What kind of thinking is needed to learn mathematics? Learning is not like a headless fly. Many students still do poorly in math in senior three. Without a solid foundation, they will be at a loss in their future studies. Let's share what kind of thinking is needed to learn mathematics.
What kind of thinking is needed to learn mathematics? 1 1, transforming thinking
Transformational thinking means that when we encounter obstacles in the process of solving problems, we can change our ideas into another form from different directions by changing the direction of the problems, and then find a better solution. This kind of thinking can often achieve good results when we encounter difficulties and nails.
2. Logical thinking
Logical thinking is an important ability to learn mathematics and the most important thinking ability, because mathematics is a highly logical subject. It is a thinking process of observing, comparing, analyzing, synthesizing, abstracting, summarizing, judging and reasoning things with the help of concepts, judgments and reasoning.
Generally speaking, we use logical thinking to solve problems first. First of all, we judge what knowledge points the topic examines, then we analyze the problem through the knowledge points we have learned, and then infer the correct answering process.
3. Reverse thinking
In short, reverse thinking is the process of knowing the result. We can explore the opposite side of the problem in depth, and sometimes we can find the real solution to the problem in this reverse thinking.
What kind of thinking is needed to learn mathematics? 2. How to learn math well?
1, pay attention to calculation
Computational learning of mathematics, like literacy learning of Chinese, is the most basic.
Illiteracy, poor Chinese reading ability; If you calculate badly, you can't learn math well. Moreover, good calculation will be of great help to children's math learning.
Parents can let their children do oral calculations for 2 minutes every day. At first, you can only complete 20 oral calculations in 2 minutes, but then you will find that children will be faster and faster, and the correct rate will be higher and higher.
2. Pay attention to mathematics in life.
In fact, the study of mathematics has a great influence on life and can provide a lot of help.
For example:
Buy things, calculate interest rates, make profits, etc. , all in math. You can consciously ask your child math questions in your life and let him answer them. It's simple. You take your children to buy food, 5 yuan for a catty of apples, 20 yuan for your aunt, and change.
Don't underestimate these. In primary school mathematics learning, solving problems accounts for the most points, and solving problems is nothing more than judging which addition, subtraction, multiplication and division to use to solve them. These problems are actually problems in life. With more contact in life, children will naturally answer.
Step 3 preview actively
Before explaining new knowledge, it is an important means to read the teaching materials carefully and develop the habit of previewing actively. Therefore, cultivate self-study ability, learn to read books under the guidance of teachers, and preview with teachers' carefully designed thinking problems.
For example, if you teach yourself an example, you should find out what the example is about, what the conditions are, what you want, how to answer it in the book, why you answer it like this, whether there is a new solution and what the steps are.
Grasp these important problems, think with your head, go deep step by step, and learn to use existing knowledge to explore new knowledge independently.
Some parents have a headache and their children are inefficient in class; The key reason for this is that there is no preparation; Naturally, you can't be targeted.
4. Thinking is the core of mathematics learning methods.
Some children are familiar with formulas, properties, rules, etc. But when they encounter practical problems, they don't know how to start and how to apply what they have learned to solve them.
If there is such a problem for students to solve, "if the height of a cuboid is removed by 2 cm, it becomes a cube, and its surface area is reduced by 48 square centimeters." What is the volume of this cube? "
Although children are familiar with the formula for finding the volume, many students can't figure out the way to solve the problem because the problem involves a wide range of knowledge and requires students to gradually master the thinking method when solving the problem under the guidance of teachers and parents. In terms of units, this problem involves length units and area units; Graphically speaking, it involves rectangles, squares, cuboids and cubes;
From the relationship of graphic changes: rectangle → square; In thinking and reasoning: cuboid → reduce a part of cuboid with a square bottom → reduce the equal product of four faces → find the' area' of a face → find the length of a rectangle (that is, the length of a square) → the volume of a cube;
Enlightened, after the child analyzes, students can answer according to their ideas (they can draw pictures).
Some students quickly replied:
Let the base length of the original cuboid be x, then 2X×4=48 = 48.
X = 6 (that is, the side length of the cube),
The volume of a cube is 6× 6× 6 = 2 16 (cubic centimeter).
Therefore, in the process of learning, the biggest role of teachers and parents is: inspiration.
Children, under the guidance of teachers and parents, actively think and solve problems and master learning methods!
5. Cultivate reading interest
During the holiday, I talked to a senior teacher about children's math learning and shared a key point:
"How is your child's math?" The teacher asked.
"The problem is not difficult, and the results are not bad. When you encounter a problem, it seems that you can't get in. " I really have a headache when I mention my daughter's math.
"Does she usually like reading?"
"I don't particularly like it, but I don't watch it at all. I usually like to read comics and the like. " I thought about it.
"Oh, have you read popular science books and some famous books?" The teacher then asked.
"No, I don't think she can see any books that are useful for learning, and she doesn't want to read them." I'm a little embarrassed to answer.
"There are some problems." The teacher paused and said, "If children want to learn math and physics well in middle schools in the future, primary schools must read more books, especially good books with profound humanistic qualities. Children who read more books have active thinking and broad horizons, and they can show their advantages in the senior grades. "
"Most of the students with good math scores can read books at the age of 6 or 7. In primary school, they read many good books with deep humanistic quality, and they love thinking and reading. The depth and breadth of these children's problems sometimes stumbles me.
After listening to what she said, I understand better that "the more students read, the clearer their thinking and the more active their wisdom."
The Importance of Reading to Mathematics
Many parents always feel that the changes brought by reading are slow, and the exam is just around the corner. They still feel that it is better to make up lessons directly and the effect is more obvious.
In fact, the function of reading is not only to enrich cultural accumulation and improve Chinese literacy, but also to help children ignite the spark of thinking, broaden their horizons, deepen their thinking and improve their learning ability.
Therefore, reading is not only a matter of Chinese, but also the first for any subject. Studies have found that children who start reading a lot in grade one or earlier have greater potential in the subsequent primary and secondary schools, especially in mathematics, physics and chemistry, than children who start reading in grade three.
Because the former has deep reading ability and habits in his later study career, that is, he has strong understanding ability, while the latter has shallow thinking and weak understanding ability when reading. This phenomenon is more obvious in the watershed grade of grade two.
Therefore, don't wait until primary and secondary schools encounter difficulties to make up lessons endlessly, but let children solve literacy problems at the age of 4-7, love reading at the age of 6-9, and read a lot and read good books after the age of 9.
What kind of thinking is needed to learn mathematics 3. A good way to learn math well.
First of all, preview methods
Junior one students are often not good at preview, and they don't know what role preview plays. Preview is just a form, and you can't see the problems and doubts at a glance. When students preview, they should be required to do the following: 1. Read roughly, first browse the relevant contents of the textbook and master the general situation of this section of knowledge. Second, read carefully and repeatedly, experience and think about important concepts, formulas, laws and theorems, pay attention to the formation process of knowledge, mark difficult concepts, and attend classes with questions. In terms of methods, classroom preview or unit preview can be used.
Second, the method of listening to lectures
Under the guidance of teaching methods, we should deal with the relationship between "listening", "thinking" and "remembering".
"Listening" means directly accepting knowledge with the senses. Students should pay attention to: (1) Listen to the learning requirements of each class; (2) Listening to the process of knowledge introduction and knowledge formation; (3) Understanding the analysis of key points and difficulties (especially the doubtful points in preview); (4) Listen to the reflection of problem-solving ideas and mathematical thinking methods; (5) Listen to the summary after class.
"Thinking" refers to students' thinking. Without thinking, students can't play the main role. (1) Think more, think diligently, and think with listening; (2) Thinking deeply, that is, tracing back to the source and being good at asking questions boldly; (3) Good thinking refers to association, conjecture and induction through listening and observation; (4) Establish critical consciousness and learn to reflect. It can be said that "listening" is the key to "thinking", and "thinking" is the deepening of "listening" and the core and essential content of learning methods. Only when you think can you learn.
"Notes" refers to students' class notes. Generally, senior one students don't take good notes. They usually copy what the teacher wrote on the blackboard, and often use "notes" instead of "listening" and "thinking". Although some notes are well written, they are of little use. Students are required to: (1) take notes and obey the lecture, and grasp the opportunity of recording; (2) Remember the main points, questions, ideas and methods of solving problems; (3) Remember to summarize and think after class. Make it clear that "remembering" serves "listening" and "thinking".
Mathematics learning methods suitable for students
An Understanding-Definition
Mathematics, like other subjects, also has many conceptual things. The basis of learning mathematics well is to understand the true meaning of definition. For example, the meaning of square, cube and absolute value in mathematics. We know that a square is the product of two identical numbers. Of course, a cube is the product of three identical numbers, and the absolute value is a value greater than or equal to 0. Knowing the true meaning of the definition, we took the first step and laid a solid foundation for the following study.
The Third Understanding-Diligence in Practice
As I said before. Mathematics is not learned by rote, but worked out with a pen. Therefore, for a formula or a definition, only by doing a few more questions about this problem can we use it naturally and truly understand its meaning. Therefore, for mathematics, we must not be lazy, just look at it without doing it. Only by using more brains and hands can we learn mathematics more flexibly.
The second kind of understanding-practice
The difference between mathematics and other disciplines is that there is no need to memorize, because mathematics is not a problem, but a calculation, which is the biggest difference. How to practice specifically.
Many problems in mathematics are based on definitions. As I said before, once you understand the definition, it's easy to start. For example, if you want to merge similar items, you must first define them, that is, similar items. Simply put, it is something that everyone has. If you understand the definition, you will get twice the result with half the effort.