Teaching design under the seventh grade mathematics of People's Education Press.
Propositions and theorems
Teaching purpose: 1, knowledge and skills: understand the concept of proposition and distinguish the topic setting and conclusion of proposition.
2. Through the process of judging the truth value of the proposition, we have a preliminary understanding of the truth value of the proposition.
3. Initially cultivate students' ability to transform different geometric languages.
Emphasis: the concept of proposition and the proposition and conclusion that distinguish proposition.
Difficulties: distinguish between propositions and conclusions.
teaching process
First, create a situational review import.
The teacher showed the following questions:
1. What are the methods for judging parallel lines?
2. What are the properties of parallel lines?
Students can actively think about the questions raised by teachers, review and consolidate relevant knowledge points, and lay a good foundation for the study of this class. (Note: There are three ways to judge parallel lines, and there are also inferences of parallel axioms. )
Second, try to explore new knowledge.
The teacher made the following statement.
(1) If two straight lines are parallel to the third straight line, the two straight lines are parallel to each other;
Add the same number on both sides of the equation, and the result is still an equation;
③ the vertex angles are equal;
④ If two straight lines are not parallel, the congruence angles are not equal.
Students can analyze the characteristics of each sentence under the guidance of the teacher. Thinking: Can you tell me what these four sentences have in common? And I can conclude that these sentences are all judgments about something. I feel that some mathematical languages are judging something.
The teacher defined this proposition.
A statement that judges a thing is called a proposition.
(3) the composition of the proposition.
A proposition consists of a topic and a conclusion. The topic is what is known, and the conclusion is what is derived from what is known.
(2) Can the formation of the proposition be written? If, then? The form of.
True proposition and false proposition:
The teacher asked questions:
If two angles are equal, they are diagonal.
If a & gtb.b & gtc, then A = B.
If two angles are complementary, they are adjacent complementary angles.
Third, try to feedback and understand new knowledge.
There are right and wrong propositions:
The correctness of the proposition is proved by our reasoning, and the true proposition thus obtained is called a theorem. As a true proposition, this theorem can also be used as the basis for further reasoning.
1.- Both sides of the equation are multiplied by the same number, and the result is still that the equation ‖ is it a proposition? What are their topics and conclusions?
2. Proposition-Is it correct that two parallel lines are cut by a third line and the internal dislocation angles are equal? Proposition-If two angles are complementary angles, then they are adjacent complementary angles. Is that correct? Give some examples of propositions to judge whether they are correct or not.
Summary and expansion: Teachers guide students to complete the summary of this lesson and emphasize important knowledge points.
Homework: Exercise 5.3 1 1.
Cultivation of Mathematical Thinking Ability in Junior Middle School
First, break the traditional model and build a thinking classroom.
Junior high school is a critical period for students to establish emotional awareness, and students' goodwill towards teachers is the basis of classroom interaction. Should teachers avoid teaching? Cramming at the last minute? Teaching methods, because this teaching method can easily make students increase their sense of dependence on teachers and reduce their awareness of autonomous learning. In class, teachers should strengthen interaction with students and increase questions appropriately. In addition, teachers should combine the actual situation in teaching, set questions as close as possible to the interests of middle school students, and break the original boring way of preaching. Only by establishing a good emotional communication platform between students and teachers can students become interested in the classroom and effectively exercise their thinking ability in the process of autonomous learning.
Second, exercise thinking ability in the process of solving problems.
(A) to strengthen the ability to examine questions
Examining questions is the first step to solve problems. Looking closely at today's middle school students' answer papers, we can find that improving the ability to examine questions is a key step to solve the problem because there are many wrong questions in the examination. In daily teaching, teachers should pay attention to cultivating students' consciousness of carefully examining questions, such as letting students mark key conditions with pens or asking students to examine questions in a low voice. All these help students understand the topic.
(2) Set up thinking problems and leave room for students' imagination.
Whether it is the setting of classroom examples or after-class exercises, teachers need to use their brains. Teachers should attract students with topics close to their lives, let them practice and strengthen the consolidation of knowledge. The topic of divergent thinking is very beneficial to the cultivation of students' various thinking abilities. Moreover, this kind of topic is generally novel in form and impressed by students, which is beneficial for students to absorb this kind of knowledge. For example, there are 200 grams of salt water containing 15% and 150 grams of salt water containing 40%. There is enough salt and water to make 300 grams of salt water containing 20%.
1. If the requirement is to use existing salt water, but use as little salt and water as possible, how to design the configuration scheme?
2. Is there any other configuration scheme? This kind of topic is a topic of divergent thinking. The first question gives students more space for independent thinking, enabling them to use logical thinking ability to expand their imagination, comprehensively apply what they have learned, and finally get a reasonable configuration plan. The second question is based on the first question. Students can discuss with each other and cultivate their sense of seeking differences. In this way, in the whole process of solving problems, students' thinking ability has been effectively exercised.
(C) cultivate a sense of reflection on right and wrong issues
Sorting out and reflecting on wrong questions is the most effective way to correct mistakes, deepen impressions and improve grades. Middle school students' autonomous learning ability is weak, and they are not good enough in this respect. Therefore, teachers should pay attention to cultivating students' ability to reflect on right and wrong questions, and make rigid requirements for students' study habits, so that students can disperse their thinking and gain new enlightenment in the process of continuous summary and reflection.
Students may often encounter such a situation: for example, when doing a problem, they can't get the answer after repeated thinking, but once others put forward their opinions or read the answer analysis, they immediately think of the way to do it. In fact, this is because students do not have a firm grasp of what they have learned. Therefore, students should cultivate the consciousness of reflection and arrangement of right and wrong questions, remember their unfamiliar knowledge while understanding the standard answers, and make more efforts in the links that cause obstacles to solving problems. In addition, in the process of sorting out the wrong questions, students can often get new methods to solve problems or have a deeper understanding of the problems, which are all exercises of thinking mode.
Third, the conclusion
In the process of mathematics teaching, on the one hand, teachers should accurately transfer knowledge to students; On the other hand, we should also pay attention to the cultivation of students' learning methods and thinking ability. Mathematics learning is an interesting and flexible process. In math class, students' thinking will be more easily exercised. Therefore, teachers must grasp the characteristics of junior high school students in this period, build a thinking and emotional classroom, so that students can improve their ability while studying, and finally achieve the goal of new curriculum reform.
Author: Qiu Aigan Unit: No.7 Middle School, Shangrao County, Jiangxi Province