1 how to cultivate mathematical spatial thinking
situational teaching
To cultivate students' innovative thinking, teachers should first put themselves in the right position in teaching, give full play to their leading role in daily mathematics teaching, guide students to stimulate their subjective initiative in mathematics learning, let students take the initiative to participate in teaching, explore research, and then transform them into their own knowledge, so that students can give full play to their own opinions and boldly verify, thus cultivating innovative thinking. 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, stimulate students' ability to explore, analyze, solve and extend problems, and thus better cultivate students' creative thinking ability.
For example, in the lesson of "Central Symmetry" in the first volume of the ninth grade mathematics of the newly edited People's Education Press, in order to let students fully understand the concepts of two graphs with point symmetry and master their properties, the teacher created a situation, and combined with the graphs on page 62 of the textbook, let the students observe first, and then answer the question: What do you find when one of the graphs rotates around point O 180? Let students observe the relationship between two figures from the perspective of rotation transformation, thus introducing the definition of central symmetry. Let the students realize the internal relationship between knowledge. Center symmetry is actually a special form of rotation transformation (the rotation angle must be 180 degrees when the center is symmetrical), which is permeated with mathematical thinking methods from general to special. Then compare the concepts of "axial symmetry" and "central symmetry", so that students can explore the difference between axial symmetry and central symmetry independently. Guide students to experience the mathematical thought of "observation, conjecture, induction and verification", improve their ability to analyze and solve problems, and effectively cultivate their creative thinking.
Query 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 students' initiative and multi-directional thinking. In junior high school mathematics teaching, teachers can adopt questioning teaching method, encourage students to ask questions boldly in class, and stimulate students' enthusiasm for seeking truth.
For example, in the "Variance" class taught by Math People's Education Edition in the eighth grade of junior high school, after the teacher has taught the concept and formation process of variance, the teacher can ask the students: After learning variance, everyone has a preliminary understanding of each other, 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 compete 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 answer questions immediately after being asked. Because students dare to question, many problems are exposed and solved, and students effectively master the knowledge point of variance.
2 Mathematical thinking training skills
Be good at using discovery method to inspire students' thinking
Discovery method is a heuristic teaching method. Its theory came into being in 1950s and formed in 1960s and 1970s. It is a teaching method widely used by teachers under the current new curriculum reform. Draw a circle, the teacher doesn't talk about drawing, let the students draw first, satisfy their curiosity of operating compasses, and let the students discover the methods and steps of drawing a circle by themselves. Throughout the class, the students' thinking is in a state of excitement. Everyone has the opportunity to operate, observe with eyes, reason with mouth and think with brain. Students observe and find problems by themselves, actively explore and draw conclusions, and the teaching effect is good.
Constructing equal and harmonious teaching links to enlighten students' thinking.
Suhomlinski said: "The joy of success is a great emotional force." This enlightens us that teachers must put down their dignity in teaching, walk among students, and create an equal and harmonious teaching environment for students with confident and passionate dialogue and language, so that students can study in a happy, relaxed and free atmosphere, so that every student can look forward to and experience success in this kind of learning. For example, in class, we can say something like "Your answer is very creative!" "You found a little secret, it's amazing!" ..... These passionate and encouraging evaluations let children relax their tension and anxiety, protect their enthusiasm for learning, make them feel that learning mathematics is happy, and gradually love mathematics, so as to maximize the potential of students and promote their positive 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 students' thinking ability, relying on intuition of objects, models, operations and languages, and guiding students to have concrete image perception of various mathematical phenomena. The operation of learning tools is an external materialized 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 play 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, get perceptual knowledge, compare, analyze, synthesize and abstract the essence of things, get concepts and laws, and find out ways to solve problems.
3 Mathematical thinking training skills
Inspire students' thinking and imagination with comparative analysis
For example, after teaching the divisibility of complete numbers, I gave an example: "What is the minimum number of a number greater than 10, divided by 6 equals 4, divided by 8 equals 2, and divided by 9 equals 1?" It should be said that this problem is difficult, and students will be 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, 65, 438+00 and 9?" Students can quickly find the answer to this question: this number is the least common multiple of 6, 8 and 9 10, and the least common multiple of 6, 8 and 9 is 72, so this number is: 72+10 = 82;
Then I guide students to compare and think about the above examples with this comparison question. Students will soon know that the above problem can be obtained soon if it is divided by 6, 8 and 9, and the remainder is 10. In this way, by allowing students to associate and compare, they can not only improve their imagination ability, but also improve their innovative thinking ability.
Through analysis and induction, cultivate students' innovative thinking
For another example, after teaching the formula for calculating the area of a plane figure, I asked the students to sum up a formula that can summarize the area calculation of each plane figure. After discussion, the students come to the conclusion that all the area formulas learned in primary school can be summarized by trapezoidal area calculation formula, because the trapezoidal area calculation formula is: (upper bottom+lower bottom) × height ÷2. When the top and bottom surfaces of rectangle, square and parallelogram are equal, the formula can be changed to: bottom surface (length and side length) × height (width and side length) ×2÷2 = bottom surface (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 area formula of a trapezoid is also applicable to a circle. When the upper bottom of the trapezoid is zero, that is, the trapezoid becomes a triangle, 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 formula of plane figure area 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.
On the basis of students' independent inquiry and teachers' incentive evaluation, teachers should continue to guide students to answer practical questions with what they have learned, scientifically design exercises, further consolidate new knowledge and skills, introduce students into effective and 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 students' self-summary and teachers' evaluation, the following exercises are designed: (1) Calculate several exercises of two-digit times two-digit on the same table, and correct each other after calculating the results vertically.
(2) Calculate 21× 48 63× 24 84×1242× 36. What rules will you find after you get the results? Can you cite other formulas with similar laws? In addition to consolidating students' writing ability, several groups of regular formulas are specially arranged for students to observe, discover and explore carefully, so that students can feel endless fun, and then explore more actively, and finally find palindrome formulas. There are two equal formulas in each group, such as: 63× 24 = 42× 36 84× 12 = 265438. Opening up to students to find formulas with similar laws has played a very 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, conduct reasonable guidance in time, guide and stimulate students' independent inquiry and cooperative learning in time, make a clear picture for students, and harmonize independent construction and value guidance.
Conduct language expression training and develop language thinking ability.
Thinking is the content of language, and language is the external expression of thinking. Strengthening students' language training can not only improve their oral expression ability, but also promote their 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 problems, point out their known conditions and requirements, analyze the quantitative relations in the problems, and reasonably determine the problem-solving ideas, and then ask students to express them in clear, accurate and orderly language. For example, "the school garment processing factory plans to make 670 sets of clothes, which has been done for 4.5 days, with an average of 82 sets per day and the remaining 3.5 days." How many sets per day on average? " This application problem allows students to examine the problem first and point out the known conditions and requirements. After students' analysis, it is pointed out that "670 sets" is the total workload, "4.5 days" is the completed work time, and "82 sets" is the work efficiency at the beginning. "3.5 days" is the remaining workload time, which are all known conditions of this topic.
This topic requires the efficiency of the rest of the work. Then ask the students to analyze the quantitative relationship in the problem and determine the thinking of solving the problem, that is, the first step is to calculate the 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; Step 2: Find the remaining workload and subtract the completed workload from the total workload. The formula is 670 MINUS the completed workload to find the remaining workload; The third step is to find the average number of sets to be done 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 done every day. Finally, students are required to dictate the whole steps and ideas of solving this application problem in clear and accurate language. This can skillfully combine language training with promoting the development of students' thinking ability. Strengthening language training can also make students 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.
Articles on how to cultivate mathematical spatial thinking;
★ How to Cultivate Logical Thinking in Mathematics
★ How to cultivate mathematical thinking in the second grade of primary school
★ How to cultivate mathematical thinking ability
★ How to cultivate students' mathematical thinking in images
★ How to stimulate students' mathematical thinking
★ How to establish mathematical logical thinking
★ How to temper students' mathematical thinking
★ How to exercise primary school students' mathematical thinking ability
★ How to improve the math scores of senior three?
★ How to improve the teaching quality of junior high school mathematics