Metacognition was put forward by American psychologist freire in 1970s. According to Freville's view, metacognition refers to cognition, and its essence is individual's self-awareness, self-criticism, self-control, self-regulation and self-experience of cognitive activities and results. The so-called metacognitive ability refers to students' self-awareness and self-monitoring ability in the process of mathematical cognition. In the process of mathematics teaching, the significance of cultivating students' metacognitive ability mainly includes the following three points:
1. can effectively improve students' learning ability. The process of mathematics learning is not only a cognitive process of perception, memory, thinking and imagination of mathematical materials, but also a metacognitive process of actively monitoring, controlling and regulating this cognitive process through self-awareness. In the process of mathematics learning, students' learning ability is not only the ability of perception, memory, thinking and imagination on the basis of mastering certain scientific learning methods, but also the ability of consciously monitoring, controlling and adjusting the cognitive process. The latter is metacognitive ability, which determines and affects the display of cognitive ability. Therefore, metacognitive ability is the commanding height of learning ability, and improving metacognitive ability can effectively play the main role of students and improve their overall learning ability.
Can effectively develop students' intelligence. Mathematics is the gymnastics of thinking. The essence of mathematics teaching is the teaching of thinking activities. Therefore, the monitoring and regulation of metacognition on cognitive activities is mainly the monitoring and regulation of thinking activities. There are three main points in this monitoring and adjustment: (1) monitoring and adjustment of thinking direction. The key point is to ensure that thinking moves along the correct target trajectory; ⑵ Monitoring and adjustment of thinking methods. The key point is to adapt the thinking method to the requirements of thinking processing content; ⑶ Monitoring and adjustment of thinking strategies. The key point is to make thinking activities adopt effective strategies to better serve the learning objectives. Obviously, the monitoring and adjustment of these three aspects can make thinking show excellent quality in activities and greatly improve the quality and efficiency of thinking activities. Thinking is the core of intelligence, so students' intelligence will be developed and improved.
3. It can effectively improve learning efficiency. From the above two analyses, it can be seen that the quality of students' learning process, the level of learning benefits and the size of learning effects largely depend on the level of metacognition process. Good strategy selection, correct strategy effect evaluation and timely feedback control will produce satisfactory learning results. This is the positive correlation between the cultivation of metacognitive ability and learning efficiency.
In addition, metacognitive ability is closely related to innovative ability, which is an important measure to implement innovative education.
Second, the basic strategies to cultivate metacognitive ability
1. Improve students' understanding of the importance of metacognition. Let students realize that the learning process is a cognitive process of observation, memory, thinking and imagination. In this process, the methods of observation, memory, thinking and imagination are directly related to the quality and success of learning. In order to improve the quality and efficiency of learning, we must pay attention to whether our learning methods are suitable for the requirements of learning tasks. Once a problem is found, it must be quickly adjusted and improved. Only in this way can the learning activities be smoothly promoted and the learning effect be significantly improved.
For example, solve the application problem: "Xinhua Ranch has 650 goats and sheep, of which goats account for 30% of the total, and then buy some goats. At this time, the number of goats accounts for 2/3 of the total. How many goats do you buy? " Students first consider the number of goats, so they use 650× 30% = 195 to find the number of goats. After buying some more goats, goats account for 2/3 of the total, that is, 650 goats plus 2/3 of the total number of goats bought again. However, the total only includes the number of goats bought, which is exactly what is required. Students find this problem-solving thinking problematic. According to this self-cognition, we quickly control and adjust the thinking of solving problems, and think from the number of sheep: from 70% of the total number of sheep, we get 650 × 70% = 455. After buying some goats, the number of sheep accounts for 1-2/3 = 1/3, ranging from 455 to 65438.
Attach importance to the teaching demonstration of metacognitive activities. In the teaching process, teachers' understanding of new textbooks and the application of mathematics knowledge are not smooth sailing, and they are always full of self-adjustment and adjustment cognitive activities. In teaching, teachers should not hide their plans, monitoring and evaluation when solving problems, but should show the whole process of solving problems, including twists and turns, and show metacognitive activities with practical actions, so that students can gradually experience the truth and significance of "doing this" and learn how to treat and solve problems when encountering setbacks. Of course, the process of classroom teaching can also be organized according to the requirements of metacognitive teaching demonstration. When students have wrong ideas in the process of solving problems, they should first be guided to show their thinking process of solving problems freely and independently, and then reflect, so as to find out the mistakes, correct them and standardize their thinking. This kind of teaching is conducive to cultivating students' reflective cognitive ability.
3. Teach students learning strategies. Learning strategy knowledge is the basis of students' self-monitoring and self-improvement, and students should be helped to understand and master it in a planned way. For example, to learn new knowledge, we should combine "doing (operation), speaking (expression), thinking (thinking), imagining", "number (quantity), formula (calculation), shape (diagram)" with "listening to knowledge, listening to methods and listening to thinking". When solving application problems, we should master the strategy of "carefully examining the problems, seriously imagining and carefully correcting them"; The strategy of "combination of numbers and shapes, two-way reasoning and contradiction transformation" and the strategy of "carefully analyzing the characteristics of the topic after solving the problem and summarizing the law of solving the problem" should help students understand and master. Only by understanding and mastering can students effectively improve their self-regulation ability.
4. Strengthen the training of metacognitive ability. Metacognitive ability is gradually cultivated through practical training on the basis of metacognitive knowledge. Among them, training is the key to the growth of metacognitive ability. The cultivation of metacognitive ability must run through the whole teaching process in a planned way. For example, when teaching new knowledge, before the teacher gives an intuitive demonstration, it is necessary to tell students the specific observation contents and methods, so that students can clearly understand the objectives and requirements of observation, and think and monitor their own observation activities during the observation process, so as to master the "know-how" of monitoring. After drawing the conclusion of new knowledge, students should be guided to think "How do we learn new knowledge?" Is there a better way? "Through continuous reflection, strengthen monitoring awareness and improve monitoring ability. Another example is to solve application problems. Before solving the problem, the teacher should tell the students the strategies of examining, solving and summarizing the problem. After solving the problem, let the students talk about how they check, solve and summarize the problem, and evaluate their thinking activities in the whole process of solving the problem. After such training, with the passage of time, students' metacognitive ability will gradually improve and reach an ideal situation.
Third, the key to cultivating metacognitive ability
1. Teachers should update their teaching concepts and consciously cultivate students' metacognitive ability. The teaching process is the unity of teaching and learning, and it is necessary to cultivate students' cognitive ability and metacognitive ability. Only when metacognitive ability is cultivated and improved can students' learning ability and learning level be effectively developed and optimized. Therefore, mathematics teachers must clearly understand the significance of cultivating students' metacognitive ability and consciously put it on the important agenda of teaching reform.
4. Teachers should seriously improve teaching and implement the task of cultivating metacognitive ability. Specifically, the teaching process is carefully designed with the viewpoint of unifying students' cognitive activities and metacognitive activities as the commander-in-chief, and students' learning activities as the main line, so that every step forward in students' cognitive activities, every student can get learning feedback information corresponding to this step, evaluate and regulate their cognitive activities in time, so as to achieve the synchronous development and improvement of cognitive ability and metacognitive ability.
3. Teachers should guide students to summarize metacognitive activities and constantly improve students' metacognitive ability. Before the end of each class, students can be arranged to sort out their own learning situation and ask them to review what they have learned in this class. How much do you know about this knowledge? What are the most interesting processes? What areas need further study? Is there a problem? Inspire students to re-recognize their learning process in the whole class, make clear the degree of mastering new knowledge and experience the fun of success.