First, everyone learns valuable mathematics.
What is valuable mathematics? I think that mathematics in life, interesting mathematics, is conducive to the development of students, and mathematics that can be learned well in a limited time is valuable mathematics. Therefore, our mathematics teaching should be closely linked with students' reality, and create vivid, interesting and intuitive mathematics teaching activities based on students' life experience and existing knowledge, so as to stimulate students' interest in learning and let students understand and know mathematics knowledge in a vivid and concrete situation within a limited time.
The new curriculum standard clearly points out that "mathematics teaching should be practical, operational and exploratory" and "students' learning mathematics should become the process of students' exploring mathematics". It can be seen that inquiry learning is beneficial to students' development.
For example, when teaching "parallel lines", teachers can break away from convention and adopt the viewpoint of movement change to teach; The teacher can ask the students to spread a piece of white paper on the desktop, throw two sticks at random on the paper, and finally draw them with strokes. What does it matter if we look at their position? Through the activities from dynamic to static, students can clearly know that there are two main positional relationships between two straight lines in the same plane: intersection and parallel. Make it clear that two straight lines that do not intersect in the same plane are called parallel lines. This design pays attention to students' exploratory and research-based learning in solving problems and creates opportunities for students to engage in mathematics activities. Students are not listening to math, nor watching math, but doing math.
Second, everyone can get the necessary math.
Necessary mathematics includes the basic knowledge of mathematical value, the consciousness and ability to develop and solve mathematical problems, the ability to read, write, discuss and communicate in mathematical language, and the basic ideas and methods of mathematics.
In mathematics teaching, teachers should not only let students learn mathematics knowledge, but also let students feel and experience the value, ideas and methods of mathematics in the process of learning and doing mathematics. Let students realize that mathematics is a subject of exploring patterns, helping people to collect, sort out and describe information, build models, solve problems and directly create value in society.
For example, when teaching "the invariance of quotient", teachers can first express 3 ÷ 1 = 3, and then ask students to illustrate the formula that quotient is 3. This greatly mobilized the students' enthusiasm, and the students talked about many formulas respectively. For example: 9 ÷ 3 = 3, 12 ÷ 4 = 3, 24 ÷ 8 = 3 ... and then guide students to observe and discuss: The dividend and divisor of these formulas are different, why are the quotients different? What are the rules? Inspire students to discover the invariance of quotient. The purpose of this design is to guide students to observe and discuss, train students to make preliminary analysis, synthesis, comparison, abstraction and generalization, and judge and reason simple problems, so as to complete a process of induction from special phenomena to universal laws. Inductive reasoning has the function of "discovery" and some proving functions, and it is an effective cognitive strategy. Only when students master certain mathematical methods can they solve corresponding mathematical problems quickly and effectively.
The purpose of learning is to apply. In real life, it is often difficult to have all the data, projects and relationships needed to solve problems. At this time, we should constantly create meaningful problem situations, encourage each student to explore mathematics, and learn to collect and sort out information and solve problems with peers.
For example, when teaching "general application problems", you can show such a problem. The average height of a class is 140 cm for boys and 142 cm for girls. What is the average height of the class? Then ask the students to choose: A, (140+142) ÷ 2 =141b, the conditions are insufficient, and it is impossible to do C. The average height of the whole class is between 140 cm and/kloc-0. Then discuss and communicate in groups and get the correct answer and answer: (1) Why choose C? Why is the average height of the class uncertain? (2) Make up the conditions, and you can get the average height of the class? (3) Under what conditions, Formula A is also correct, and how do you prove it? This kind of teaching not only enables students to understand the relationship between general thinking methods and special methods of "general application problems", but also learns to think flexibly from a special angle under the guidance of universal principles. Through the process full of exploration and independent experience, students can gradually learn to solve problems with mathematical thinking methods, gain self-successful experience and enhance their confidence in learning mathematics well.
Third, different people get different development in mathematics.
Personality is the real form of human existence, and different people are developing in different ways, which means that teachers should face up to and admit the differences of students in mathematics teaching, and teachers should establish such an idea; Every student can learn mathematics, allowing students to learn mathematics at different speeds, and can learn mathematics in their own way, with different development in mathematics.
For example, when teaching "12-7", Students can use different methods to calculate: "reciprocal method" (want to add and subtract), "ten-break method" (disassemble the minuend) 12-7 = 2+( 10-7) = 5 "continuous subtraction" (disassemble the minuend) "transformation method" (the difference is unchanged)/kloc.