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Important words to say three times.
Trumpet posted an article, which is still a topic triggered by the 19 questions in the recent nine-province joint entrance examination mathematics paper, combined with Dr. Zhang Jianyue's article.
If you have friends who listened to a live broadcast I did a few days ago, you will know that there are some points of view that I have the same idea as Mr. Zhang:
The 19 questions in the nine-province joint examination have a high knowledge background, but it is not about your mastery of knowledge, because not many people have learned this knowledge, but about your ability to accept concepts, understand abstract concepts, and use concepts to solve problems.
If you want to solve this kind of problem, it doesn't depend on how much knowledge you learn, because as long as the propositioner comes up with it, he can choose one of the various advanced mathematics knowledge for variation, and let you do it, and you have no way to prepare for the exam.
The level of the first teacher is not enough, most of the high school mathematics teachers no longer have the ability to advanced mathematics, and so do I;
Second, students do not have enough ability, level and energy, and do not have so much time to study advanced mathematics, especially without a clear scope for preparing for the exam.
If so, how can you prepare? What kind of auxiliary work can parents do?
The advice I give below is not for all children, keep in mind the last paragraph of Dr. Zhang's article:
Even my own children may not need these suggestions, they can't read the books I recommend, and they can only learn if they have the spare time!
Remember the words "Learn"!
The first is to abandon the inherent idea of ignoring concepts and only paying attention to problem solving.
It is necessary to pay attention to concepts, and attach importance to the learning and analysis of concepts;
Learn to solve problems from a conceptual perspective.
It seems like these two sentences are nonsense, right?
But let's take a look at the 19 questions in the nine provinces, is it too deep in its practical skills?
No.
That is, if you read the concept and understand the concept, you may be able to make it (the idea of the question is this idea, of course, the effect presented is not satisfactory, this is another topic, this question is actually average.) ）。
But in reality, how many children can actually read this concept, understand this concept and apply it?
It is true that the abstract concepts in high school mathematics textbooks are still not enough, but the important thing is such a habit and awareness, how to interpret concepts, how to understand concepts, and how to accept some more abstract concepts.
So first of all, we should start by paying attention to the concepts in high school textbooks.
The second point is to get in touch with some abstract mathematical language expressions.
The scope of high school mathematics instruction is limited, but the scope of the newly defined examination is unlimited and uncertain.
So what's so certain?
It must be the form of expression, which is also an important part of the examination of students' receptivity, comprehension, and application, so abstraction will be a more important feature.
Exposure to this abstract form of mathematical language in advance will have a great impact on students' mindset when facing concepts, and will gradually improve their abstract comprehension ability.
For children who are capable, new ways of expressing themselves are sometimes just a layer of window paper that they have never seen before.
Where to get in touch?
On the one hand, school teachers can consciously adapt and decentralize some of the content of advanced mathematics;
On the other hand, students may consciously strengthen the reading of mathematics-related books, such as some simple popular science books and some advanced mathematics textbooks.
The third point is to learn some mathematical content that requires in-depth thinking, and do some mathematical problems that require the use of essential thinking methods.
The regular in-class math follows the following pattern in the problem-solving mode:
Analyze the conditions - identify the structure of the question type - call the method in memory - solve the problem.
Although these methods are also derived from mathematical thinking, after summarizing and refining, they reflect more method memory than thinking activities, and their thinking is relatively shallow.
It is precisely because of this that brushing questions is popular.
Now it may be necessary for those children who have the ability to think more deeply and use more original thinking methods such as reduction, induction, summarization, and combination of numbers and shapes to solve problems that they have not seen before.
For example, will the last question give you a bunch of definitions in the future, so that you can prove a certain conclusion?
This requirement is actually very high, most parents do not have this ability, ordinary school teachers may not teach, and students themselves have the ability to learn completely on their own, what should I do?
Go to a good school, get into a good class, that's the only way.
Speaking of which, by the way, in the future, test papers from various famous schools and educationally developed areas must be included in the scope of attention.
If you find that the child is more talented in some aspects, and wants to impact the difficulty of the finale question in the future, you may have to start as soon as possible, which is probably one of the reasons why the finale of the college entrance examination mathematics finale question has such a changing trend - it is difficult for ordinary people to prepare for this, and it can only reflect whether there is talent.
So how do you prepare?
As an official account writer who often recommends and reviews books, I still do my old job and push books.
Although parents may not be able to help their children study, they can buy books to make themselves feel more comfortable......
Tao Zhexuan Teaches You to Learn Mathematics
This book is a book written by Tao Zhexuan himself when he was a student based on his experience in learning mathematics and solving mathematical problems, because he was the same age as today's middle school students, so it is more meaningful to learn from how people think when facing problems.
This book has a certain degree of difficulty, and children who have been exposed to mathematical competition can read it, and the effect is better.
Math Girl
Mom, why is it so expensive!
I have the first four books in this set, very good books, typical Japanese mathematics popular science book style, but the discussion of mathematics is integrated into the sweet campus life, and there are some early love plots.
So I didn't push it, to prevent everyone from saying that I was not serious, and the knowledge of the last few books is a bit deep, and the discussion is a bit abstract, and I am not sure if the children can understand it.
But who would have thought that the college entrance examination would see such a changing trend now?
Then this set of "Math Girl" is within the recommended range.
Books are quite expensive, so you can buy them from the first one, and this book can be read by students.
The Princeton Calculus Reader
I've written reviews of this book, and it's a relatively down-to-earth book for understanding calculus.
It is relatively fluent to read, and there are not too many too abstract and cumbersome proofs (all attached at the end), which is suitable for children with high school math graduation level to get their first exposure to calculus.
There is also a Princeton Reader of Probability Theory, which I have not personally read, and it is said that it is okay.
Mathematicians Explain Primary School Mathematics
A reader in my trumpet asked me what he should do as an elementary school math teacher.
Friends, if you pay attention to my tuba, I suggest you can buy this book first, and similarly, if parents are concerned about the learning of primary school mathematics, I also recommend reading this book.
The author sorts out and explains the relevant concepts in primary school mathematics in detail.
Math Lessons for Kids
For children's mathematics lessons, I have also pushed this book, which is a popular science book on the history of mathematics for elementary school children, which is still good, you can take a look, it is a preliminary contact.
Fun Bayesian Statistics: Statistics in Rubber Duck, Lego, and Star Wars
This book is not too expensive, there is finally one that is not cheap.
This book is a popular science book based on Bayesian statistics, but it is not very simple, and it is still possible to see it at the level of high school students.
The Invitation of the Queen of Mathematics Introduction to Elementary Mathematics
A popular science book on number theory.
You will find that a large number of the books I recommend are Turing's books, if according to the logic of the message in a comment area, whoever I recommend is taking whose benefits, then Turing is probably my relative, I must have taken a lot of money from Turing.
Even so, I still have to say that high school compulsory brushing questions is not the only choice for high school mathematics synchronous brushing questions, and it is not necessarily the best choice.
What can you do!
Ohm Society Learning Comics: Comic Linear Algebra
It is not this book that is recommended, but this series.
I have to say that the Japanese have thrown us eight streets in the popularization of mathematics science, and the abstract mathematical content is displayed in figurative cartoons, although there are still some flaws, after all, mathematics is abstract, but it is not bad.
Similar to the following one.
Simple Linear Algebra
Also written by the Japanese, alas.
The History of Calculus: From Newton to Lebeig
This book is a book on the history of mathematics about calculus, and when it comes to the history of mathematics, we need to pay attention to it, and there is a trend in mathematics teaching - HPM (History and Pedagogy of Mathematics).
It is also an aspect of mathematics popularization that students can understand the relevant content of the history of mathematics in the study of mathematics.
"Mathematics: Great Problems and Extraordinary People"
Another form of writing on the history of mathematics uses initials to connect one mathematical topic after another—theorems, puzzles, and arguments.
History of Minimalist Algorithms
I don't know if you have noticed, but the books I recommend this time include various fields - algorithms, probability, calculus, history of mathematics, number theory, linear algebra, etc., I didn't recommend it that way before, but now I can't.
33 Lectures on Mathematical Modeling
By the way, there is also modeling, which is also recommended.
The books here are very expensive, comparable to Wan Wei, there is really no way to do it, because many of them are imported books, and they are relatively niche, so the cost will be higher.
If you go to Pinduoduo to buy it, the cheap book may be of ..... quality
In fact, if there are conditions, I recommend that you go to the library to borrow and try to read, and there will be some books available for reading on WeChat.
Mathematics and Life
I've written about this book, so I don't need to talk about it.
It is also a series of books, you can read the first one first.
Math of Joy
This is a book that is more suitable for middle school students or children in the upper grades of elementary school.
"Academician Mathematics Lecture Album Set"
This set of books is a popular science book written by several academicians in China, and those who are interested can also learn about it.
The books recommended above are basically reading thresholds, there is no way, this is the reality determined by mathematical abstraction, but on the other hand, through reading these books, if children can smoothly accept and understand, it will invisibly improve their mathematical knowledge and abstract ability, and it will also be helpful in the face of the finale questions in the future, isn't it?
This article was originally published from the public account: Enron's Math Tavern
Posted in the headlines only for copyright protection