When children are crazy about doing math problems, they always complain that "I can only count when I buy things." Why is it so complicated to learn? " I am glad that when she questioned junior high school mathematics, I answered this question in time with three sentences from Nagano Yuji's mathematics series:
These three books are so interesting that people who are afraid of mathematics like me can read them all at once. After reading two books, How to Awaken the Mathematical Brain and How Mathematicians Think, I bought the physical book "The Magic Book of Mathematics for All Mankind" on WeChat reading. This shows how attractive this set of books is.
1. "How to wake up the math brain"
The key chapter of this book is the third chapter, which expounds "mathematical thinking" from seven aspects. Based on the basic knowledge of junior high school mathematics, it tells us that "mathematical thinking" can be owned and done by anyone.
The reason why most people don't realize or always use "bad mathematics" as an excuse is often because we avoid theoretical or mathematical concepts invisibly. The seven aspects of "mathematical thinking" are: arrangement → sequential concept → transformation → abstraction → concretization → reverse thinking → mathematical aesthetic feeling.
This book left me with two deep impressions: one is that mathematical examples are very interesting, and it is easy to understand mathematical concepts and their origins; The other is to learn thinking methods through the verification process of examples. As the author said, "Cultivating application ability is the beauty of mathematical thinking."
2. What do people who are good at math think?
The key chapters of this book are the first to the seventh chapters, which are still based on junior high school knowledge, connecting scattered knowledge points in series, so that people who are not good at mathematics can also apply the "seven skills" to their work and life unrelated to mathematics. These "seven skills" are: concept understanding → seeing through the essence of things → solving problems reasonably → grasping causality → supplementing information → convincing → looking at the whole from the part.
This book is very similar to How to Wake up the Math Brain, but it is a little harder to understand and less interesting. This may be because this book is aimed at adults who study mathematics again, so the examples are more comprehensive and slightly more difficult. For people like me who bury the theorem of mathematical formula in the deepest part of my memory and can't dig it out, I can only try my best to understand the enlightening significance brought by mathematical formula.
3. The mathematical magic book of all mankind
In fact, this book is the first one published by the author, and it is called the "Mathematical Collection" to really improve the mathematical ability and quickly save the examination results. The key chapter is the third part-10 the solution of any math problem. This book is based on the knowledge of senior high school mathematics, and every problem-solving idea gives its function, purpose, specific methods, examples and thinking steps. This "10 solution idea" is:
Problem-solving thinking 1: reduce power and dimension.
Idea 2: find the cycle and law.
Idea 3: Find symmetry.
Solution 4: Reverse thinking
Idea 5: Consider multiplication instead of addition.
Thinking of solving problems 6: Relative comparison
Solution 7: Inductive Thinking Experiment
Idea 8: Visualization of Mathematical Problems
Problem solving idea 9: equivalent replacement
Problem solving ideas 10: trace the starting point through the end point.
Mastering these 10 problem-solving ideas can help students easily deal with math problems in junior and senior high schools, integrate all math knowledge and form their own learning methods. Interested students must read this book and verify whether it is really so powerful by the way.
But I am more interested in the preface and the second part of this book 1. The author explained why we can't learn math well. How to learn math? What's the difference between people who are good at math and those who are not good at math?
Write it at the end,
To be honest, I don't know how helpful these three books are for students to learn mathematics well, but they have profoundly inspired me to re-examine the significance of mathematics.
When we study Chinese, English or other subjects, we seldom doubt the purpose of studying this subject. But for mathematics, most people can't understand the significance of learning it. The author quoted Einstein's famous words in both books:
"Education is what remains when a person forgets everything he learned at school. Through this force, we can cultivate people who can think and act independently and solve various problems facing society. "
As the saying goes, learning mathematics is to let us learn how to think, how to act and how to solve problems ... Maybe we will eventually forget these complicated formulas and difficult theories, but mathematics subtly guides our thinking. It must be said that mathematics has played a vital role in the construction and perfection of people's logical thinking mode. I think this may be the answer to the opening question "Why do you want to study math?"? .