are roughly 30 topics.

However, for all these types, the process of solving problems is four steps.

Step 1: Reading and Understanding the Problem

This step is very important; don’t rush. Through careful reading, clarify the known conditions of the problem and the questions being asked.

Step 2: Observing and Thinking

Observe and analyze the requirements and patterns of the problem, compare them with known problem types in your knowledge system, and think about the problem-solving approach.

Step 3: Exploring and Solving

This is the specific problem-solving process. When the problem is of a type you have encountered before, the requirement here is to be meticulous; otherwise, it becomes a trial-and-error process. If you encounter difficulties, you need to return to the previous step, observe and think again, and look for new ideas.

Step 4: Verifying the Answer

Verification is definitely not simply redoing the problem. Whether each problem requires verification and what kind of verification method to choose are both very important. (If you are interested in verification, please let me know in the comments, and I will write a dedicated article on this topic.)

Compared to the 30 topics, the four abilities corresponding to the above four steps are more crucial for developing children’s mathematical thinking and are key to achieving high scores in exams.

I suggest that parents grasp these four steps when tutoring their children.

What is learned in Olympiad mathematics?

There are various opinions about the learning system of Olympiad mathematics. According to GS’s classification, it can be roughly divided into seven modules:

These seven modules encompass all the content involved in elementary Olympiad mathematics. Learning Olympiad mathematics is essentially about mastering the knowledge points of these seven modules and enhancing children’s thinking abilities during the learning process.

This is the most obvious benefit. With the aforementioned “advanced learning,” participating in school mathematics exams is like a dimensionality reduction attack.

Xiaoban and his classmates in the Olympiad class typically experience this during elementary school exams: the B paper is usually full marks, while the A paper may occasionally lose one or two points due to carelessness. Additionally, based on my observations, any child who excels in Olympiad mathematics is also known to excel in school mathematics.

The improvement in performance and interest stems from the enhancement of children’s mathematical thinking skills through Olympiad learning, specifically in three categories:

Whether a child has learned something from Olympiad mathematics can basically be judged by whether the three major thinking abilities mentioned above have shown significant improvement.

A few years ago, this benefit was certainly the top advantage. The reasoning is simple: using Olympiad scores to screen students ensures better quality of student sources.

However, since the double reduction policy, there are no more Olympiad competitions, and using Olympiad scores as a direct stepping stone for transitioning to middle school is basically not feasible. Nevertheless, in the selection activities for transitioning to middle school across the country, Olympiad mathematics remains the king of assessment.

QA: Which children are suitable for learning Olympiad mathematics?

Children learning Olympiad mathematics can be roughly divided into three categories.

Category 1: Extremely rare mathematical geniuses

This type of child is born for mathematics; they possess mathematical talents far beyond the norm, and this exceptional talent means they comprise no more than 1% of the population.

Category 2: A few outstanding children

The so-called outstanding children often appear around us as “other people’s kids.”
They are characterized by being very smart, having strong self-learning abilities, and good study habits. They usually develop evenly across various fields, perform well academically, and have a wide range of interests. This type of child accounts for about 3-5%.

Category 3: A group of potential talents

The majority of children, about 70-80%, belong to this category. They can achieve good mathematics scores in school through their own efforts and guidance from teachers, and they can also gain from learning Olympiad mathematics.

Their mathematical talent is not particularly high, and for them, the purpose of learning Olympiad mathematics is to: walk an extra fifteen meters.

Category 4: A few should say goodbye

Some children are indeed not suitable for learning Olympiad mathematics, and if there are no good teachers to guide them, saying goodbye to Olympiad mathematics is the right choice for them.

The first and fourth types of children are easy to distinguish; one understands with just one explanation, while the other does not understand no matter how it’s explained. Making a choice is not difficult; it’s about decisively moving forward or decisively giving up.

What makes parents more troubled are the second and third types of children.

Second type children are excellent in all aspects, but because they are viewed as outstanding children, they have high self-expectations. For them, finding their true interests and suitable development direction is crucial. However, as long as the right choice is made, their execution ability is not an issue.

Third type children, being potential talents, means they can go either way. For these children, the role of parents is relatively significant. If parents work hard, the child can win several awards and smoothly progress through good elementary, middle, and university paths. Conversely, if planning is poor, it may lead to a lot of effort with unsatisfactory results. Their parents tend to worry and feel anxious.

For these two types of children, learning Olympiad mathematics should be their default option, but how much effort to invest in learning and whether to continue learning should depend on the child’s interest and learning situation, varying from person to person.

Finally:

If you are interested in the topic of planning elementary school mathematics and want to hear more details, I invite you to join this Friday morning at 8:30 AM when Tiao Ma and I will be in the 【One Sentence East, One Sentence West】 live stream for a special session on “Elementary School Mathematics Planning.”

Click to make an appointment, and you will receive a reminder when the broadcast starts.

Additionally, if you have other topics regarding elementary mathematics that you would like to hear about in the live stream, please write them down in the comments section of this article. Thank you!

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