Classroom teaching is inseparable from students' questions and answers. How to deal with students' questions and answers in class, stimulate students' thinking and improve learning efficiency should be a subject that every teacher constantly explores. After students answer questions in class, our teacher should not simply affirm or deny with "right" or "wrong", but should ask questions such as "why" and "what do you think" to stimulate students' thinking and let them fully expose their thinking process. In this way, teachers can not only understand students' thinking defects, but also let students correct their mistakes from reflection, thus promoting the development of students' self-awareness.
Because students are fully exposed to the existing problems in the process of thinking, teachers can "prescribe the right medicine" in time, inspire and induce, so that teachers can give full play to the leading role, maximize the students' main role, and enable students to truly grasp the initiative in learning.
Digging Knowledge Connotation and Cultivating Mathematics Interest
Nowadays, due to various factors, especially the strict and abstract requirements for its logical structure, it is sometimes impossible to show the occurrence and development process of knowledge completely, comprehensively and systematically. Therefore, as a teacher, if his teaching only stays in the form of this abstract structure, students' thinking will be hindered by the lack of concrete and vivid new information. In teaching, teachers should let students know the background, source, status and function of problems in mathematics. That is, introduce some new and more systematic knowledge connotations relative to textbooks, so as to stimulate students' interest in learning and achieve the purpose of activating thinking.
At the same time, interest is also important, because interest is the best teacher. People's interest in mathematics can undoubtedly be transformed into a powerful and lasting motive force for learning mathematics, which is very conducive to the development of mathematical thinking. How to cultivate students' interest in learning mathematics? The first is to adopt flexible and diverse teaching methods. For example: talk about concepts through reading and discussion; Talk about nature with discovery method and comparison method; Do exercises or review your lessons by talking, practicing or discussing. Let students take the initiative to participate, learn and use. The second is to enhance the interest in mathematics learning. Personally, I think that teachers should lose no time in adding some interesting questions about the history of mathematics and life when preparing lessons or attending classes. For example, before teaching "similar triangles", we can briefly introduce the story of ancient Thales measuring the height of the golden pagoda with a wooden stick. Another example is to explain the story of Zu Chongzhi's study of pi, the story of Chen Jingrun's brave exploration of Goldbach's conjecture, and the story of "one hundred dollars for one hundred chickens" in ancient China. In this way, under the guidance of the teacher, students can successfully transfer their motivation and interest in listening to stories to learning new knowledge, and feel that mathematics is no longer boring, but interesting and regular.
2
How to inspire students' thinking in mathematics teaching
Protect students' unique viewpoints and pave the way for students to think about problems.
Mathematics learning is a kind of thinking learning, and the end result of improving mathematics ability should be the improvement of thinking ability. Teachers are often limited by their own thinking and reference books when preparing lessons and choosing examples. The solutions they think of may be limited and complicated, while some students are quick-thinking and positive. They are often not limited to the teacher's answer, but will "why are you doing this?" Is there any other simple way? So it is likely that there will be new discoveries.
Therefore, in the classroom question and answer, teachers should not and can't limit the thinking activities of dozens of students within the framework set by themselves, which will not be conducive to the cultivation of creative talents. When answering questions in class, teachers should seize the opportunity to "pave the way" when students are confused in thinking, interrupted in thinking and confused in methods, so as to help students get rid of thinking obstacles, gradually explore new ideas, master new methods and constantly improve their thinking level.
Evaluate students in a timely and positive manner.
Zankby, a famous educator, said: "Once the teaching method touches students' emotional and will fields and their spiritual needs, this teaching method can play a highly effective role." Students' learning activities can't be smooth sailing, and there must be many mistakes and cognitive biases. At this point, teachers should not completely deny it, but guide students to think for themselves and find out the mistakes; Teachers should give enthusiastic appreciation to the correct answers. Change the possible negative evaluation into positive evaluation, especially for the students who answered incorrectly, we should try our best to find some bright spots, try our best to dilute students' inferiority complex in the failure of answering, and constantly strengthen students' internal motivation for learning.
If teachers are indifferent to students' classroom performance, indecisive about a very creative answer, or only pay attention to their own performance without paying attention to what students are thinking and saying, this will make the classroom atmosphere tend to be silent, virtually killing students' creative desire, not to mention activating students' thinking. Therefore, evaluation is an indispensable means in classroom teaching. Through evaluation, students can clearly understand the success or failure of solving problems and the advantages and disadvantages of thinking; Through evaluation, students can grasp the general situation of a class or the whole problem. Therefore, evaluation is a powerful measure and method to activate students' thinking.
three
How to Cultivate Children's Mathematical Thinking
Cultivate students' critical thinking ability
Without criticism, there is no innovation. Therefore, critical thinking is also an important aspect of thinking quality. Critical thinking refers to being good at strictly estimating thinking materials and carefully examining the thinking quality of thinking process in thinking activities. Designing some trap thinking problems can cultivate students' critical thinking ability.
For example, in teaching, we often see such a phenomenon: only about 60% of students have basically mastered a problem after learning it from the front, and some students have made mistakes in the problem because they used the wrong concepts, rules, formulas and theorems. Therefore, it is necessary to strengthen the cultivation of students' critical thinking ability from the opposite side. In teaching practice, when I finish learning a certain mathematics knowledge, I will deliberately set traps for students and create the following situations: First, let students talk without thinking; The second is to induce students to "be fooled" and "be fooled", and only after analysis and criticism can they suddenly realize. The correct understanding of things by this method is beyond the reach of positive training.
Reconnect with the reality of life and cultivate children in life.
When I was a child, I didn't need to teach my children math books deliberately, because there was math everywhere in my life. One day, a three-year-old child wanted to eat lollipops, so I asked him, how many do you want? He thought about it, put up three fingers and said, "I want three." So I bought him three lollipops, and he ate happily. At this time, I asked him, "How many lollipops did you buy, little friend?" He said happily, "three". "How many have you eaten now?" One. How much more? He thought for a moment and said, "There are two more." I think you should just ask him, "How much is 3-2?" Of course he doesn't know. Therefore, life is fertile ground for mathematics. Mathematics teaching should be linked with life and close to real life.
four
How to Cultivate Primary School Students' Innovative Thinking in Mathematics
Let students take the initiative to participate in inquiry and cultivate innovative ability.
First, establish an open classroom teaching system. Students' learning content should be fully open and selective in class; Make students' learning objectives open and flexible; Make students' learning time and space open and broad; Make students' learning achievements open and diverse; Only in this way can we arouse students' open mind, make the classroom really alive, make students really move, make the world of innovation infinitely vast, and make innovation opportunities everywhere.
Second, let students fully explore independently and realize self-creation. Teachers and students should establish a new relationship, from the role of "soloist" to "accompanist". From then on, it is no longer mainly to impart knowledge, but to help students discover, organize and manage knowledge and guide rather than shape it. In the classroom, teachers should reasonably use the heuristic principle, skillfully guide, create inquiry situations, give students the opportunity to ask questions and explore, make students clear the specific content of autonomous learning, master flexible and diverse inquiry methods, and discover the laws by themselves, so as to cultivate students' innovative consciousness and ability, and finally achieve the goal of self-creation.
It is difficult to ask questions and activate thinking.
Learning begins with thinking, and thinking begins with doubt. It is the best opportunity to enlighten students by asking questions skillfully at the key points of teaching, so that students can't get what they want, but they can't talk. At this time, teachers should give instructions and guidance, so that they can be triggered at any time, drive their thinking activities, and make them consciously become the masters of learning.