Education
Lao Hu's point of view: from life to mathematics from mathematics to life.
Take Primary 4 mathematics "The Meaning of Multiplication and Division and the Relationship between Parts" as an example.
Author: Hu Yuanming.
From life to mathematics From mathematics to life
Take Primary 4 mathematics "The Meaning of Multiplication and Division and the Relationship between Parts" as an example.
1) Let's take a look at some examples of the teaching process of a primary school mathematics teacher:
Teaching process: 1. Introduce the conversation and reveal the topic.
In the previous lesson, we learned the meaning of addition and subtraction and the relationship between the parts. Is there a relationship between multiplication and division?In this lesson, let's study it together.
2. Reveal the meaning of multiplication and division in the process of solving problems, and clarify the relationship between each part.
a) Reveal the meaning of multiplication and clarify the names of the parts in multiplication:
1.Summarize the meaning of multiplication.
1) Get information, ask questions.
The courseware presents the situation diagram of Example 2 and question (1) on page 5 of the textbook, and students obtain mathematical information and ask mathematical problems.
2) Solve problems and construct the meaning of multiplication.
Guide students to solve problems independently in different ways, and then present a debriefing as a class.
2.Preset learning situation.
Birth 1: It can be calculated by addition, 3 + 3 3 3 = 12 (branches).
Sheng2: It can be calculated by multiplication: 3 4 = 12 (branches) (board book).
Think: Which method do you prefer to compare the two equations?Why?(Multiplication, easier).
What kind of addition equation can be abbreviated as multiplication?(Addition with the same addition).
Teacher: Based on the previous experience, can you tell us what multiplication is?
Answer, teacher's summary: The simple operation of finding the sum of several identical additions is called multiplication. (Board Book).
Fourth, the summary of the whole lesson.
What have you gained from learning today?Can you give an example of what kind of problem can be solved by multiplication or division?
2) The above part of the teaching process is an excerpt from the teaching design of a primary school mathematics teacher in XX Primary School in the Economic Development Zone. This lesson is the second lesson of the first unit of the second volume of the fourth grade of the People's Education Publishing House, and the topic is "The Meaning of Multiplication and Division and the Relationship between the Parts".
Judging from some of the excerpts of the teaching process, it is not difficult to find that there are some problems in the introduction and summary of the teacher. The introduction process is what we often call scenario creation. Obviously, the teacher's introduction in this lesson was too short and concise, and a simple transition sentence hurriedly introduced the new lesson, which may have made many students enter the new lesson without understanding before they have sat down. At the end of the lesson, the bell rang, so the teacher hurriedly asked the students and himself to make a brief summary, and did something hastily.
In the discussion and exchange session after class, we had a brief exchange on the introduction and summary of the teacher's lesson, and believed that the introduction and summary links should be more abundant, especially the basic characteristics of mathematics, that is, life is mathematics, and mathematics is life. For example, the introduction is the beginning of a lesson and is crucial to the quality of teaching in a lesson, so it should have two basic characteristics, namely, quickly drawing students' attention to the class and the introduction activity should be closely related to the content of the new lesson. As far as this lesson is concerned, the teacher can import from the students' actual life phenomena, that is to say, there are countless cases of addition and subtraction and multiplication and division in life, so the teacher should import from the students' daily life, so that the students can easily enter the learning of the new lesson, and at the same time, it is also convenient to understand the content of this lesson.
For example, in the summary session, the bell has already sounded after class, and it is obvious that the summary session is very hasty and does not achieve the ideal effect of the summary. In addition, the question asked in the summary session is "Can you give an example of what kind of problem can be solved by multiplication or division?"."We don't think it's appropriate to put it in this summary session, because life examples should be an important learning goal of this lesson, that is, to use multiplication and division to solve practical problems in real life and stimulate interest in mathematics learning. In other words, the teaching content that allows students to give examples should be upfront and require a few minutes of activity time to achieve this learning goal. We suggest that activities to achieve this learning goal can be combined with items such as students in the classroom, desks, squares for school bags, and electric rods overhead, so that students can easily understand the teaching content and feel the joy of learning mathematics.
3) We believe that as far as the discipline of mathematics is concerned, its most essential feature is that mathematics is brought to life, that is, mathematics is life, and life is mathematics. That is to say, the content of mathematics textbooks is closely related to our daily social life, and the content of mathematics textbooks comes from our daily social life, so mathematics teaching activities are inseparable from social life.
Mathematics is the ideal teaching method for our mathematics teachers, and it is also the teaching goal pursued by our mathematics teachers. In the context of the current examination-oriented education, it is obvious that our classroom teaching activities cannot be separated from the teaching materials, and we must also integrate the teaching activities into social life, which obviously poses a certain challenge to teachers. In the course of listening to lectures, we found that it was common for some teachers to "teach textbooks on textbooks", especially when they rarely integrated students' social life into the content of textbooks, resulting in boring, lifeless and inefficient classroom teaching activities, which obviously violated the original intention of mathematics teaching activities. As the famous mathematician Hua Luogeng said: "One of the reasons why people have a boring, mysterious and difficult impression of mathematics is that it is divorced from reality." β
So, how can mathematics teachers closely integrate the content of textbooks with social life?We believe that mathematics teachers should pay attention to three important aspects in teaching:
First, the design of learning objectives should be scientific and reasonable. We believe that each lesson (lesson time) should reflect the three-dimensional objectives, especially the "emotional attitude values" learning objectives. For example, the learning objective of this lesson is "to use multiplication and division to solve practical problems in life and stimulate interest in mathematics learning", which is the learning objective of "emotional attitudes and values" in this lesson. Obviously, this learning goal cannot be missing, otherwise this lesson will lack the soul, and at the same time, it will lose the meaning and value of mathematics learning. Therefore, in the process of instructional design, mathematics teachers must take into account the importance and necessity of the learning goal of "affective attitudes and values".
Second, the introduction link should start from social life. When we open the primary school mathematics textbook, we find that the first sub-item content of each lesson is basically a real life situation diagram. Obviously, the main purpose of the design and compilation of mathematics textbooks is to hope that the teaching process of front-line teachers should be closely linked with social life, so that mathematics and students' social life can be integrated, and of course, this will also help promote the development of students' core literacy. However, the life situation maps in the textbooks are often oriented to all cities and villages, as well as developed cities and backward border areas, and obviously have common characteristics. However, our teachers' classroom teaching activities are personalized, regional and unique, so the situation map in the textbook is not completely suitable for each teacher's classroom introduction link, which requires our teachers to design personalized situational introduction activities. Only by entering the classroom teaching activities from the children's social life can the children feel the charm of mathematics and the joy of learning.
The third is the achievement of the learning goal of "emotion, attitude and values". We believe that the summary link is the last link of a lesson, and it is also the overall summary of a lesson, rather than the achievement of learning goals, so the achievement of learning goals obviously cannot rely on the summary link. The learning goal of this lesson is to "use multiplication and division to solve practical problems in real life and stimulate interest in mathematics learning", and it is obvious that to achieve this learning goal, we need to carry out some related activities to achieve it. We always believe that the achievement of the learning goal of "emotional attitude and values" is very important for a lesson, which is not only the sublimation and improvement of the teaching content of a lesson, but also the most "climax" stage of the lesson. On the other hand, if the learning objectives of "affective attitude values" in a lesson are not fully achieved or the learning objectives of "affective attitude values" are missing, then the classroom teaching activities will appear boring or bland.
Of course, in addition to grasping the above three important links, teachers can also closely link the content of subject knowledge with social life in the process of classroom teaching. In fact, in the process of classroom teaching, common sense of life can be infiltrated at any time, so that classroom teaching can really "live" and let students really "move", which is the original appearance and ecology of classroom teaching.
Conclusion. The Mathematics Curriculum Standards point out: "Mathematics teaching should reflect life, and everyone should learn valuable mathematics. Teachers need to create conditions for students to learn and understand mathematics based on their life experiences and existing knowledge. "Mathematics is a true representation of social life, and mathematics permeates every aspect of our lives. Mathematics is inseparable from life, and life is also inseparable from mathematics, so mathematics is an art full of magic and creativity. We teachers should not only fully enjoy the magic of mathematics ourselves, but also let students feel the beauty and fun of mathematics in classroom teaching activities.
In our ideal mathematics classroom, every lesson should go from social life to the content of the textbook, and finally from the content of the textbook to social life, so that the textbook and social life can be integratedIn our ideal teaching activity, teachers take a group of lovely children to swim in the math paradise, so that math and life can be integrated. In the process of learning mathematics, children can perceive the beauty of mathematics, feel the harmony between numbers and shapes, feel the elegance of geometry, and feel the magic of mathematics. In the kingdom of mathematics, our teachers lead children to find the rules, order and fun of mathematics learning, so as to illuminate the way for children to go far. As Galileo Galilei said, "Mathematics is the key to interpreting the universe." β
Finally, let's conclude with a quote from the French mathematician Descartes
Mathematics is a tool of knowledge and a source of other tools of knowledge. All the sciences that study the order and measurement are related to mathematics ......Mathematics is the most powerful knowledge tool left by human knowledge activities, and it is the root cause of some phenomena. Mathematics is immutable and objective, and God will build the universe according to mathematical laws. β
Hu Yuanming, Zhengzhou Educational Science Planning and Evaluation Center).