1 how to cultivate students' mathematical innovation ability
Create an innovative atmosphere
Classroom teaching is the main channel of teaching and the main position of cultivating students' innovative consciousness. Because of their young age and lack of knowledge and experience, primary school students are not as creative and creative as adults, but they are curious, curious and thoughtful. Therefore, in classroom teaching, teachers should create a pleasant and harmonious teaching atmosphere, let teachers and students communicate with each other, and let students dare to think, ask and speak. Teachers should provide students with opportunities to show their individuality, encourage bold thinking, affirm students' original thinking and methods, fully mobilize students' enthusiasm and initiative in learning, and develop their innovative potential.
For example, in the third grade, when talking about verbal arithmetic, it shows 80÷20=? After students work out the results with their mouths, teachers can change the teaching method of "thinking process" and let students express their thoughts with their mouths. When the students were afraid to speak at first, the teacher encouraged them: "What did you think when you calculated? Go ahead, as long as you are willing to use your head, it doesn't matter if you are wrong. " Encouraged by the teacher, the students expressed three ideas. One of them said, "I take 80 as 8, 20 as 2, and 8 ÷ 2 = 4, so 80÷20=4." The teacher praised him at once: "You are so clever. Your idea is a division rule that we will learn later. Now that you have found it, you will use it.
Create a problem situation
The creation of the so-called question situation means that teachers create a kind of "disharmony" between the teaching content and students' knowledge-seeking psychology, so as to introduce students into the situation related to the questions raised, induce them to carry out innovative thinking activities, and stimulate students' interest in learning and desire for innovation. In teaching, teachers should strive to create problem situations, so that students have a sense of mystery, exploration and innovation, and are eager to know the mystery.
For example, when teaching "area unit", the new lesson is introduced in this way: show a picture frame and ask students, "How long does it take to nail this rectangular picture frame?" What do you want from a rectangle? " After the student answered, he asked, "How much glass do you need if you want to put glass on this frame?" At this time, students are focused, curious, active, enthusiastic and interested in learning, and teachers can prompt them to enter the situation of exploring the concept and unit of area. In this way, the whole class is going on vividly under the guidance of self-study, observation, operation and discussion of teachers and students.
2 math classroom teaching skills
Provide practical opportunities.
Hands-on operation is a dynamic process of multi-sensory participation. In line with the curious and active psychological characteristics of primary school students, it can not only stimulate students' interest in learning, but also enable students to develop their thinking, intelligence and innovative consciousness while personally perceiving things. In mathematics classroom teaching, students can draw a picture with their hands, brains and words in pleasant practical activities, measure it, fold it and spell it, so as to gain knowledge and improve their skills.
For example, when teaching "the understanding of circle", first prepare some materials and tools for each student to draw a circle, so that students can find ways to do it themselves according to the materials, and as a result, different drawing methods appear. In this process, students think this method is too stupid and ugly to draw, so they wonder if they can make a tool to draw a circle, which naturally produces a "compass", so there is a learning situation in which teachers and students participate together. Practice shows that as long as teachers give students the initiative to learn and create opportunities, students will be open-minded and active, and they can explore ways to solve problems. In the process of exploration and learning, students understand the internal relationship between knowledge, master the methods to solve problems, and also experience the process of knowledge formation.
Infiltrate mathematical thinking method
Modern mathematics teaching theory holds that mathematics teaching itself is the process of mathematical thinking activities and the analysis of this process. Teachers' understanding of the basic ideas and methods of mathematics, combined with the characteristics of students and textbooks, and consciously strengthening the infiltration of mathematical ideas and methods will be beneficial to the teaching of mathematical knowledge, the initial cultivation and gradual development of students' mathematical quality, so that students can gradually realize the wide application of basic ideas and methods of mathematics in practice, further clarify the purpose of learning mathematics, improve their interest in learning mathematics and improve their overall quality.
For example, when deducing the formula for calculating the area of a circle, the unknown is transformed into the known by "turning a circle into a square" and "turning a curve into a straight line", and the idea of transformation is used. Guide the students to actively explore and cooperate in groups, and cut and paste the rectangle, trapezoid or triangle they have learned together, and then deduce the area formula of the circle. This is the transformation idea. Let the students close their eyes and imagine that if the circle is subdivided infinitely, the shape of the spelled figure will be closer and closer to the rectangle (or trapezoid or triangle). In the study of "limited cutting and infinite imagination", the ultimate state test of imagination is permeated with limit thought. Through the infiltration of this series of thinking methods, students' understanding of formulas is deepened and their innovative ability is cultivated.
3 math classroom teaching skills
Optimize innovative psychology and stimulate innovative consciousness.
The process of innovation needs to be driven by innovative emotions. In addition, personality also plays an important role in innovation activities, and the display of innovative personality has both subjective factors and internal psychological state. Therefore, to cultivate students' innovative ability, teachers are the leading factor. While imparting knowledge, teachers should create a good classroom psychological environment, communicate with students more, create a harmonious and relaxed learning atmosphere, and optimize students' innovative psychology.
In the process of innovation, mathematics teachers in charge of teaching important subjects in middle schools should actively start teaching innovation ideas and guide students to popularize exploration through typical examples; Guide students to seek novelty and explore through new knowledge; Through fast thinking training, guide students to explore intuitively; Through multiple solutions to one question, students are guided to seek differences and explore skillfully, and their innovative consciousness is stimulated.
Create an innovative education environment and cultivate innovative consciousness.
Innovative consciousness is a psychological orientation of finding problems and actively exploring. In order for students to find problems in class and actively explore, we must create an innovative atmosphere for them. The basis of implementing "innovative education" in classroom teaching is a harmonious relationship between teachers and students, which makes the classroom full of "love" atmosphere. Only in a relaxed and happy emotional atmosphere can students have a strong interest in what they have learned. Teachers should be good at stimulating students' interest in learning, so that every student can actively participate in the process of "exploring and trying", so as to give play to their imagination and tap their innovative potential.
Some knowledge in mathematics is abstract, so it is difficult to arouse students' imagination and stimulate students' thinking only by oral description. At this time, let multimedia teaching enter the classroom, create a more intuitive and convenient classroom teaching scene, abstract what you have learned into images, turn boredom into fun, turn students from hard study into pleasure, give full play to students' leading role, cultivate students' enthusiasm for autonomous learning, and let students realize innovation in autonomous learning.
4 math classroom teaching skills
1. Use the psychology of "students are eager for unknown problems that they can do" to cultivate students' interest in innovation. Interest comes from thinking, which requires a certain knowledge base. Show appropriate questions in teaching and let students "jump up and pick peaches". Moderate questions, students want to know, will attract students, stimulate their cognitive contradictions, cause cognitive conflicts, and arouse strong interest and curiosity. Students learn because of interest, but because of thinking, and put forward new problems, consciously solve and innovate.
2. Reasonably satisfy students' competitive psychology and cultivate students' interest in innovation. Students have a strong competitive psychology. If they fail repeatedly in their studies, they will lose confidence in their studies. It is necessary for teachers to create suitable opportunities for students to feel the joy of success and cultivate their innovative ability. For example, for different groups, geometric design competitions, math joke parties, logical reasoning story speeches, etc. They are all held, so as to spread the wings of imagination, give full play to their different specialties, fully show themselves in the activities, find the combination of life and mathematics, feel their own victory psychology, experience the success opportunities and happiness brought by mathematics, and cultivate their own interest in innovation.
3. Cultivate students' interest by using the beauty of graphics in mathematics. There are a large number of geometric figures in life, some of which are produced according to important theories in mathematics, and some are geometric figure combinations, which have strong aesthetic value. In teaching, we should make full use of the beauty of lines and colors of graphics to give students the greatest perception and fully appreciate the beauty brought by mathematical graphics to life. In teaching, we should try our best to connect beautiful graphics in real life with classroom teaching, and then apply graphics to artistic creation and the design of living space, so as to make students have the desire to create graphic beauty, drive them to innovate and maintain their long-term interest in innovation.
4. Use historical figures, allusions, interesting stories of mathematicians' childhood and the generation of a conclusion in mathematics to stimulate students' interest in innovation. Students generally like to listen to interesting stories, and tell stories about the history of mathematics development and mathematicians in history, such as the vicissitudes of mathematical theory, the deeds of mathematicians' growth, the contributions of mathematicians in scientific and technological progress, the origin of some conclusions in mathematics, etc., which can not only make students understand the history of mathematics and enrich their knowledge, but also increase their interest in mathematics and learn innovative spirit.