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On how to cultivate the ability of primary school students to learn mathematics independently
At present, students' passive learning is quite common. Students can't solve practical problems with what they have learned, because they passively accept knowledge in class and learn as much as the teacher gives them. Most students only have what the teacher "instills" in their minds. Without a teacher, they won't study. This situation is the result of the disadvantages of exam-oriented education.

Prota Goethe, an ancient Greek biologist, said, "The mind is not a container to be filled, but a torch to be lit." In order to make students have real wisdom, classroom teaching should create a positive, open and participatory situation, so that students can rediscover and recreate what they have learned in autonomous learning and realize the independent release of thinking.

It is an important goal of the new curriculum to cultivate students' autonomous learning ability and let them learn to learn. The new curriculum advocates students' independent development and independent learning. The so-called "autonomy" refers to students' own needs for learning and strong desire for knowledge. In this state, when students participate in all aspects of teaching activities, they will show positive learning attitude, good attention and will to overcome difficulties, and have creative enthusiasm. Therefore, it is particularly important to guide students to participate in and study independently in all directions, with high quality and at multiple levels, and to cultivate high-quality talents with initiative and creative consciousness. It has become a top priority to improve educational concept and change educational behavior.

So, how to cultivate students' autonomous learning ability in primary school mathematics teaching? Let's talk about my experience in combination with teaching practice.

First, create a harmonious autonomous learning atmosphere

Teachers should get along with students on an equal footing, become good teachers and friends of students, and let students have a relaxed environment and plenty of space. The equal relationship between teachers and students will make the classroom full of affection. Students will be unrestrained, fearless and omnipotent in a relaxed, happy and safe atmosphere, and their desire to participate and passion for expression will naturally be released.

Second, provide enough independent learning space.

Give students ample opportunities to express themselves and let them discover and feel for themselves in the process of speaking, thinking and doing. For example, in the teaching of "combination of graphics", I ask each student to spell a learning tool that he likes first, and then put it together in groups. On the basis of different individual arrangements, they cooperate and accept each other, giving full play to the characteristics and advantages of learning the same body. The whole posing activity is accompanied by talking (how many learning tools are used), comparing (which puzzle is more beautiful and which group cooperates well) and helping (encouraging and helping each other in the group). Students' active participation fully experienced the whole process of autonomous learning and the hardships and fun of autonomous learning. In the whole activity, the teacher will always be the organizer, promoter and mentor of the students.

Third, adopt multi-directional independent learning evaluation.

Evaluation is an important link in mathematics curriculum reform. The means and forms of evaluation should be diversified, and the process evaluation should be the main one. The description of evaluation results should use encouraging language to give full play to the incentive function of evaluation. Evaluation should pay attention to students' personality differences and protect students' self-esteem and self-confidence. Teachers should be good at using a lot of information provided by evaluation to adjust and improve the teaching process in time.

Fourthly, cultivate students' habit of autonomous learning.

1. Cultivate students' good preview habits.

Students can preview at three levels: first, take a look at the textbook before class; The second is to read textbooks and do exercises; The third is to be able to make a simple summary after reading the textbook and find out your own gains or puzzles. What level the students reach is related to the teacher's insistence and supervision. Different chapters should have different levels of preview requirements.

2. Cultivate students' good reading habits.

Reading is the basis of learning. When reading, the eyes first perceive the information of words or images from books or screens. Then the brain carries out thinking activities such as analysis, synthesis, deduction and induction to extract the information needed for processing.

3. Cultivate students' good thinking habits.

Thinking is the core of learning. Students should think about problems in their study. The quality of a student's study depends largely on his ideological ability. Teachers should teach students how to analyze specific problems through educational and teaching practice. They should learn to understand from special to general, and then from general to special. They can grasp the essence through phenomena, make classification and comparison, and can be divided into two parts and combined into one, so as to realize multiple solutions to one problem or multiple solutions to one problem ... They should cultivate students' multi-faceted thinking quality through different classes and problems.

4. Cultivate students' good review habits.

Students can review in three ways. The first is to review first, and then do your homework; The second is to do your homework first and review it when you have time; The third is to arrange time for review, pay attention to sorting and induction, and form a knowledge structure. Teachers should awaken students' awareness of "learning" from the perspective of "teaching", especially for students who lack cognitive foundation and have weak self-management ability, the proportion of teachers' guidance should be appropriately increased. Only when students have a successful learning experience can they further explore and learn actively. With the deepening of learning, students' autonomous learning ability will be further improved. Then, how to change students from passive learners to active learners, so as to cultivate more and better people who can adapt to modernization? I think teachers should do the following in teaching:

(1) Guidance-Give full play to students' main role

Students are the main body of learning. In order to make them master knowledge accurately and skillfully use knowledge to solve practical problems, they must be motivated to learn. Therefore, in classroom teaching, we should guide students to actively participate in teachers' teaching activities, pay attention to cultivating their good habits of diligent hands-on, diligent mouth-opening, diligent observation and diligent thinking, combine students' perception and thinking, and let students devote themselves to learning under the guidance of teachers. For example, when the teaching score is multiplied by the application questions, the following teaching links can be designed: A, reading questions and reviewing questions, so that students can watch the scene diagram in the example to obtain information. B, draw a line graph, and write the equivalent relationship between quantity and quantity through information. C, take the equivalence relation as a breakthrough, and list the formulas, thus solving the problem. This step-by-step guidance, coupled with the teacher's appropriate guidance, in the form of "thinking-problem-guidance-solution", allows students to always maintain a positive attitude and give them limited classroom teaching time, not only mastering knowledge, but also learning the methods of learning mathematics.

(2) operation-cultivate interest in inquiry

The new curriculum standard requires creating learning and research situations in teaching, so that students can discover problems independently through experiments, investigations, information collection and processing, expression and communication, and gain the development of knowledge, skills, emotions and attitudes. Students' pleasant hands-on operation can not only enrich their perceptual knowledge, stimulate their interest in learning, but also improve their hands-on ability. For example, when teaching the formula for calculating the area of "triangle", the following teaching procedures can be designed: a. Guide the operation, let the students put two identical triangles together to form a learned parallelogram, and tell how its area is calculated. B, let students perceive the connection between triangles and parallelograms, and guide students to observe the relationship between the base heights of two triangles and the base heights of parallelograms. C. What conclusion can be drawn from the relationship between the base height of triangle and parallelogram? Thus, the calculation formula of triangle area is summarized. Students can discover and summarize the calculation method of triangle area through hands-on operation, observation, perception and understanding thinking, and they can also learn the method of inquiry in the process of participating in the formation of knowledge, cultivate the ability of practical operation, experience the joy of learning and stimulate students' awareness of independent learning.

(3) Discussion-organizing group study

Learning is an active and personalized process, and there are many ways. Discussion and communication in group learning activities is an effective way to cultivate students' active participation, exploration and discovery, communication and cooperation. Therefore, in teaching, we should be good at turning the examples in textbooks into a series of enlightening questions and guiding students to discuss and communicate. For example, in the teaching of "Comparison of Fractions", students can first observe the scene diagram of the scores of the same denominator and numerator in the book, and then ask: a. Tell which score is larger and which score is smaller from the analysis of the scene diagram? B, what are the characteristics of every two size comparison scores? C, what rules did you find? In view of these three problems, organize group discussion and study. In the discussion, students not only have a deeper understanding of what they have learned, but also promote students to develop the habit of studying textbooks, improve their thinking, generalization and expression skills, and realize how to communicate and cooperate with others.

(4) Reflection-self-test and self-evaluation.

At the end of each class, leave some time for students to conduct self-test and self-evaluation, so as to realize students' practice and reflection after autonomous learning. This will not only make students feel happy after acquiring knowledge, but also make them feel the place where they still need to work hard. For example, after the new teaching of "addition and subtraction of scores of different denominators", let students conduct self-test and self-evaluation. What did you learn in this class? The student replied, "I learned to add and subtract fractions with different denominators." B how did you learn it? The student replied: "By observing the scene map, starting from the fraction unit, calculate the addition and subtraction of fractions with the same denominator." C.what else do you want to know? The student replied, "I also want to know how to add and subtract an integer and a fraction"? D, what is your future direction? The student replied: "Be good at discovering the connection between knowledge and the regularity of solving problems". In this way, students are often self-evaluated and self-evaluated, so that students can review their gains and losses in each class and state their learning goals and aspirations, which not only consolidates their knowledge, but also effectively enhances their motivation and ability of autonomous learning.

In short, cultivate students' autonomous learning ability, let students take the initiative to learn, let students truly appreciate the fun and practicality of mathematics learning, let students discover and like mathematics, let students actively participate in problem situations, take the initiative to discover and acquire knowledge, so as to gain the ability to solve problems and improve students' quality to the greatest extent. I believe that as long as we dig deep into teaching materials, persist in reform, pay enough attention to students in teaching, and constantly cultivate and train, students' autonomous learning ability will certainly develop with the passage of time. Let everyone learn valuable mathematics; Everyone can get the necessary mathematics; Different people get different development in mathematics. In the future, all of us will keep our sky blue and students' hearts warm.