Mathematics situation is an important source for students to master knowledge, form ability and develop psychological quality, and it is a bridge between real life and mathematics learning, concrete problems and abstract concepts. With problems, thinking has motivation; There is a problem, and the thinking is innovative. "Good mathematical problem situations can focus students' attention, stimulate their enthusiasm for thinking, arouse students' more associations, and more easily mobilize students' existing knowledge, experience, emotions and interests, so as to participate in the process of knowledge acquisition and problem solving more independently. So, how to create high-quality problem situations in mathematics teaching? This paper talks about some practices and experiences based on teaching practice.
First, from the need to solve practical problems, create problem situations.
Setting questions or suspense with thinking value can stimulate students' thirst for knowledge. We should consciously mathematize the problems in daily life, let students gradually acquire the "skills" of applying mathematics in daily life and social life under the guidance of teachers, and let them realize that mathematics is an integral part of life, and life can not be separated from mathematics everywhere. We should cultivate their habit of using mathematics knowledge anytime and anywhere and mobilize them to take the initiative to learn mathematics. Use mathematics creatively. For example, when teaching the power of rational numbers, you can set the following questions as an introduction: How thick is a piece of paper with a thickness of 0. 1 mm if it is folded in half for 20 times in a row? Please estimate how thick it will be if it is folded in half for 30 times in a row. As long as we learn today's content-the power of rational numbers, we can solve this problem.
When teaching "three points not in a straight line determine a circle", we can design such a question: Master Zhang accidentally broke a round mirror while cleaning, and only found a small fragment. He wants to make a mirror that is the same as the original one, and find out the center and radius when doing it. He felt embarrassed. Can you help him solve it? You can help him solve this problem through today's study.
These are inseparable from mathematics. Let students use what they have learned to solve problems in daily life, which not only stimulates their interest in learning, but also improves their ability to solve practical problems with what they have learned, and makes mathematics move towards life. "Life Mathematics" emphasizes the connection between mathematics teaching and social life. In the process of imparting mathematical knowledge and cultivating mathematical ability, teachers naturally inject life content. In the process of caring for students' lives, teachers guide students to learn to use what they have learned to serve their own lives. This design is close to students' life, meets their needs, and leaves some reverie and expectation for students, so that they can connect their mathematics knowledge with real life and make mathematics teaching full of life and times.
Second, starting from the original knowledge, create a problem situation
Teachers construct questions or problem groups according to students' existing knowledge, and use the method of examining questions to guide students to realize the transition from old knowledge to new knowledge and cultivate students' thinking ability of transferring knowledge. For example, when learning "power of power", students have mastered "the meaning of multiplication of power and same base powers". In order to guide students to find a way to solve new problems-power law, the following questions can be given.
Calculate the following categories and explain the reasons.
( 1)(6? 2)? Article 4, paragraph 2 (a)? 2)? Article 3.3 (a)? m)？ Article 2, paragraph 4 (a)? m)？ n
After answering the above four questions, let the students compare their conclusions. What are their formal characteristics? (For example, what happened to the base and exponent), after analysis and discussion, students can give the law of power: power is power, the base is constant, and the exponent is multiplied.
When talking about the "triangle midline theorem", let the students draw any convex quadrilateral and connect the midpoints of each side in turn. Students will be surprised when they find that these figures are parallelograms, which leads to the topic.
Introducing new courses from students' existing knowledge background not only consolidates old knowledge, but also stimulates students' enthusiasm and initiative in thinking and cultivates students' ability to explore and acquire new knowledge.
Therefore, in teaching, teachers should be good at creating problem situations in the transition or transformation of old and new knowledge, triggering cognitive conflicts and expectations, and urging students to apply old (existing) knowledge to explore new knowledge.
Third, starting from the inquiry learning method, create a problem situation.
Carrying out inquiry learning is conducive to overcoming the disadvantages of the traditional teaching mode in which teachers instill knowledge into students, stimulating students' desire for knowledge and enterprising spirit, cultivating students' innovative spirit and practical ability, and making students truly masters of learning. What is inquiry learning? The so-called inquiry learning is to select and determine research topics from the subject field or real social life, create a situation similar to academic research in teaching, and acquire knowledge and skills, develop emotions and attitudes, especially the development of inquiry spirit and innovation ability through students' independent inquiry activities such as finding problems, experiments, operations, investigations, information collection and processing, expression and communication.
Question: Kobayashi, a salesman of a bus company, intends to investigate a bus line of the company. It is known that buses stop at 10 station from the starting station to the terminal station in turn. How many different bus lines can passengers take from the starting station to the terminal?
Teacher: Can you solve this problem?
Once the above questions were raised, there was an uproar in the classroom and everyone discussed them one after another. Teachers can take the opportunity to ask: if we draw the driving route as a line segment and regard each stop as a point on the line segment, what is the essence of the problem? This leads to "exploring the number and law of line segments", so the atmosphere in the classroom becomes more active, and students begin to draw pictures, discuss with each other and devote themselves to exploring conclusions.
Fourth, starting from the actual problems in production and life, create problem situations.
For practical problems, students can see and touch them, and some have experienced them personally. It is helpful for students to establish the consciousness of integrating theory with practice and applying what they have learned, especially in the process of solving problems, and to cultivate students' comprehensive, profound and creative thinking.
For example, marketing problems, profit calculation of factory establishment, loan interest calculation, road traffic conditions, environmental resources investigation, sports competition research and so on. These materials can be obtained from students' real life, newspapers, magazines and computer networks. For example, when establishing the concept of function, you can design such a learning situation: organize students to conduct social surveys on Sunday and go to the market to investigate the sales of a certain commodity. We put forward two requirements:
(1) Understand the unit price of a commodity and write down at least two sets of data and amount;
(2) What is the change law among unit price, quantity and amount in the sales process?
Then in the next math class, the students' survey results are displayed and analyzed to guide students to get the concepts of constants and variables, and then the concept of functions is summarized by using this correspondence.
In this way, students can feel that mathematics knowledge is around us through activities, and the concept of function is not abstract, which stimulates students' interest in learning mathematics.
5. Starting from vivid and interesting stories, create problem situations.
It is every child's nature to like stories. There are many interesting stories related to mathematical knowledge. Teachers should pay attention to language description in class, and the plot will be more touching. Emotional stories can touch people's hearts, make students more excited and full of vitality, and also stimulate students' interest in learning.
Before teaching "Plane Cartesian Coordinate System", tell a story about Descartes inventing Cartesian Coordinate System. Mathematician Descartes is studying whether algebraic calculation can replace geometric proof. One day in his dream, he opened the door of the Mathematics Palace with a golden key, and there were dazzling beads everywhere. He saw a spider on the window frame busy weaving a web and flying in the air along the spinning. An idea flashed through his mind: Jingwei in front of him didn't do his best. After waking up, inspiration finally came. Can't the spider's position be determined according to its distance to both sides of the window frame? Doesn't the web laid by spiders in the process of crawling just show that straight lines and curves can be produced through the movement of points? So Descartes invented the rectangular coordinate system, and the teacher naturally brought the students into the mathematical kingdom of "plane rectangular coordinate system" to be studied in this class.
There are many ways to create classroom teaching situations. Teachers should create a teaching situation that is suitable for students' ideological reality, healthy and beneficial in content, closely surrounding the teaching center and full of appeal according to specific conditions. Put students in problem situations, stimulate the internal motivation of learning, and let students learn more, faster and better.