"Effective mathematics learning activities can't just rely on imitation and memory. Hands-on practice, independent exploration and cooperation are important ways to learn mathematics. " It is believed that the process of students' learning mathematics should be a rich and vivid thinking process in which students personally participate, and students should go through a process of practice and innovation.
When we do research study, we must first make clear what research study is. In a narrow sense, "inquiry learning" mainly refers to the learning method of students exploring problems independently in the discipline field, and the process of acquiring knowledge, skills and attitudes through their own inquiry activities such as problem discovery, investigation and research, hands-on operation and expression and communication.
With the development and perfection of the new curriculum reform, the traditional mechanical learning mode, in which teachers teach blindly and students passively accept knowledge and then practice repeatedly, can no longer meet the needs of the times and quality education. The educational model and teaching concept advocated by the new curriculum also show the importance of inquiry learning. The famous educator Suhomlinski once said: "There is a particularly strong need in children's spirit, that is, they want to feel that they are discoverers, researchers and explorers." From this, we find that people have long realized that whether a child can succeed in the future depends not only on his own knowledge, skills and intelligence, but also on non-intellectual factors such as his interest, attitude, willpower and self-confidence. Research-based learning will greatly promote the cultivation and improvement of students' comprehensive quality, which is conducive to the all-round and harmonious development of students and the overall optimization of teachers' quality structure.
First, wonderful introduction and willingness to explore.
The ancients said, "Learning begins with thinking, and thinking originates from doubt", and "Enlighten its stupidity and attract its interest". Halmos, a famous American mathematician, said: Theorems, proofs, concepts, definitions, theories, formulas and methods are not the core of mathematics, only problems are the core of mathematics. With questions, thinking has a direction; With questions, thinking has motivation. Therefore, teachers should play a guiding and auxiliary role in time, design a problem situation suitable for students' ability level, so that students can actively find and ask questions and have the impulse and desire to explore them. Then the study of exploring questions is half the battle.
At the same time, students are curious and willing to try and explore challenging problems. Sometimes finding problems is more important than solving them. Math situations include math problems, which are not given by teachers alone, but stimulate students to find, put forward and think in situations, trigger their inquiry, and provide good interest and desire for learning and inquiry for future math learning.
Second, set doubts and guide thinking and participate in exploration.
Students are the main body of learning, and teachers' thoughts can never replace students' thoughts. Every student has his own ideas. After teachers bring students into a problem situation, they should make students actively think and participate in inquiry, and let students process and understand new knowledge in their own way on the basis of original knowledge and actively construct their own knowledge system. Of course, this requires students to actively participate in inquiry activities.
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For example, when teaching triangle calculation, let the students recall the derivation process of parallelogram area and triangle area, and let the students transform the triangle into a plane figure with the learned area through cutting and spelling according to their own knowledge and experience. Students independently explore and exchange results, and derive the area formula of triangle according to the relationship between the original figure and the new combined figure. Exchange of students' deduction results: triangle area = base × height ÷2. In this way, students have enough time and space to explore and communicate, and students who participate in inquiry learning activities are active in thinking and their abilities in all aspects are improved.
Third, flexible application and practical exploration.
Bruner said, "Exploration is the lifeline of mathematics." Without exploration, there will be no development of mathematics. Similarly, without students' own thinking and inquiry, there is no real mathematics learning. Of course, the final result of learning lies in application, which is not only the acceptance of inquiry results, but also the summary and application of inquiry methods, forming students' own inquiry strategies and experiencing the diversity of problem solving. Therefore, teachers should sum up the main points in time and correctly, make clear the methods to be mastered and the truth to be understood, help students sum up the acquired knowledge and experience, learn to draw inferences from others, and form their own knowledge system. This improves students' general thinking level and application consciousness. Therefore, teachers should pay attention to the continuity, creativity and inquiry of problems when designing application problems. For example, when studying Statistics, let students collect all kinds of expenses about daily life and family, draw statistical charts, calculate all kinds of data, arrange personal expenses reasonably, and enhance financial management awareness; When learning "km knowledge", let students experience the concept of "km" by walking from home to school, and calculate the distance by estimating the time. Another example is to teach go on road trip's question, so that students can find the most economical way to spend money through exploration, discussion, communication and demonstration, and develop their logical thinking ability, language expression ability and knowledge application ability. In short, we should take various activities to enable students to explore and learn in activities and form certain mathematical abilities.
Fourth, experience evaluation leads to in-depth exploration.
In the sense of evaluation, evaluation is oriented, inspiring and developing. Evaluation can increase the motivation of students' active development, and teachers should attach importance to the positive role of evaluation in research-based learning teaching. Psychology also tells us that as long as a person experiences the joy of success once, it will arouse endless pursuit of ideas and strength. In inquiry learning, there are such evaluations: first, we should recognize students' initiative, enthusiasm and innovation in the process of inquiry learning, so that students can get the happiness and emotion they experience in inquiry learning, and enhance their belief and determination to continue and be brave in inquiry; Secondly, we should give timely guidance and evaluation to students' desire to gain new information, experience success and take the initiative to explore through inquiry activities, so that students can consciously reflect and feel their own inquiry process and point their thinking to the thinking method of mathematics learning, thus improving their ability to learn mathematics, acquire new knowledge and solve problems.
In the new curriculum reform, inquiry learning, as the basic idea advocated by quality education, has become an important measure in primary school mathematics teaching, and it is also an opportunity and challenge for mathematics teachers. It requires teachers to let students explore independently as much as possible, give them sufficient study time and space, and let students master the strategies of exploration and thinking. Only in this way can we truly apply what we have learned; Only in this way can students know, discover, explore and innovate with inquiry attitude and methods in their future study life, so as to meet the needs of lifelong learning and future social development.