Under the careful organization of the professor of Beijing Institute of Education and the coordination of Li, a special-grade teacher in Beijing, I had the honor to attend the first and second classes in the experimental school of Beijing University of Aeronautics and Astronautics on June 5438+1October 65438+May, 2020. This lecture is a nutritious spiritual feast, with rich harvest and many feelings.

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From the geometric point of view, through the function image, the change of independent variables leads to the change law of function values, and the transition to the algebraic point of view to describe the unequal relationship between variables, thus producing the concept of function. The monotonicity of function is proved by different 66-number models, which strengthens the understanding, understanding and application of monotonicity of function.

The function model chosen by teacher Cong has changed from the univariate quadratic function and inverse proportional function that students are familiar with to the check function. The choice of function model has a certain gradient, which is in line with students' learning situation.

In the teaching process, teacher Cong is good at inspiring and guiding students, including teachers' demonstration and students' independent thinking, communication, discussion and sharing, so as to implement the concept and application of monotonicity of functions.

Teacher Cong's class, starting from the class function, teaches students mathematical thinking mode and attaches importance to the monotonicity and general realization of the function.

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Monotonicity of Function In the second class, on the basis of teacher Cong's teaching, Teacher Li led students to learn monotonicity of abstract functions.

When teaching monotonicity of abstract functions, Mr. Li pays attention to teaching students the way of thinking to solve problems and builds a bridge between known conditions and questions.

This is exactly what we usually ignore in teaching. It is not to solve problems for the sake of solving problems, but to teach students mathematical thinking methods, so as to lay the necessary reserves for the subsequent study of other mathematical contents.

Teacher Li digs the hidden information in the textbook, and extends the inequality relation in the concept of monotonicity of function to the relation between secant slope and 0, and then transitions to the tangent slope of curve. Organically unify the internal relations of mathematical knowledge.

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What should we teach students in classroom teaching? This is a question worthy of our front-line teachers' deep thinking.

As a classroom teaching, one is to implement the basic knowledge of mathematics; The second is the classroom teaching of mathematics subject with knowledge as the carrier to cultivate students' basic ideas and methods of analyzing and solving problems; The third is to teach students mathematical thinking mode and learn ever-changing mathematical knowledge with the same mathematical thinking mode; The fourth is to cultivate students' mathematical literacy and lay a good foundation for lifelong learning in the future.