Students' learning process is a process of thinking about mathematics while constructing knowledge and experiencing learning happiness. Only when students experience the joy of mental work and feel the charm of thinking can learning really happen. )
According to the basic idea of 20 1 1 version of mathematics curriculum standard, mathematics activity refers to the activity of engaging in mathematics learning. My understanding is that as long as it is related to learning, explicit activities such as operation activities, discussion and exchange activities are all mathematical activities, and implicit activities such as students' thinking, analyzing and solving problems can be regarded as mathematical activities. ) that is, mathematics learning is nurtured in activities, in which there are mathematical discoveries and mathematical thinking. (Whether it corresponds to the core literacy of mathematics: observing the world from a mathematical perspective, thinking about the world in a mathematical way, and expressing the world in a mathematical language) In view of this, mathematical activities should have the following characteristics:
1. carries the essence of knowledge.
My understanding: There is a popular saying that some math classes are not like math classes, but like science classes, art classes and Chinese classes ... Why? I think the main reason is that this math class pays too much attention to the external form or packaging, while ignoring the most important "knowledge essence". We should know that mathematics as a subject teaching has its unique knowledge essence, which is the foundation and foundation of a mathematics class, and all external forms and activities serve it. )
The foundation of deep learning is understanding. Only by understanding the essential connotation of knowledge can we extrapolate and transfer the application. Therefore, mathematical activities based on deep learning must first carry the essence of knowledge.
Professor Zhang Dianzhou defines the essence of mathematics as: the internal connection of mathematical knowledge, the formation process of mathematical laws, the refinement of mathematical thinking methods and the experience of mathematical rational spirit. In addition, we believe that the beauty of seeking truth and simplicity in mathematics is also one of its essential connotations.
Take "a number multiplied by a fraction" in the first lesson of grade six as an example. As shown below. In the textbook of Soviet Education Edition, the actual situation of making silk flower is presented. With the help of question strings, guide students to contact the meaning of fractions, and combine intuitive operation with existing knowledge and experience to solve problems by division. Based on the calculation results, it is pointed out that 10 1/2 can also be calculated by multiplication, that is, 10? 1/2。 This process embodies the internal relationship between mathematical knowledge. In the second volume of Grade Three, students have been able to solve the practical problem of finding the score of a number by integer multiplication and division according to the meaning of the score, which is an important foundation for students to learn. ) also reflects the role of mathematical reasoning in exploring the meaning of multiplying a number by a fraction. With the help of the meaning of fractions and intuitive operation, the students found 65438+65438 of 00 flowers. 2. Does 10 still work? 1/2, it can be seen that the fraction of a number can also be calculated by multiplication. Here, if you have time, you can also give students enough time to explore and guide them to express 10 1/2 in different ways from different angles, that is, 10/2. It can also be seen as dividing each flower into two parts on average and taking one of them, so the problem is transformed into finding 65438. 1/2) also embodies the idea of mathematical modeling (I understand that it is a new understanding for students to calculate the score of a number by multiplication. Through the previous exploration, let students realize that multiplication can be used, which is equivalent to teaching students another way to express the world in mathematical language. When they encounter this kind of problem again, they can consciously express it with this model.
2. Highlight mathematical thinking.
The essence of mathematical activities is mathematical thinking. If mathematics activities only stay in the external form of hands-on operation, it will lose the value of mathematics activities to promote students' deep learning and develop mathematics literacy.
This is worth thinking about by every math teacher. It is often seen that some teachers think that as long as there is hands-on operation in mathematics class, they respect students and embody the new curriculum concept, but they have never paid attention to what the purpose of hands-on operation is and what students get from it, and have never considered whether such operation activities are valuable. Is it necessary? Especially in high school math class, if it is only a low-level operation without promoting students' deep thinking, then such operation is inefficient or even ineffective.
3. Conform to the real learning situation.
The value of mathematical activities is to let students experience the process of knowledge formation on the basis of existing experience and produce profound experience and independent thinking. Therefore, the activities designed by teachers for students in the classroom should be based on students' cognition and are effective mathematical activities suitable for students' reality.
Children don't walk into the classroom with empty heads. Therefore, math class should fully understand children's learning situation, take learning as the guide, create appropriate math activities, activate children's existing experience and explore the unknown world. )
Before the sixth grade, the first book "Integer Divided by Fraction", through investigation, found that nearly 60% of the students in the class had mastered the calculation method of fractional division in various ways. There are still some students who haven't learned it before, but they can transfer the calculation method of integer division fraction learned in the first class to the calculation of integer division fraction and calculate it correctly. It can be seen that students have a certain reasonable reasoning ability, so we need to rethink: Is it necessary to design teaching activities with students' understanding of "calculation method of integer divided by fraction" at zero starting point? You know, in class, students should not cooperate with teachers to complete the teaching process, and teachers should serve students' learning.
Therefore, we should fully respect the learning situation, guide students to actively participate in learning activities with effective questions and activities, and promote the formation of students' mathematical ability. In this class, I start from the cognitive starting point of students' reasonable reasoning, lead the class with questions, and urge students' cognition, behavior and emotion to actively participate in learning, thus igniting the sparks of students' thinking and effectively improving their mathematical thinking ability.
For another example, before teaching multiplication in senior two, students' understanding of multiplication was not blank. Many students have been able to recite multiplication formula skillfully before class. In addition, some students already know the calculation formula before class. If we still attend classes according to our own expectations and don't respect students' cognitive basis, then our class will fail, because such classes are not for students to learn.