1 how to cultivate students' mathematical thinking in images
Association can promote memory.
Mathematics is a highly systematic subject, and its knowledge is closely related. Learning new knowledge should be based on related old knowledge. This requires students to have a certain memory ability, and memory often depends on association. Association in primary school mathematics mainly includes: ① Close association. If students elementary arithmetic integers, they will think of the order of elementary arithmetic of integers; Students think of additive commutative law, additive associative law, multiplicative commutative law, multiplicative associative law, multiplicative distributive law and so on.
In order to simplify fractions, students think of the characteristics of approximate fractions and numbers divisible by 2, 3 and 5. 2 Similar associations. For example, from divisor to common divisor and greatest common divisor; Correlation from multiple to common multiple and minimum common multiple; Integer digits should be aligned first, decimal points should be aligned first, and fractions with different denominators should be divided first. ③ Contrast and association. Such as expansion and contraction, increase and decrease, increase and decrease to, odd and even numbers, prime numbers and composite numbers. Therefore, association is a thinking process from one thing to another, a form of thinking in images, and a means to promote students' memory, which is helpful for students to firmly master systematic mathematical knowledge.
Before students acquire mathematical knowledge, they must have correct and rich representations.
Representation is a visual description of objects and phenomena perceived in the past, which can not only reflect reality with an intuitive image, but also has a certain generality. Without appearances, there is no thinking in images. Mathematical knowledge is abstract. In teaching, if teachers can "materialize" abstract knowledge so that students can see, touch, operate and feel it, it will be beneficial to students' learning.
If the score is an abstract concept, then students can use concrete things to operate first in teaching. Divide a circular cardboard into two parts, a rectangular piece of paper into four parts, and a rope into five parts, and then color 1 respectively, and compare with the rest. Through this practical operation and summing up the perceived things in the operation, the image of "everything can be divided into several parts on average, and each part is a fraction of it" is left in students' minds. With this image, we can summarize the concept of score. From image to abstraction, it helps students to master mathematics knowledge firmly.
2 methods to cultivate students' thinking ability in images
Attention should be paid to the application of teaching AIDS and learning tools in teaching.
It is necessary to use teaching tools and teaching AIDS to provide students with sufficient opportunities for observation and operation, so that students can perceive things and phenomena with multiple senses. Through comparison and generalization, it reflects the intuitive characteristics of objective things and phenomena, so as to get the correct representation. The demonstration of teaching AIDS and the application of learning tools should pay attention to multi-angles, different orientations and diversity. For example, in terms of understanding, we should observe both acute and right-angled objects and obtuse objects; It is necessary to display graphics from different angles at different sizes and at different positions. It is necessary to demonstrate both the static angle and the dynamic angle. The more comprehensive and profound the students' observation of objective things and phenomena, the more correct and rich the representations they get, and the higher the level of thinking in images.
Cultivating students' spatial concept with practice
The concept of space is the representation of the shape, size, length and mutual position of objects. To cultivate and develop students' concept of space, we must combine teaching with practice. If students want to get the appearance of the length unit of 1 cm, they must first measure the thumbtacks and fingers with a ruler. 1 cm is about 1 thumbtack, and the width of index finger is about 1 cm. In order to get the representation of the area unit size of 1cm 2, let students first measure the thumb surface with a square with a side length of1cm, and the thumb surface size is about1cm 2. By measuring and comparing the length of 1cm and the size of 1cm in practice, students left an image in their minds and formed the concept of space. It can be seen that the process of cultivating and developing students' spatial concept is also the process of cultivating and developing students' thinking ability in images.
Attention should be paid to the combination of numbers and shapes in teaching
Numbers are abstract mathematical knowledge, while shapes are concrete objects, figures, models and learning tools. Number and shape are closely related. Only by thinking in images in terms of shapes and observing, calculating, comparing, analyzing and abstracting on the basis of perceptual materials can students acquire the knowledge of numbers. For example, if the number is less than 10, students should first count the sticks: 1 stick, 2 sticks, 3 sticks, 10 sticks, and then count the pictures of the text: 1 panda, 2 deer, 3 butterflies, 10 balloons. In this combination of numbers and shapes, students' thinking in images is also trained and their thinking ability in images is cultivated.
3 How to cultivate students' mathematical thinking ability
Organize interesting math activities in games to develop students' autonomy in thinking.
In math class, if the teacher moves a lot, then the student may just be an audience, and there are many opportunities for quiet, and the opportunity for personal experience is lost, so it is difficult to show the student's dominant position. Teachers should change the presentation form of knowledge through a series of activities, so as to be close to reality and life and cultivate students' autonomy in thinking.
For example, queuing is an example of life that students have to experience every day. Students can learn the knowledge of cardinal numbers and ordinal numbers independently through rows of games. After learning the lesson "Understanding RMB", students can buy and sell in groups by creating simulated shopping malls. In the interesting independent activities, the students not only learned about RMB, but also learned to exchange it simply. In this way, students' learning autonomy is more obvious. Students really appreciate the mathematics in life, and feel the close relationship between mathematics and study and life, so as to learn to observe things around them from a mathematical perspective. Therefore, autonomous participation in activities is a magic weapon to help students think positively and master knowledge.
Organize mathematical knowledge expansion activities to develop the flexibility of students' thinking.
The new curriculum standard of primary school mathematics emphasizes that students are the main body of mathematics learning, and pays attention to letting students use what they have learned to solve practical problems flexibly. The source of inducing students' thinking is the classroom. In the process of organizing mathematics activities, we should activate students' thinking and encourage them to innovate. Only in this way can we really learn and use living knowledge. For example, when teaching "One-digit abdication minus two-digit", I created an activity scene of buying toys, and asked students to buy a toy worth 8 yuan with 36 yuan money to see how much money was left. Students get several different calculation methods through activities and communication. Some groups think that 8 yuan can reduce 10 yuan first, and add useless 26 yuan to get 28 yuan; Some groups think that 28 yuan can be obtained by subtracting 6 from 36 and then subtracting 2; Other groups think that 6 minus 8 is not enough, so subtract 8 from 16 to get 8 and add 20 to get 28 yuan.
After discussion, the students think that different calculation methods can be used in different situations. I ask students to use their own calculation methods after class to see when you will choose what method. The next day, the students said happily: I have 2 1 yuan, and I need 6 yuan to buy a pencil box. I will use 10 yuan to subtract 4 yuan from 6 yuan and add 1 1 yuan, leaving 15 yuan; I have 32 beads, and there are 24 after giving them to my brother, because 12 minus 8 equals 4 plus 20 is 24. Students can see, think, discuss and calculate in class, which not only broadens their knowledge horizons, but also flexibly applies what they have learned in math class to their daily lives, making students feel that learning math is very useful. Such mathematical activities cultivate the flexibility of thinking.
How to improve students' mathematical thinking ability
Find a breakthrough in cultivating mathematical thinking ability
The agility of mathematical thinking is mainly reflected in the speed problem under the correct premise. Therefore, in mathematics teaching, on the one hand, we can consider training students' operation speed, on the other hand, we should try our best to let students master the essence of mathematical concepts and principles and improve the abstraction of the mathematical knowledge they have mastered. Because the more essential and abstract knowledge is, the wider its scope of application and the faster its retrieval speed will be. In addition, the operation speed is not only the difference in understanding mathematical knowledge, but also the difference in operation habits and thinking generalization ability. Therefore, in mathematics teaching, students should always be asked about speed, so that they can master the essentials of quick calculation.
In order to cultivate students' thinking flexibility, we should strengthen the variability of mathematics teaching, provide students with a wide range of thinking association space, enable students to consider problems from various angles, quickly establish their own ideas, and truly "draw inferences from others." Teaching practice shows that variant teaching plays a great role in cultivating the flexibility of students' thinking. For example, in concept teaching, let students describe concepts in equivalent language; In the teaching of mathematical formulas, students are required to master all kinds of variations of formulas, which is conducive to cultivating the flexibility of thinking.
Cultivating thinking ability is closely related to cultivating language expression ability.
People's thinking and language are inseparable. Language is a tool of thinking. Psychology believes that people generalize the acquired feelings, perceptions and representations with the help of language, and form concepts, judgments and inferences. Through language expression, it is also helpful to adjust one's thinking activities and make them gradually perfect. In mathematics teaching, to cultivate students' thinking ability, students need to be guided to analyze, compare, synthesize, abstract, summarize, judge and reason. Teachers need to let students express these thinking activities in language, and then affirm or correct their thinking process.
Experienced teachers always pay attention to let students express their own calculation process and problem-solving ideas in language, and as a result, students' thinking ability has been improved rapidly. Due to the limited classroom teaching time, in order to give students the training opportunity to express their thinking in language, we can combine different ways such as named speech, group discussion and two people talking at the same table. Teachers should also pay attention to helping poor students consciously and systematically, encourage them to speak, promote their positive thinking, and make great progress in their math scores and thinking ability.