Specifically, students' effective mathematics learning activities mainly show the following characteristics:
1, the process of students learning mathematics is an active construction process based on experience.
As mentioned above, students have had a lot of daily life experience before coming to school. As students grow up, the experience they get from school will be more and more important than the experience they get in their daily life outside school. It is based on these experiences in and out of school that students can connect old and new knowledge through various activities and think about the quantitative relationship and spatial form in reality, thus developing their understanding of mathematics. In mathematics, the relations and changes of quantities are all represented by symbols (relational symbols, operational symbols, graphs, charts, etc.). This characteristic of students' physical and mental development and the abstract characteristics of mathematics jointly determine that students' mathematics learning is basically a combination of symbolic language and real life, and the mutual integration and transformation between them has become an important way for students to actively construct.
2. The process of students learning mathematics is full of colorful mathematical activities such as observation, experiment, guessing, verification, reasoning and communication.
Judging from the law of the occurrence and development of students' cognition, in traditional mathematics learning, the single learning mode of teachers' teaching and students' practice can no longer meet the needs of students' development, and this mode even creates obstacles for students' learning. Mathematics learning centered on students' development should provide a variety of activities for students to actively participate and communicate in these rich activities. With the development of mathematics today, with the help of computers, its application mode has been greatly expanded. Nowadays, people collect data, process data and solve problems in various ways. It is necessary for school mathematics education to change the face of traditional mathematics in order to keep consistent with the mathematics used in people's daily life. The purpose of students' learning mathematics in school is not only to gain the ability of calculation (its proportion will be greatly reduced), but more importantly, to gain their own experience in exploring mathematics and the ability to solve practical problems by using mathematics, and to gain the rational spirit of respecting objective facts and the attitude of persistent pursuit of science. Therefore, in mathematics teaching, students must take the initiative to observe, describe, operate, guess, experiment, collect, sort out, think, reason, communicate and apply, so that students can witness the vivid and vivid process of mathematics, experience how to "do mathematics" and how to realize the "re-creation" of mathematics, and feel the power of mathematics to promote mathematics learning. Teachers should leave enough thinking space for students in the process of mathematics learning, so that students can really engage in thinking activities and express their understanding, not just imitation and memory.
Teachers should give full consideration to students' subjectivity when designing teaching, so that students can experience the process of "doing mathematics" independently and provide them with necessary opportunities for reflection activities. Research shows that people's general cognitive development, including the development of cognitive ability and the improvement of cognitive level, largely benefits from profound reflection activities.
3. Students' mathematics learning process should be a process with rich personality and diversified learning needs.
People's intellectual structure is diversified. Some people are good at thinking in images, some are good at calculation, and some are good at logical reasoning. There is no difference between good and bad, just showing different characteristics and adaptability. In addition, each student has his own life background and family environment, which leads to different students' thinking modes and problem-solving strategies.
Research shows that every student has the potential to analyze, solve problems and innovate, and the key is to provide good materials in the course content to promote students' development. According to the law of students' physical and mental development, children have an innate self-centered desire and curiosity to explore, and we should fully adapt to and make use of this psychological characteristic of children. Therefore, mathematics courses should choose those contents that have practical significance to students and are related to real life. Students always think of themselves as explorers, researchers and discoverers. Often, when their views are inconsistent with the collective, they will have the desire to prove their thoughts, so the course content should be challenging in difficulty. However, challenging students does not mean embarrassing them, but encouraging them to gain a successful experience in the process of learning. Therefore, the content of the course should be within the scope of students' "nearest development zone", so that the sense of success will always accompany students' learning journey and ensure that students will not give up their efforts and lose development opportunities because of too many failures.
From the research on the process of students' learning mathematics, it is found that students are the main body of learning, and all new knowledge can be incorporated into their cognitive structure and become effective knowledge only through their own "re-creation" activities. According to the axiomatic system, the curriculum centered on subject knowledge presents the sorted knowledge to students with adult logic, which will inevitably form students' learning habits and ways of passive absorption, mechanical memory, repeated practice and enhanced storage. To change students' learning style, on the one hand, we should change the form of teaching materials, make bold breakthroughs in presentation methods, and realize multimedia teaching materials. The multimedia of teaching materials is to use multimedia, especially hypermedia technology, to establish a structured, dynamic and visual expression of teaching content. More and more textbooks and reference books have become multimedia, which not only contain words and graphics, but also can present three-dimensional scenes of sound, animation, video and simulation. On the other hand, teachers should carry out sincere communication between students and between teachers and students in the classroom, encourage students to have sincere confrontation between various viewpoints through various activities, and let students construct their own knowledge structure purposefully and meaningfully from experiences and activities through thinking and communication, so as to gain rich learning experience.