In recent years, our school has implemented "task-driven group cooperative learning based on learning plan". Before class, according to the teaching content of a class and students' cognition, the teacher determines the teaching objectives and difficulties, prepares the study plan with questions as the main line, and assigns certain inquiry tasks to students, so that students can preview the new class with questions and promote students' autonomous learning better. In class, the problems exposed by students are the center and the starting point. Teachers communicate with students at any time according to their questions, which really makes students feel that they are the masters of learning and the adjusters of self-development. Using lesson plans, students' thinking is always in a state of high tension and excitement, which greatly improves students' learning enthusiasm and changes the previous "want me to learn" into "I want to learn". This teaching mode is very suitable for the problem-solving teaching of theorems, laws and exercises in mathematics class. However, in the previous teaching of mathematical concepts, teachers despised concept teaching, only showed students textbooks in class, and asked students to do examples and exercises with a little hint, so that students had a little knowledge of mathematical concepts and their enthusiasm for learning was not high. In order to break through this teaching difficulty, I changed the original teaching method and made full use of the teaching plan to create a practical and efficient classroom.
Mastering concepts is the basis of learning mathematics well, the premise of learning theorems, formulas, rules and mathematical thinking methods well, the key to improving problem-solving ability and the basis of solving examples and exercises. According to the traditional teaching methods, students' perceptual knowledge of concepts is very shallow, and the learning concepts are too rigid to be flexibly applied to learning, so students' learning ability can not be improved and cultivated. Now, we make good use of the teaching mode of "task-driven group cooperative learning with learning plan as the carrier", highlight problem design, strengthen problem solving, enrich students' perceptual knowledge, break through the difficulties of concept teaching in mathematics, use learning plan to ask questions, drive group cooperation, group cooperation and teacher-student cooperation, so that students can fully perceive the generation process of concepts and make them feel at home in the application process of concepts. Therefore, when teaching the concept of binary linear equation in the first section of Chapter 8 in the second volume of the seventh grade of People's Education Press, I set up the following teaching procedures.
First, create scenarios and introduce questions.
In the teaching plan, some practical questions are set according to students' existing knowledge and experience, so that students can explore before class with specific tasks, thus stimulating students' interest in learning, arousing their curiosity and mobilizing their enthusiasm. By solving problems, let students feel the characteristics of the new concept of binary linear equation, and prepare for learning the new concept of binary linear equation. For example:
1, 3 1 problem of "chickens and rabbits in the same cage" in Sun Tzu's Art of War;
"Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. What are the geometric figures of chickens and rabbits? "
2. A class of 39 students went boating in the park, and * * * rented 9 boats, each big boat can take 5 people, each small boat can take 3 people, and each boat is full. Q: How many big boats and small boats have you rented?
Second, ask questions and feel the characteristics.
Set two questions on the lesson plan for students to explore: ① What is the arithmetic relationship in the above questions? (2) How to use mathematical expressions?
Through the observation and comparison with the linear equation of one yuan, the process of the concept of linear equation of one yuan is obtained by analogy, and it is easy for students to establish an understanding of the essential characteristics of linear equation of two yuan. Let students take the existing knowledge as the growing point, that is, the concept of linear equation of one variable, and guide students to observe and perceive the essential properties of linear equation of two variables. It makes it easy for students to understand, master and internalize new knowledge, and at the same time, taking problem solving as the carrier, the mathematical thought of analogy naturally permeates students, which conforms to the cognitive law of students' gradual learning from shallow to deep.
Third, seize the opportunity and name it in time.
On the basis of letting students fully feel the characteristics of the new concept, seize the opportunity and name it at the right time: that is, the equations such as x+y=35 and 2x+4y=94 are called binary linear equations. Then let the students summarize, refine and describe the definition of binary linear equation. They are likely to come to the conclusion that the equation contains two unknowns, and the degree of each unknown is 1, which is called binary linear equation.
Fourth, refine the summary and standardize the definition.
Because students' cognition is superficial and their ability is limited, it is inevitable that they will make mistakes in knowledge, which is very normal. In teaching, teachers should properly design questions, let students try and make mistakes, and fully expose the defects in knowledge. At the same time, we should respect students and encourage them to actively participate in the whole process of knowledge formation, which is advocated by the new curriculum and the concrete implementation of the "people-oriented" educational concept. In the teaching of learning teaching plans, we should actively encourage students to participate in the attempt, think in the attempt and make progress in thinking.
According to the students' preliminary understanding of some features of the new concept, the teacher designed the following set of exercises on the teaching plan: the following equations are binary linear equations (
)
( 1)3x+2y
(2)x+2=0
(3)x+xy= 1
Let the students judge one by one and find out the basis of each question. Especially the "xy" in (3), students will question it. At this time, teachers should not rush to uncover the mystery, seize students' curiosity and thirst for knowledge, and let students explore independently and discuss in groups. There is naturally a heated discussion atmosphere in the classroom that "a stone stirs up a thousand waves". Then, through the guidance of the teacher, students can finally improve their understanding of the definition of binary linear equation: an equation with two unknowns and the number of terms of the unknowns is 1 is called binary linear equation. The teacher writes on the blackboard and writes down the "item" with a red pen. In this teaching process, teachers let students explore, analyze and summarize themselves to get a correct understanding. The implementation of this teaching link is conducive to deepening students' understanding and mastery of concepts, so that students can truly experience the process from special to general and the process of knowledge generation and formation, and gradually achieve the goal of cultivating students' ability of abstract generalization.
Five, definition analysis, grasp the essence
In order to deepen the understanding of the definition, students can write a binary linear equation by themselves. By making mistakes and comparing in groups, students can tell the basis more deeply and dig out the key words of "two", "item" and "1". This definition will be more profound and grasp the essence of the definition. You can even cite counterexamples or variants, analyze mathematical concepts from the opposite or side, highlight the essential elements hidden in the object, and deepen students' comprehensive understanding of the concepts.
VI. Consolidate practice and deepen understanding
Students' mastery of concepts is a cyclic process from concreteness to abstraction, from abstraction to practice, and from practice to abstraction. Whether students really thoroughly understand and firmly grasp the concept needs to be experienced through practice, that is to say, the understood concept may not really be mastered, and only through repeated flexible application can the understanding of the concept be consolidated and deepened. To this end, I set the following two questions:
1, it is known that the equation 3xm+3-2y 1-2n=0 is a binary linear equation. How to find the values of m and n?
2. The equation (m-3)x|n|+ 1+(n+2)ym2=0 is known.
Is a binary linear equation, find the values of m and n?
Through the above two questions, we can find that when the same concept appears in different situations, students who are already familiar with the definition can still feel new inspiration in the process of solving problems. Therefore, in order to further sublimate students' understanding of concepts, we can design different scenarios and different types of questions, so that students can consolidate and deepen their understanding of concepts in the process of solving problems, so that students' thinking can be developed in depth, breadth, flexibility and creativity, and can be upgraded to rational knowledge, which can be incorporated into the existing cognitive structure and transformed into creative ability to analyze and solve problems.
In short, in this class, teachers guide students to discover and solve problems step by step and experience the essence of mathematics, which truly reflects that students are the masters of learning and teachers are the organizers, guides and collaborators of classroom learning. In classroom teaching, more attention is paid to effectiveness, while the elements of expression and the pursuit of mode and form are less, and more attention is paid to knowledge generation, scenario creation and learning effect, thus making the teaching of this concept course colorful.