First, create a reasonable problem situation.
In the teaching process, teachers should guide students to think and find reasonable solutions by creating reasonable problem situations.
For example, when explaining "the definition and standard equation of ellipse", I guide you to explore the formation process of this very beautiful figure and how to make a standard ellipse. To this end, I asked the students to prepare a rope of about 30 cm and two thumbtacks in advance. Teachers and students cooperate to demonstrate the formation process of ellipse on the blackboard, summarize the definition of ellipse, establish coordinate system according to literal translation method, and deduce the standard equation of ellipse. In this way, the classroom atmosphere becomes active and students learn vividly driven by problems.
In this class, because the ready-made conclusions are not directly taught to students, they create problem situations and design a series of questions according to the context of students' thinking development, so that students can actively explore the process of knowledge construction. Therefore, remarkable teaching effect has been achieved.
Second, timely development of variant teaching
Every link of mathematics teaching is a process of making students build new knowledge through migration and transformation on the basis of existing old knowledge. Therefore, paying attention to the transfer and transformation of knowledge plays a very important role in improving students' thinking ability. In the process of teaching, even the most common traditional questions can be properly deformed and transformed, which not only consolidates the original knowledge, but also develops the potential of students. Therefore, when preparing lessons, we can put the same or similar problems together, so that students can sum up the law of solving problems from the perspective of thinking methods. We can also split some more complicated problems into small ones and break them one by one to guide students to reach the final conclusion.
For example, after | 2x+ 1 | < 3, I designed the following problem group:
Variable 1: | x-2 | < 2x+ 1
Variant 2: | x-2 |
Variant 3: | x+1| x+7 | ≥1
The solution set of variant 4: | x-2 |+| x-5 | < A is not an empty set, so the range of the number a is realistic.
Variant 5: For any real number X, the inequality |x-6|+|x-9|≥ a holds, and the range of the number A is realistic.
Variant 6: If the minimum value of f(x)=|x-a|+|3-x| is 2, find the value of a.
Starting from the most basic absolute inequality, this paper sets the variant 1 and extends it to the type of | f (x) | < g (x). Variants 2 and 3 are two absolute values, which increases the difficulty. Variant 4 introduces parameters, and Variant 5 and Variant 4 are distinguished, which helps students to distinguish two easily confused concepts: solution and the establishment of constants. Variants 6 and 5 are different levels of problems. In this way, six different questions are derived from one basic question, which is difficult to learn, and students will not feel that the learning span is too big.
Third, sum up in time and develop thinking.
In the process of variant teaching, the knowledge acquired by students through independent exploration and discussion is still chaotic. At this time, teachers can guide students to summarize all the knowledge, rationalize and systematize the knowledge, and guide students to reflect on it in time, so as to achieve the effect of drawing inferences from others.
In a word, inquiry teaching has many forms. Teachers should combine the teaching content, teaching environment and students' foundation, formulate an operable and effective teaching plan, fully mobilize students' subjective initiative, make inquiry teaching become the mainstream, serve teaching and students, and make new contributions to mathematics teaching under the new curriculum reform.