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How to Cultivate Mathematical Spatial Thinking

Einstein famously said: "Interest is the best teacher". Students will become active in learning when they are interested. In mathematics teaching, according to the actual situation in the classroom, students' psychological state and teaching content, it is of great significance to arouse students' interest in learning and learn mathematics well. Below I have arranged for you how to cultivate mathematical spatial thinking, hoping to help you!

1 How to cultivate mathematical spatial thinking

Situational teaching method

To cultivate students' innovative thinking, teachers should first put themselves in a correct position in teaching, give full play to their leading role in daily mathematics teaching, guide students to stimulate their subjective initiative in mathematics learning, and let them take the initiative to participate in teaching, explore and study, so as to transform them into their own knowledge, and let students give full play to their own opinions and make bold verification, so as to cultivate innovation. In teaching, teachers can use situational teaching method to attract students' attention to classroom teaching, skillfully transform the content of mathematical theory into the thinking situation of mathematical problems, and stimulate students' ability to explore, analyze, solve and extend problems, so as to better cultivate students' creative thinking ability.

For example, in the lesson of "Central Symmetry" in the first volume of ninth grade mathematics published by New People's Education Press, in order to let students fully understand the concept of two figures about a point symmetry and master their properties, the teacher created a situation, combined with the figures on page 62 of the textbook, so that students could observe first, and then answer the question: What did you find by rotating one of the figures 18 around point O? Let the students observe the relationship between two figures from the perspective of rotation transformation, so as to introduce the definition of central symmetry. Let students realize the internal relationship between knowledge. Central symmetry is actually a special form of rotation transformation (the rotation angle must be 18 degrees in central symmetry), which permeates the mathematical thinking method from general to special. Then, the concepts of "axial symmetry" and "central symmetry" are compared, so that students can explore the difference between axial symmetry and central symmetry independently. Guiding students to experience the mathematical thought of "observation, conjecture, induction and verification" improves students' ability to analyze and solve problems and effectively cultivates students' creative thinking.

questioning teaching method

to cultivate students' creative thinking, teachers need to adopt divergent thinking teaching mode in junior high school mathematics teaching, so that students' mathematical thinking is not bound by stereotypes or patterns, give full play to students' intellectual factors, guide students to develop their creative thinking ability, adopt various teaching ideas, and mobilize the activity and multidirectional thinking of students. In junior high school mathematics teaching, teachers can adopt questioning teaching method, encourage students to question boldly in class, and stimulate students' enthusiasm for seeking truth.

For example, in the class of "Variance" taught by People's Education Edition (Volume II) in the eighth grade of junior high school mathematics, after the teacher has finished teaching the concept and formation process of variance, the teacher can ask the students: After learning variance, everyone has a preliminary understanding of variance, so are there any questions to ask? You'd better ask other students. "As soon as this question was raised, it immediately aroused students' enthusiasm for learning. They scrambled to ask questions, such as "What is the specific application of variance?" "What is the difference between variance and standard deviation?" , and so on. Some students answered the questions immediately after they were asked. Because of the students' courage to question, many questions have been exposed and solved, and students have effectively mastered the knowledge point of variance.

2 mathematical thinking training skills

Good at using discovery method to inspire students' thinking

Discovery method is a heuristic teaching method, and its theory came into being in the 195s and formed in the 196s and 197s, which is widely used by teachers under the current new curriculum reform. To draw a circle, the teacher doesn't talk about drawing, so let the students draw first to satisfy their curiosity in operating compasses and let the students discover the methods and steps of drawing a circle by themselves. Throughout the class, students' thinking is in a state of excitement. Everyone has the opportunity to operate, observe with their eyes, reason with their mouths and think with their brains. Students observe and find problems by themselves, actively explore and draw conclusions, and the teaching effect is good.

Constructing equal and harmonious teaching links and enlightening students' thinking

Suhomlinski said: "The joy of success is a great emotional force." This enlightens us that teachers must put down the dignity of teachers in teaching, go among students, and create an equal and harmonious teaching environment with confident and passionate dialogue and language for students, so that students can learn in a happy, relaxed and free atmosphere and every student can look up and experience the success in this kind of learning. For example, in class, we can say more words like, "Your answer is very creative!" "It's amazing that you found a little secret!" ..... These passionate and encouraging evaluations let the children relax their nervousness and anxiety, protect the students' enthusiasm for learning, make them feel that learning mathematics is happy, and gradually love mathematics, so as to maximize students' potential and promote students' active thinking activities.

Attach importance to intuitive teaching and cultivate students' thinking

To cultivate students' logical thinking ability, we should first make rational abstract generalization, reasoning and judgment based on the characteristics of their thinking ability and the intuition of objects, models, operations and languages. The operation of learning tools is an external materialization activity, and its particularity lies in that it can arouse and promote students' activities with the help of hands, realize and reflect their internal thinking activities, and plays a very important role in promoting the internalization of students' thinking. Therefore, teachers must attach importance to intuitive teaching. "Operation is the source of intelligence and the starting point of thinking", and operation is the first step to inspire students to think positively. Through a variety of senses to perceive things, to acquire perceptual knowledge, to compare, analyze, synthesize and abstract the essence of things, to draw concepts, rules and to find out solutions to problems.

3 mathematical thinking training skills

. Use comparative discrimination to enlighten students' thinking imagination

For example, after teaching the knowledge of divisibility of numbers, I showed an example: "What is the minimum number of a number greater than 1, divided by 6 to 4, divided by 8 to 2 and divided by 9 to 1?" It should be said that this problem is difficult, and students will feel at a loss to solve it. At this time, I showed a comparative question: "What is the minimum number of a number divided by 6, 8 and 9?" Students can quickly find the answer to this question: this number is the least common multiple of 6, 8 and 9 plus 1, and the least common multiple of 6, 8 and 9 is 72, so this number is: 72+1=82;

Then I guide the students to compare and think about the above example with this comparison question. Students will soon know that the remainder of the previous question is 1 if it is divided by 6, 1 if it is divided by 8, and 1 if it is divided by 9. Therefore, it can be quickly obtained that this number can be divisible by 6, 8 and 9 at the same time as long as it is subtracted by 1, and the least common multiple of 6, 8 and 9 is 72. In this way, by making students associate and compare, not only can students' imagination ability be improved, but also their innovative thinking ability can be improved.

through analysis and induction, cultivate students' innovative thinking

Another example is that after teaching the area calculation formula of plane graphics, I asked students to sum up a formula that can sum up the area calculation of each plane graphic, and I asked students to discuss it. After discussion, the students concluded that all the area formulas learned in primary school can be summarized by trapezoidal area calculation formula, because the area calculation formula of trapezoid is: (upper bottom+lower bottom) × height. When the upper and lower bottoms of rectangles, squares and parallelograms are equal, the formula can be changed into: bottom (length and side length) × height (width and side length) ×2÷2 = bottom (length and side length) × height (width and side length);

Because the area formula of a circle is derived from the area formula of a rectangle, the trapezoidal area formula is also applicable to a circle. When the upper bottom of the trapezoid is zero, that is, the trapezoid becomes a triangle, and the area formula of the trapezoid becomes: bottom × height ÷2. This becomes the area formula of triangle. In this way, students can not only master the area formula of plane graphics they have learned, but also cultivate and improve their innovative ability.

4 Mathematical thinking training skills

Strengthen the sublimation of practice and further expand students' thinking

Based on students' independent inquiry and teachers' incentive evaluation, teachers should continue to guide students to answer practical questions with what they have learned, scientifically design exercise questions, realize the further consolidation of new knowledge and skills, introduce students into effective interesting problem situations, let students effectively participate in learning and exploring the inherent laws of knowledge, expand personalized thinking, and cultivate and improve students' thinking ability. Take "two-digit times two-digit" as an example. After the students have finished their self-summary and the teachers have made an evaluation, the following exercises are designed: (1) Work out several exercises of two-digit times two-digit at the same table, and correct each other after calculating the results vertically.

(2) Calculate 21×48 63×24 84×12 42×36, and what rules will you find after you get the result? Can you cite any other formula with similar laws? In addition to consolidating students' writing ability, several groups of regular formulas are specially arranged for students to carefully observe, discover and explore. Students feel that there is endless fun, and then they actively explore in depth. Finally, they find the palindrome formula, and the two formulas in each group are equal, such as: 63×24=42×36 84×12=21×48. It is open for students to find formulas with similar laws, which plays a good role in cultivating students' creative ability. When doing consolidation exercises, it is easy to have some unexpected situations. If these problems cannot be solved in time, it will hinder the later inquiry learning. Therefore, teachers should play the role of a good guide, not a bystander. In the classroom, teachers should pay attention to observing students, make reasonable guidance in time, guide and motivate students' independent inquiry and cooperative learning in time, so as to get rid of the clouds and see the sun for students and unify independent construction and value guidance harmoniously.

develop language expression training and develop language thinking ability

thinking is the content of language, while language is the external expression of thinking. Strengthening students' language training can not only improve students' oral expression ability, but also promote students' thinking ability. When guiding students to do general application problems, teachers can strengthen students' explanation training on their own problem-solving steps and ideas, first let students examine the problem, point out its known conditions and demands, analyze the quantitative relationship in the problem, determine the problem-solving ideas reasonably, and then ask students to express it in clear, accurate and orderly language. For example, "the school garment processing factory plans to make 67 sets of clothes, which has been done for 4.5 days, with an average of 82 sets per day, and the rest will be completed in 3.5 days. How many sets per day on average?" This application problem can let students examine the problem first and point out the known conditions and requirements. After analysis, students point out that "67 sets" is the total workload, "4.5 days" is the completed working time, and "82 sets" is the working efficiency at the beginning of work. "3.5 days" is the remaining workload time, which are all known conditions of this topic.

and what this topic asks for is the work efficiency used by the rest of the work. Then, students are required to analyze the quantitative relationship in the problem and determine the thinking of solving the problem, that is, the first step is to find the completed workload, and the formula is 82×4.5=369 (sets) according to the fact that the total workload is equal to the work efficiency multiplied by the working time; The second step is to find the remaining workload, and subtract the completed workload from the total workload. The formula is 67 MINUS the completed workload to find the remaining workload; The third step is to find the average number of sets to be made every day, that is, the work efficiency used by the remaining workload. The formula is: the total amount of remaining work is divided by 3.5 days, and the result is the average number of sets to be made every day. Finally, students are required to dictate the whole steps and ideas of solving this application problem in a clear and accurate language. This can skillfully combine language training with promoting the development of students' thinking ability. Strengthening language training can also enable students to talk about other people's problem-solving ideas and explain their own learning methods, so that students can develop their thinking ability effectively while developing their language.

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