Phenomenon: 1. Openness is achieved by designing open questions, such as "the nature of parallel lines" teaching.
2. Students' group activities are open, such as "Multiplier is the product of a number" teaching.
The question behind the phenomenon is:
1. Alternative thinking (substitute for individual students and teachers), students lack independent thinking.
Substitution phenomenon: individual students substitute thinking-demonstrating and presenting results, but not showing the thinking process.
Teachers think instead of students ―― when students are sick, teachers take medicine; Students are out of order and teachers are in order.
Piece-together phenomenon: several students piece together answers, lack of rigorous and structured training in thinking, and a vicious circle.
2. Teaching lacks basic resources, and students' thinking lacks interaction and collision.
3. Students' thinking is spotty and lack of structural improvement.
"Bug" in teaching philosophy: Without specific students in mind and every student, there will be no real problems in teaching, and teaching may be "going through the motions" and it is unlikely to produce real educational effects for students.
The connotation of openness:
1. Open to students' thinking ―― Developing students' cases
2. Open to all students.
Teaching strategies:
Openness is the premise.
(1) Openness of problem design: there should be room for exploration and thinking.
For example, the teaching of "roots and coefficients of quadratic equations in one variable"
Closed design: find two roots of the equation, compare the relationship between two sums and two products, and the coefficient of the equation.
Open design: Students are required to determine two roots and make an equation according to these two roots to study the relationship between roots and coefficients.
Open one: two roots can be composed of integers, decimals, rational numbers, letters, etc.
Open 2: Study on the relationship between the sum, difference, product and quotient of two roots and the coefficient of the equation.
Another example is the teaching of "the nature of parallel lines"
Closed design: draw two parallel lines cut by the third straight line and find a pair of congruent angles. What did you find? And prove the experimental verification; Then find a pair of inner corners. What did the handmaiden find? And carry out geometric proof.
Open design: two parallel lines are cut by a third line to form a three-line octagon. What is the relationship between these angles?
"Bug" in teaching philosophy: reviewing foreshadowing and hinting, distrusting students.
Unity needs to go hand in hand and ignore differences.
Limited by the arrangement of knowledge points in textbooks, they lack the consciousness of using textbooks.
(2) The shift of teaching focus.
(4) Providing opportunities for independent thinking ―― the premise of generating basic resources.
④ Capture the problems, obstacles and highlights in students' thinking ―― the collection of basic resources.
④ The "parallel" presentation of student resources as interactive resources ―― the premise of student-student interaction and teacher-student interaction.
(3) Open teaching flow chart.
From the perspective of teacher-student interaction, the classroom teaching process can be summarized as the following processes:
Capture, judge, adjust and promote generation
―――――――→
↑ ↓
Open import → student resource generation → teacher's response and feedback → teaching process generation (new resource generation) → open expansion.
↑ ↓
←―――――――
Interactive deepening and promoting teaching
If there is an open problem design, but the opportunity to solve the problem is not delegated to students-→ false opening
If you delegate the opportunity to solve problems to students, but you don't have the consciousness to capture students' resources-→ waste time.
If the student resources are captured but not used, they will be unilaterally moved to semi-opening.
If students' resources can be effectively used and teachers can respond effectively, then the interaction between the two sides is truly open.
2. Capture is the key
Capture: Pay attention to the students' state, and don't turn a blind eye.
Students should pay attention to sample collection and not blindly patrol.
We should be aware of the misuse of resources, not just looking for the right solution.
You must have a sense of value judgment of resources, and you can't show all the mistakes.
3. Resource utilization is the key.
Tandem phenomenon: one after another. Lack of time and effective use of resources
Random phenomenon: Teaching follows students. Lack of capture and judgment, lack of inspiration and promotion.
The "series connection" of variable resources presents "parallel connection".
The random presentation of change is a process presentation from concrete to abstract.
4. The goal is to promote effective response from generation to generation.
(B) communication between mathematics and real life
1. Phenomenon: Mathematical problems+life situations-superficial communication and superficial understanding.
2. The "worm" in the teaching concept: open classroom consciousness and display consciousness.
3. The connotation of communication-enhancing the vitality of teaching content
Activate book knowledge
Realize the communication in three aspects: a. Realize the communication between book knowledge and life world.
B realize the communication between book knowledge and students' experience world and growth needs.
C. realize the exchange of book knowledge with people who discover and develop knowledge and history.
Step 4: Strategy
(1) The introduction of problem situations and the extension of problems in the overall background of knowledge
(2) Communication with real life before, during and after class.