Mathematics gives people not only knowledge, but also ability. Educator Rousseau believes that mathematics should enable students to learn from life and various activities, gain direct experience with real life, and actively learn. As a mathematics teacher, we should be good at making mathematics teaching alive, making students' life experience classroom, making mathematics better reflect life, making life into the classroom and making mathematics into life.
First, contact life, create a mathematics teaching situation
Students learn from their environment, so education is inevitably carried out in their lives. Therefore, teachers should guide students to enter the mathematical situation with the help of mathematical application problems in real life, so that students can enter the classroom with "life problems" and solve life problems with mathematics.
Case 1 In the teaching of "the first n sums of geometric series", the teacher can set questions before class: If the teacher gives you 1000 yuan every day within one month (calculated by 30 days), but within this month, you must give me 1 cent interest, 2 points on the first day and 4 points on the third day.
This is an example for students to experience directly, which is both interesting and practical. Creating life situations like this and introducing classroom teaching not only improves students' confidence and desire to learn mathematics well, but also enhances students' ability to solve practical problems consciously, which lays the foundation of "interest" for the following classroom teaching.
Second, go into life and experience the value of mathematics.
Mathematics has many applications in all aspects. Teachers should fully grasp, provide students with opportunities, and pay attention to choosing problems that reflect the needs of life as teaching application problems, so as to deepen students' understanding of the essence of mathematics, understand the relationship between mathematical knowledge and practice, and let mathematics really enter life.
Case 2 Application of arithmetic progression
Before winter, in order to prevent cultivated flowers and plants from being affected by frost, gardeners need to buy plastic films to build "houses" for flowers and plants to keep out the cold. It is known that the plastic film sold in shops is a roll wound on a shaft, in which the inner diameter of one roll is 12 cm, the outer diameter is 8 1 cm, and the film thickness is 0? 0 1 cm, and the width of this film is just suitable for the gardener's requirements. After calculation, the gardener bought a roll of plastic film and asked, how long is this roll of film?
Maybe someone will ask: can't you know the length of the film by measurement? Sure, but what we are interested in is: Can we calculate the length of the film without unfolding it?
At this time, we can guide students to approximately regard the film as a circle around the axis, calculate the circumference of each circle, and then add up the circumference of each circle. Due to the thickness of the film, the length of each turn of the film is calculated according to the length of the thickness center line of the film. Considering the general situation, we can assume that the inner diameter is D, the outer diameter is D, the thickness is T, the radius of each circle from inside to outside is r 1, r2, r3, … the circumference of each circle is c 1, c2, c3, …
r 1=d2+t2，c 1 =π(d+t)；
r2=d2+t2+t，C2 =π(d+3t)；
r3=d2+t2+2t，C3 =π(d+5t)；
……
Obviously, the circumference of each circle constitutes a arithmetic progression with a tolerance of 2 π t. ..
Because the total number of turns of the film is equal to D-d2t, the sum L of the perimeters of each turn is
l= 12？ D-d2t 2π(D+t)+D-d2t- 12πt =π(D2-D2)4t .
Substituting specific figures, can you work out that the length of this film is 503734? 5 cm, about 5040 m.
At this point, students will find that it is not easy to really spread such a long roll of plastic film. Want to know how long the plastic film is, can only rely on mathematical knowledge. In this way, teachers make rational use of living resources, which effectively induces students' curiosity and desire to conquer, and stimulates students' enthusiasm for learning and using mathematics to solve problems.
Third, return to life and apply what you have learned.
In the teaching process, we should bring the boiling life into the classroom at any time, make the world of books conform to the students' existing experience and background, emphasize "returning to life", make knowledge no longer something divorced from life, and let students realize that "mathematics is knowledge".
Fourth, participate in inquiry and improve the ability of mathematics application.
Mathematics has a wide range of applications, from the daily sales of rice, oil, salt, sauce and vinegar tea to astronomy, geography and aerospace.
In a word, making classroom life and classroom teaching full of challenges to wisdom and satisfaction to curiosity can not only stimulate the vitality of teachers and students, but also better guide students to experience and feel mathematics in life, and learn and use mathematics well. This not only embodies the "people-oriented" teaching concept, but also makes students feel that the world is a world full of mathematics, so that students can grasp the close relationship between mathematics and real life and narrow the distance between mathematics and reality, thus achieving the goal of "improving students' mathematics literacy, meeting the needs of personal development and social progress, and thus making students love life and mathematics more" in the new curriculum standard.