How to strengthen the thinking training of junior high school students in mathematics teaching

Do more puzzles and solve some classic math problems.

Longyuan Periodicals Networkcn

Abstract: Junior high school teaching plays a key role in the whole teaching stage, and is a key link in education and teaching. Middle school mathematics is different from the basic curriculum of primary school, it has a certain degree of difficulty, which is a difficult point for many students to learn.

Mathematical thinking is a necessary ability for students to learn mathematics well, which can broaden students' horizons, broaden students' thinking, and make junior high school students feel the fun of mathematics. In order to achieve the purpose of high-quality teaching, combined with the current situation of junior high school mathematics teaching in China, this paper briefly explains how to find effective countermeasures to cultivate students' mathematical thinking according to the actual situation, so that they can improve their learning enthusiasm and develop good learning habits. Keywords:

junior high school students; mathematical thinking; capacity building; Effective countermeasures.

In recent years, the reform of the new curriculum has been further promoted, and mathematics is an important tool for human thinking training, and it is also a very important thinking carrier. The teaching of mathematics in junior high school must adhere to new concepts, insist on cultivating students' mathematical thinking, help students form rigorous logic, and solve difficult mathematical problems. According to the survey, the most troublesome subject for many junior high school students is mathematics, which is difficult for them to grasp the key points of mathematics, unable to transform mathematical abstract knowledge into simple topics, and has low interest in classroom learning and poor learning quality.

Cultivating students' mathematical thinking ability and allowing them to use symbols, numbers, inductive reasoning, etc. to infer mathematical answers with special skills is an inevitable move in the new curriculum reform. It can solve the shortcomings of indoctrination teaching in the past, students' imagination, and improve students' learning efficiency. In this paper, we will talk about the effective countermeasures for cultivating the mathematical thinking of junior high school students, so as to promote the further development of students.

1. Build a good teacher-student relationship.

Teachers are the leaders of education and teaching, and students are the main body of education and teaching, and there is a very close relationship between the two, and they are also the two major elements of classroom teaching. A good teacher-student relationship is the key to improving the quality of classroom teaching, and it is also the main channel for building positive communication between the two, which has a positive effect on the cultivation of students' mathematical thinking. Junior high school teachers should strengthen their contact with students, use their spare time to communicate with them, understand their current situation of mastering mathematics knowledge, clarify their views on mathematics learning, and insist on "teaching students according to their aptitude".

The cultivation of mathematical thinking ability is not a simple process, it needs to be done step by step.

To realize, teachers must build an effective communication platform between teachers and students, respect the subjective status of students, respect different views, so as to mobilize students' enthusiasm for learning in the classroom, let them take the initiative to think, and truly cultivate their mathematical thinking.

2. Cultivate students' logical thinking ability.

Logical thinking is one of the important components of mathematical thinking in junior high school, and it is also what students learn.

An important ability to learn mathematics, it helps students to simplify abstract and complex mathematical problems.

Reduced to simple math problems. Mathematics is more rigorous than other subjects.

Tease with lack of distraction are some ways to exercise the mathematical thinking of junior high school students:

Doing math problems: Mathematics is a subject that requires continuous practice, and by doing math problems, you can improve the mathematical ability and thinking ability of high school students, and exercise their problem-solving ability.

Cultivating Logical Thinking: Mathematics is a rigorous discipline that requires rigorous logical thinking skills. Logical thinking can be cultivated through methods such as reasoning, analysis, and induction.

Improve mathematical language skills: Mathematics is a special language, and students need to master the vocabulary, symbols, and expressions commonly used in mathematics in order to better understand and solve problems.

Pay attention to the accumulation of mathematical background knowledge: Mathematics is a subject that needs to be built on the basis of rich background knowledge, and students need to understand relevant mathematical knowledge and concepts in order to better master mathematical thinking.

Organize math activities: Some math games, math competitions and other activities can be organized so that students can learn and exercise math thinking in a relaxed and happy atmosphere. For example, Sudoku, math quizzes, team competitions, etc.

Guide students to learn independently: Mathematics is a subject that requires continuous thinking and excellence, and teachers can guide students to actively think about problems, find ways and ideas to solve problems, so as to improve their mathematical thinking ability.

1. Learn the basic knowledge of mathematics: The basic knowledge of mathematics is the basis for cultivating mathematical thinking ability. Middle school mathematics includes algebra, geometry, mathematical analysis, etc., and requires mastery of various mathematical concepts, formulas, and theorems.

Develop an interest in mathematics: Learning mathematics requires interest. Teachers, parents, and students themselves should all strive to create a positive, challenging, and fun learning environment. You can find interesting math problems, games, experiments and other ways to cultivate students' interest in mathematics.

2. Solving practical problems: Applying mathematics to practical problems can enable students to understand the essence of mathematics more deeply. For example, calculate area, volume, and so on.

In the process of solving problems, students learn important mathematical thinking skills such as how to observe, ask questions, propose solutions, and verify solutions.

Improve mathematical computing ability: The foundation of mathematical thinking ability is the ability to calculate. In junior high school, students need to master basic mathematical calculation methods, including oral arithmetic, columnar calculation, and the use of calculators.

These basic skills are a necessary prerequisite for further development of mathematical thinking skills.

3. Do more math problems: Mathematical thinking ability requires continuous training and practice. Doing more math problems can improve students' mathematical thinking skills.

To allow students to choose the right questions for themselves according to their level, not only do the problems in the workbook, but also try to solve other ** math problems.

4. Cultivate mathematical thinking ability: Mathematical thinking ability includes abstract thinking ability, logical thinking ability, spatial thinking ability, innovative thinking ability, etc. These abilities can be developed in the learning process of middle school mathematics.

For example, visualizing abstract concepts, building mathematical models, analyzing problems from multiple perspectives, trying to discover different solutions to problems, etc.

1. Conduct analogical thinking ability training.

Analogy is a way of thinking that guesses that some of the same or similar properties of two or two classes of things may also be the same or similar in other properties. Analogy is the most common method of scientific research.

There are many contents that can be used for analogical thinking training in junior high school mathematics textbooks.

For example, the derivation method of the multiplication rule of the same base power is used to study the multiplication rule of the power of the same base, and the division rule of the power of the same base; Factor factorization of analogous integers studies the factorization of polynomials; Analogous to the solution of binary linear equations, and study the solution of ternary linear equations;

The concept, properties, and operations of analogous fractions, the concepts, properties, and operations of fractions; The law of analogy merges the same term to study the addition and subtraction of quadratic radicals; The area formula of the triangle is analogous to the area formula of the sector to study the area formula; Analogy with the positional relationship between a straight line and a circle, the study of the positional relationship between a circle and a circle, and so on.

2. Carry out inductive thinking ability training.

Induction is the method of thinking that studies a number of individuals of a certain thing, discovers the common properties between them, and then deduces from this that the totality of such things also has this nature. There are also many contents in junior high school mathematics textbooks that can be used for inductive thinking training. Almost all of the inductions of the arithmetic rules of junior high school algebra are based on general induction.

From a subjective point of view, the thinking of junior high school students has not yet entered the stage of logical thinking, and it is impossible to give strict logical proofs when teaching these laws.

Objectively, this is a good time to train students in their inductive thinking skills. For example, the rules of addition, subtraction, multiplication and division of rational numbers, the exchange rate, the binding rate, the distribution rate, the rules of adding brackets and removing brackets for rational number operations, the rules of operation of powers of the same base, the relevant rules of integer multiplication and division, and the introduction of the basic properties of inequalities.

In addition, the relationship between the roots and coefficients of the unary quadratic equation can be explored and discovered by induction. The study of the image and properties of functions is based on the images and properties of individual specific functions, and the inductive method is also used.

1. Cultivate students' mathematical thinking in the classroom.

The cultivation of mathematical thinking does not depend on speaking, but also on what we do in our daily teaching life. In other words, mathematical thinking is "only understood but not spoken", and students need to "understand" it little by little in learning Although the cultivation of mathematical thinking requires students to sort out their feelings in learning, we must also provide appropriate guidance to students. First, let students change from reactive to proactive.

In traditional test-oriented education, the classroom is often oppressive, the teacher speaks on the podium, the students listen below, and the teacher is the leader of the class. But now we need to let the students take the lead in the classroom and make the atmosphere of the classroom "live" There is a big difference between passive learning and active learning. Although passive learning can improve students' performance in the short term, students' interest and participation have been eroded, and students are likely to develop an aversion to mathematics.

Active learning is different, and active participation in learning ensures a long-term passion for mathematics.

2. Multiple solutions to one problem to train students' mathematical thinking.

After each solution, we can guide the students: Is there another solution to this problem? "Guiding students to solve multiple problems can train students' intelligence, make students dare to question, mobilize students' enthusiasm, and cultivate students' mathematical thinking.

3. Cultivate students' mathematical thinking in homework.

For students, a short forty minutes in class is far from enough, because the formation of thinking habits is not a matter of one or two days. Therefore, when assigning homework to students, teachers should not only lay a solid foundation, but also consider expanding students' thinking and cultivating students' mathematical thinking in the homework.

Teachers can assign assignments such as deriving formulas, so that students can expand their ideas and grasp knowledge at the same time. At the end of each unit, let the students draw a mind map, and let the students systematically review the units they have learned; Finally, it is necessary to carry out regular activities of mathematics interest groups to stimulate students' brainstorming and let students truly form mathematical thinking imperceptibly

Homework is an important means to test students' mastery of knowledge, and it is also an important way for students to expand their thinking Teachers should make good use of homework so that students can learn to learn, learn logical reasoning, and learn to establish mathematical thinking.