Mathematics, as the basic subject of junior high school curriculum, is naturally the main position to implement inquiry learning. Then, how to carry out inquiry learning in junior high school mathematics? Now, we will give an inquiry teaching demonstration on the section of "Binary linear equations and their solutions" in seventh grade mathematics teaching, and discuss learning with colleagues. In this section, after learning the concept, solution and application of linear equation with one variable, we will further learn the concepts of linear equation with two variables, linear equation with two variables and their solutions. In this section, we learn to master the concept of the solution of binary linear equation (group), and make clear the difference and connection with linear equation. The textbook uses students' original knowledge and experience to construct the concept of binary linear equation (group) and its solution, and uses the actual background of new knowledge to enhance students' application consciousness and understand that mathematics comes from life.
Starting from the examples that students are interested in and familiar with, we create problem situations, use the existing knowledge of linear equations to explore the concepts of linear equations (groups) and their solutions, and verify them one by one through learning, so as to understand the differences and connections between linear equations and solutions, combine mathematical knowledge with real life, make mathematics close to life, and let students gain mathematical experience. At the same time, improve students' ability to convert written language and symbolic language, use what they have learned to solve the problem of extension, so that students can further understand mathematical concepts and improve their ability to solve mathematical problems.
First, create questions to stimulate students' interest in inquiry
Creating problem scenarios can visualize abstract problems, be close to students, and stimulate students' interest in solving problems.
For example:
Teacher: Do the students like football? Let's study a football problem today, shall we?
[Question 1] Football points are as follows:
In the game, it is stipulated that if you win a game, you will get 3 points, if you draw a game, you will get 1 point and if you lose a game, you will get 0 point.
Liaoning played 9 games in the first round, 17 points. Only two games were lost in this round, so how many games did Liaoning win? How many draws are there?
Teacher: How many ways can students solve this problem?
Let the students think independently, let them answer according to their own thinking methods, and the teacher adjusts the classroom teaching procedure according to the students' specific answers.
If students solve by arithmetic first, the number of times won by Liaoning team is (17-7)÷(3- 1).
Or list a linear equation to solve the problem. For example, if the number of games won by Liaoning team is X, then the number of games won is (7-x), and the listed equation is 3x+(7-x)= 17. Then guide students to explore the concept of establishing a binary linear equation and its solution.
Explanation: If students have a good grasp of their own basic knowledge, and have found that the letters "X" and "Y" are used to represent the winning and losing numbers of Liaoning team, and two equations are listed, then the teacher will demonstrate the process of establishing mathematical knowledge from practical problems to equations with students according to their thinking, with the aim of paying attention to the development of personality and taking care of individual differences.
Second, guide students to explore their own desires
1. Students get the equation x+y=7 from the relationship between the sum of the fields that win peace, and the equation 3x+y= 17 from the relationship with the score, and then ask:
(1) For x+y=7, how to express the number of flat fields (y) by x?
(2) What value can X take? What value can y take? Can I take any value?
(3) What are the similarities and differences between it and the linear equation? The purpose of asking questions is:
① Students understand that the values of X and Y are paired in the process of thinking;
(2) Use the algebraic expression of X to express Y, so that students have a sense of elimination and pave the way for the next section.
③ The similarity between them is "algebraic expression" and "the number of unknowns is once", but the difference is "there are two unknowns". In the process of thinking and answering, students can construct the concept of binary linear equation according to the existing knowledge of linear equation.
④ When testing the values on both sides of the equation, students summarize the concept of the solution of the equation.
2. Guide students to test the quantitative relationship between the solution and the equation, so as to explore that if two equations are to be satisfied at the same time, they should be linked, and guide students to call them binary linear equations by analogy, so as to infer the concept of the solution of binary linear equations, and at the same time remind them of the differences and connections between the solutions of binary linear equations and binary linear equations, compare them, cultivate students' analogical thinking, and then students can sum up binary linear equations according to the obtained equations.
(1) algebraic expression; (2) duality; (3) once.
Characteristics of the solution of the equation;
"The two equations must be satisfied at the same time" and "the unknown values are a pair"
Third, reflection after solving the problem.
1, this textbook adheres to the principle of "student-oriented", gives consideration to individual differences, creates problem scenarios by using students' favorite "football match", and solves problems with different methods they are willing to apply, so that students can feel that mathematics is around, that mathematics problems are realistic, meaningful and challenging, and that mathematics is interesting and useful.
2. Teachers should not only design the teaching process consciously and systematically, but also guide students to understand the relationship between mathematics, feel the integrity of mathematics, and constantly enrich the problem-solving strategies. In specific teaching classes, teachers should not impose the idea of teaching plans on students, but should adjust teaching activities in time according to students' specific thinking reactions and give full play to students' main role.
In short, "inquiry learning" aims to treat learning more as a problem-solving process, so that students can master the methods to solve problems. From the process of understanding knowledge to the process of exploring problems; Only when students change their knowledge into the study and solution of problems can they know, discover, change and create with scientific attitude and methods in the complex social environment, and truly make today's learning the basis for tomorrow's participation and transformation of society. Implementing mathematics teaching through inquiry learning can not only promote students to learn mathematics, master and apply modern teaching methods, and learn to learn actively, but also promote the change of mathematics teachers' teaching concepts and teaching behaviors, learn to guide students to learn to learn independently, and promote the improvement of teachers' comprehensive quality, teaching ability and research ability.