Like many colleagues, in the daily teaching at the beginning of work, we often encounter such a phenomenon: at the beginning of class, students are full of enthusiasm, but after a long time, when they really enter the course, they are unable to do so. I prepare lessons carefully according to the textbook, but in the classroom teaching, the students' reaction is very cold and their interest is lackluster. When preparing lessons, sometimes you don't need to face the course introduction arranged in the textbook, especially in the teaching of concept class, which is often given directly. Of course, the effect of classroom teaching after introducing such a classroom can be imagined. With the rich teaching experience, I gradually realized that there was something wrong with classroom lead-in.
The main reasons for the above phenomenon are: 1. The situation created is too long, and students have limited time to concentrate, which causes students' cognitive fatigue and affects the construction of new knowledge. 2. Creating useless situations, however wonderful, is not conducive to classroom teaching if it has nothing to do with the content of classroom teaching. As a teacher, we should learn to choose teaching materials reasonably. 3. It is too difficult for students to understand and integrate into the situation without the students' life or the situation created.
Therefore, in order to do a good job in the introduction of junior high school mathematics teaching, teachers should create appropriate thinking situations for students, guide them into the role of "learning subject" and become organizers, guides and collaborators of mathematics learning. So, how to create a suitable thinking situation? The author believes that efforts and attempts should be made from the following aspects.
First, the design of the situation should start from the students' existing knowledge and experience.
The design of the situation starts from the practical problems that students are familiar with and guides students to explore independently. For example, the introduction of the course "Quadratic Equation of One Variable (1)" can start with the life examples such as "Finding the length and width of a rectangle" that students understand.
Case and Analysis —— Brief Introduction of "Quadratic Equation in One Variable (1)"
Situation creation:
Question 1: In the residential design of the Green Garden Community, it is planned to open a rectangular green space with an area of 900 square meters between every two buildings, the length is more than the width 10 meter. What is the length and width of the green space?
Analysis: If the width of the rectangular green space is x meters, the equation can be listed:
X () = 900, and (1) can be obtained after sorting.
Question 2: There were 50,000 books in the school library at the end of last year, and it is expected to increase to 72,000 by the end of next year. Find the average annual growth rate of these two years.
Analysis: If the average annual growth rate of these two years is X, we know that the number of books at the end of last year is 50,000, and the number of books at the end of this year is 50,000; Similarly, the number of books at the end of next year is () times that at the end of this year, that is, 5 (1+x) (1+x) = 5 () 20000 books, which can be listed as the equation: 5( )2=, and (2) can be obtained after sorting.
Comments: The focus of this lesson is the significance and general form of quadratic equation with one variable. By providing two practical problems that students are familiar with, let students experience the establishment of a quadratic equation model by analyzing the quantitative relationship in practical problems, and let students realize that the quadratic equation of one variable originates from reality, so as to realize the significance and function of learning equation.
Second, the design of the situation should conform to the students' existing cognitive development level.
The design of situation should be suitable for students' cognitive level, help students construct new knowledge structure, and let students experience the essence of new knowledge in the process of new and old cognitive conflicts. For example, the introduction of factorization can start with students' existing knowledge, and then guide students to explore factorization.
Case and Analysis II Introduction of Factorization (1) Course
Situation creation:
1. Calculate with a simple method:
( 1)375×2.8+375×4.9+375×2.3
(2) 12×0. 125-63×0. 125+6 1×0. 125
2. Algebraic multiplication can be calculated in the following ways:
( 1)x(x+ 1)=； (2)(x+ 1)(x- 1)=。
3. Discussion: What numbers can 630 be divisible by?
We know that to solve this problem, we need to decompose 630 into the product of prime numbers: 63=
4. Since some numbers can be decomposed into factors, can a polynomial be similarly decomposed into the product of several algebraic expressions? Write the following polynomial as the product of two algebraic expressions:
( 1)x2+x =； (2)x2- 1=
Comments: The learning goal of this lesson is to understand the significance of factorization and learn to decompose factors by putting forward common factors. Although the significance of factorization is not the focus of this lesson, understanding the significance of factorization and its relationship with algebraic expression multiplication is the basis for correct factorization. Through the calculation problem and factorization of the reverse application of multiplication distribution rate, students can experience the exploration process of writing polynomials into algebraic product form, and then understand what factorization is.
Thirdly, the design of situations should be integrated with mathematical thinking methods.
For example, the introduction of fractional operation in teaching can start with the fractional operation that students have mastered, and the algorithm of fractional operation can be obtained through analogy, which permeates mathematical thinking methods such as analogy and reduction.
Case and Analysis III Class Introduction of Fractional Operation (1)
Situation creation:
1. Calculate the following:
( 1)■×■=
(2)(-■)×(-■)=
2. What do you think of the simulated decimal multiplication and division method?
■×■=? ■÷■=?
Comments: The focus of this lesson is the multiplication and division of fractions and its application. Through observation, calculation, group communication and analogy of fractional multiplication and division, students can understand that letters can represent numbers and expressions, thus successfully obtaining fractional multiplication and division.
Fourth, the design of the situation should have a variety of activities.
According to the situation, a question string can be designed, or cooperative goal exploration activities can be carried out in groups.
Case and Analysis of Quadratic Functions, Equations and Inequalities (2)
Situation creation: two brothers race. The elder brother asked the younger brother to run 9 meters first, and then started running by himself. It is known that my brother runs 3 meters per second and my brother runs 4 meters per second. Observe the image and answer the following questions:
■
(1) When does the younger brother run in front of the older brother?
(2) When does the elder brother run in front of the younger brother?
(3) How far did the elder brother run before catching up with the younger brother?
(4) Who ran 20 meters first? Who ran 50 meters first?
Comments: This lesson focuses on using function images to solve the problem of "choice" in real life, which is a thinking method and strategy to cultivate students' combination of numbers and shapes. Therefore, this lesson combines the image introduction of a function in the form of a question string, which is in line with students' cognition and step by step. Under the guidance of the teacher, students gradually link the coordinates of points on the image with practical problems, so as to achieve "number-shape correspondence" and prepare for the following "number-shape transformation" and "number-shape division of labor".
In short, in mathematics classroom teaching, teachers should do everything possible to create problem situations in which students can actively participate and enjoy themselves, and try their best to create a relaxed and happy teaching environment. Only in this way can we stimulate students' interest in learning mathematics, enhance their enthusiasm for learning mathematics, and then improve the teaching quality of mathematics classroom. Only in such a teaching environment can students love mathematics more, and their ability and level of learning mathematics can be steadily improved.
(Editor Xiang Yan)
This article is the full text of the original. Users who don't have a PDF browser should download and install the original text first.