-Boss Li.
(Professor of Physics and Professor of Mathematics, California Institute of Technology)
In the Internet age, a lot of information is impacting us every day. How can we not be overwhelmed by information, think and analyze independently, learn to grasp the essence and create new value? It is an effective way to help us achieve this goal to learn the language and thinking of mathematics well and have the proper mathematical literacy.
The program for international student assessment Pisa defines the "mathematical literacy" of students aged 15 as: "Students can determine and understand the role of mathematics in society, draw well-founded mathematical judgments, and use mathematics effectively. This is the mathematical ability necessary for an innovative, caring and thoughtful citizen to adapt to current and future life. "
At different stages, students' learning methods, teachers' teaching methods, the mastery and development of mathematics knowledge and thinking methods are all different. We invited Mr. Gao Pei, Mr. Li Weiguang and Mr. Shang Wei from Qi Hui Mathematics Group to answer your questions and introduce your teaching characteristics in mathematics learning from primary school to junior high school.
Teacher Gao Pei
Answering questions in primary school mathematics learning
1.？ Q: Math knowledge in the first and second grades of primary school seems very simple. Why did it take so long?
A: In the lower grades, mathematics knowledge and methods are very simple to adults. In class, students learn internalized mathematical ideas and master optimization algorithms through small activities, various exchanges and activities under the guidance of teachers. In a situation in life, a child can put forward mathematical problems with the eyes of discovery and find the correct way to solve them. The child's brain has gone through many steps from concrete to abstract, forming its own method, and each step is a leap for him.
2.？ Q: What habits should we focus on cultivating students in mathematics in the lower grades of primary schools?
A: Reasonable arrangement of time, concentration, timely correction of mistakes, serious writing, orderly thinking, listening and independent thinking.
3. Q: Is calculation important? Calculation errors are all caused by carelessness, right?
Answer: The mastery of calculation needs to be based on students' understanding of the operation principle and their mastery of calculation methods. The calculation error cannot be simply attributed to carelessness.
4. Q: Why do some children do well in mathematics in the first and second grades, but their grades in the third grade begin to decline, and the fifth and sixth grades are particularly hard?
Answer: When I first came into contact with the multiplication and division of two or three digits in grade three, the mastery of the written calculation method needs to be based on the solid basic skills of addition, subtraction, multiplication and division in grade one and grade two. At this time, it also involves more complicated problem-solving teaching, which needs to be based on students' clear understanding of the significance and algorithms of addition, subtraction, multiplication and division learned in grades one and two. The decimal multiplication and division method in the fifth grade is also based on the operation law that two or three numbers are multiplied and divided by two numbers in the fourth grade mathematics study, which is very basic and interrelated. The learning of new knowledge in each stage is based on solid old knowledge and thinking methods, and the transfer of new knowledge leaves a generation point for later learning.
5. Q: What is the focus of middle and senior grades?
A: The middle and senior grades of primary schools consciously cultivate students' expressive ability and logical thinking ability, lay a solid foundation for calculation, attach importance to written expression, study independently, review and improve their comprehensive application ability, and prepare for middle school study.
Teacher Li Weiguang.
Ten Questions and Ten Answers about Junior Middle School Mathematics
1, Q: Do you still learn "number" in junior high school mathematics? How is it different from the "number" in primary school?
A: Junior high school students still learn "number", but the scope of "number" has expanded. On the basis of natural numbers and scores in primary school mathematics, negative numbers are introduced, so that numbers are extended to rational numbers, irrational numbers are introduced, so that numbers are extended to real numbers, and junior high school mathematics learns related contents within the real number range.
2. Q: Do you still learn arithmetic in junior high school mathematics? How is it different from the operation in primary school?
A: Junior high school mathematics also learns related operations such as addition, subtraction, multiplication and division, but what we learn is algebraic operation, algebraic calculation and identity deformation.
3. Q: What is the biggest change from primary school mathematics to middle school mathematics?
A: From elementary school mathematics to middle school mathematics, it is a leap from concrete to abstract, from studying constants to studying variables, that is, studying the relationship between variables by studying functions.
4. Q: What is algebra mainly studied in junior high school mathematics?
A: Algebra mainly studies numbers, equations, inequalities and functions.
5. Q: What do you mainly study in junior high school mathematics and geometry?
A: Geometry mainly studies the understanding of figures, figures and coordinates, figures and proofs, figures and transformations.
6. Q: What else do you learn in junior high school mathematics?
A: I also study statistics and probability; Practice and application.
7. Q: What is the key to learning junior high school mathematics well?
A: The key is to have a good class. We must actively participate in classroom learning activities. The middle school classroom pays attention to students' autonomous learning and independent inquiry, and cultivates the ability of autonomous learning.
8. Q: Why do you understand that your test scores are very low after studying?
A: Because the content of the exam has changed. First, there are more and more exam questions, and if students are not skilled enough, they will certainly not finish them. Second, when examining memory, there are fewer imitation questions and more comprehensive questions to examine ability. It requires students to use knowledge flexibly, discover, summarize and innovate on the premise of firmly mastering knowledge. But there are individual differences in ability, and it is not achieved overnight.
9. Q: What is our role in learning?
A: Students, teachers and parents are collaborators with the same goal. Students are the main body of learning, teachers are the guides of learning and parents are the supporters of learning.
10, q: what kind of parents and teachers should we be?
A: The Book of Changes says, "A gentleman strives for self-improvement. As parents, we should encourage our children with integrity, strength, acceptance, tolerance, optimism and never giving up. Teachers first take it as their duty to preach and teach, and at the same time, they should be like orchids, fragrant and distant, giving people beauty and hope.
-Miss Shang Wei.
Characteristics of Mathematics Teaching in Junior Middle Schools in Qi Hui
In mathematics classroom, the main line of classroom teaching is to guide learning with tutoring plan. According to the content of "autonomous learning" in the tutoring plan, students can show their learning achievements under the guidance of teachers on the basis of positive thinking and full discussion, so as to achieve their learning goals.
Learning guides effectively guide students' learning and make them the real masters of learning. Using the tutorial system, teachers have changed from traditional knowledge givers to organizers of students' learning. Teachers make full use of the characteristics of the tutorial plan, which pays attention to cultivating students' good habits, encourages students to take the initiative to learn, persist in learning, get to the bottom of the problem, discuss with each other in class, the group leader chooses representatives to speak, and the teacher travels around the group to discuss and give timely guidance, which not only cultivates the central figure of group learning, but also gives care and help to students with learning difficulties.
On the basis of the tutorial program, students gradually cultivate their self-study ability. Through group discussion, students pay attention to team consciousness and improve their expression ability.
Junior high school mathematics competition
In order to improve students' basic mathematical abilities such as calculation accuracy and calculation speed, lay a solid foundation for learning mathematics well, and create a learning atmosphere in which you chase after me, junior high schools organize math competitions. Through the competition, teachers can know the problems existing in students' calculation in time, find out the gaps and reflect, thus promoting the effectiveness of calculation teaching and improving classroom efficiency.
△ seventh grade math classroom
When the compulsory education stage is over.
Mathematical ability that students can have.
According to the mathematics curriculum standards, students can:
1. Get the basic knowledge, skills, thoughts and activities of mathematics necessary for social life and further development.
2. Experience the relationship between mathematics knowledge, mathematics and other disciplines, mathematics and life, and use mathematical thinking mode to think, thus enhancing the ability to find, ask, analyze and solve problems.
3. Understand the value of mathematics, improve interest in learning mathematics, enhance confidence in learning mathematics well, develop good study habits, and have a preliminary sense of innovation and a scientific attitude of seeking truth from facts.
May you master the language and thinking of mathematics,
Explore and think more deeply about life and the world,
Get a freer and wiser heart.