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How to design "dialogue" activities in mathematics classroom teaching, so as to break through difficulties and highlight key points?
Dialogue teaching refers to the teaching form in which teachers and students produce knowledge and teaching significance, as well as the value and significance of life in an atmosphere of democracy, equality, respect, tolerance and friendship through interactive ways such as discourse, understanding, experience and reflection. This is a kind of teaching that respects subjectivity, embodies creativity and pursues humanization. "Facing the life world, teaching is integrated into life; Stretch students' personality and let imagination and creation become the main theme of the classroom; Learning to communicate and share, making interaction and cooperation full of teaching style "is the basic idea of dialogue teaching and the basic idea of classroom design. Under the guidance of the basic idea, the classroom design of dialogue teaching should adhere to the following main principles, namely, problem-oriented, respecting differences, being close to life and paying attention to generation. The following author talks about his own views on the application of the four principles.

1. Question guidance, leading teaching.

The problem is essentially a situation, a kind of "individual wants to do something, but can't immediately know a series of actions that this kind of thing needs to take, and there is a gap and obstacle between the established state and the target state". It is the existence of this gap and the call for the successful transformation between the established state and the target state that attracts the continuous interaction between teachers and students and between people and texts in dialogue teaching. In other words, the question is the focus of the dialogue. In other words, the core of dialogue teaching is the question, without which there is no dialogue. Therefore, strengthening problem guidance is the key link in the classroom design of dialogue teaching.

Cognitive learning theory tells us that new knowledge must be combined with learners' cognitive level. When the new knowledge is inconsistent with the cognitive structure of learners, it is necessary to adjust the original cognitive structure to meet the new learning needs and establish a new cognitive structure as the basis for further learning. For example, students find it difficult to learn the concept of function. This is because in the past, the deformation of algebraic identities, the solutions of equations and inequalities were all obtained through operation, with the emphasis on "operation", while the concept of function is to examine the relationship between quantities from the perspective of change, with the emphasis on "relationship", and the expression methods are analytical formulas, tables and images. If the original cognitive structure can't adapt to new knowledge, learning will be difficult, which requires teachers to improve teaching methods, strengthen problem guidance and help students adjust and reorganize their cognitive structure. For example, for a car with a driving speed of 40 km/h, try to analyze the relationship between driving time and distance, and adopt the following problem chain: