Cultivating students' reflective ability and guiding them to reflect on their learning strategies is a starting point worthy of attention. For example, when teaching "the area of a circle", I first drew a square, a parallelogram and a trapezoid on the blackboard, and asked students to reflect on the derivation method of these graphic area formulas. Finally, it boils down to "these graphics can be transformed into rectangles to study the area formula". Then show a circle and ask the students to try to deduce the area formula. Through teachers' guidance and independent attempts, students found that "a circle can also be transformed into a rectangle to study the area formula". Here, I once again ask students to reflect on the similarities and differences between the previous deduction process and today's deduction process, so that students can realize that "the circle is divided into several equal parts and then pieced together into an approximate rectangle." Finally, let students reflect on the rationality of this "approximate deduction" moderately. It can be said that the reflection here includes both the reflection on previous learning strategies and the reflection on the rationality of current learning strategies.
It is a good opportunity to cultivate students' reflective ability and guide them to reflect in the process of optimization. For example, when I teach "Draw an angle with a protractor", let the students draw a 60-degree angle first. Results Most students drew with triangles according to the experience of last class, and a few students drew with protractors. After exchanging methods, they asked students to draw a 65-degree angle. At this time, some students who are drawing triangles in front of them seem at a loss, some are lost in thought, some are thinking about how to draw, and some are drawing with a protractor. At this time, one of my students couldn't wait to say, "An angle of 65 degrees can't be measured by a triangle." Then I pretended not to understand and threw a question: "Alas? Both triangles and protractors can draw 60-degree angles, and 65-degree angles can only be drawn with protractors. Why? " At this time, students compare and optimize the two methods in reflection, and truly experience the universality of drawing angles with protractor. Another example is that in the addition and subtraction teaching of fractions with different denominators, after revealing the example of "1/2+ 1/4", students explore various methods such as fractional decimal, drawing lines and transformation with the help of existing experience. On this basis, I guide students to compare and reflect on which method has more universal value, and get the algorithm of "addition and subtraction of different denominator scores".
It is also very important to cultivate students' reflective ability and form reflective thinking methods. When teaching "addition and subtraction of fractions with different denominators", when students understand that "addition and subtraction of fractions with different denominators" can be transformed into "addition and subtraction of fractions with the same denominator", I pointed out the importance of "transforming old knowledge and solving new problems" in time. Then, guide students to reflect on the new knowledge acquired by similar methods, so as to naturally reveal the mathematical thinking method of "transformation".
It is worth paying attention to cultivating students' reflective ability and guiding them to reflect on confusing knowledge points. For example, when learning "Rewriting Integer into Ten Thousand Units" and "Rewriting Non-Integer into Ten Thousand Units and Omitting the mantissa after Ten Thousand Units", students are seriously confused when using the symbols = and ≈ material. At this time, guide the students to reflect on which of these two situations is the exact number, which is equal to the original number, but the approximate number, and the size has changed. Students understand the truth through comparison, and the phenomenon of confusion disappears.
It is also very suitable for cultivating students' reflective ability and organizing students to discuss and communicate. I think it is a good process to train students' reflective ability to think independently after discovering problems and discuss and communicate after having their own ideas. Because in the process of discussion and communication, on the one hand, students need to let others understand their own problem-solving strategies, on the other hand, they also need to try to understand others' problem-solving strategies and constantly review and reflect on the right and wrong, similarities and differences between themselves and others in problem-solving strategies. They need to give evidence for the right and explain the reasons, find out the reasons for the wrong, compare the characteristics of different methods and optimize the correct problem-solving strategies with different methods, and so on. In the process of teaching, I often guide students to think like this: "What do you think?" "Why do you think so?" "Is this reasonable?" "Is your way to solve the problem the best?" "Is there a better way to solve the problem?" And so on, through these questions, students can be guided to gradually develop the consciousness and habit of reflection. For example, in the teaching of parallelogram area, students find the relationship between the original parallelogram and the assembled rectangle by cutting, cutting, observing and comparing (the base of parallelogram is equal to the length of rectangle, the height of parallelogram is higher than the height of rectangle, and the area of parallelogram is equal to the area of rectangle), and then deduce the area formula of parallelogram in the group. We must create an opportunity for students to communicate with each other. Without this process or a mere formality, students cannot form a correct and clear cognitive structure. When students present their transformation and deduction process and conclusions to everyone, and describe their inquiry process and explain their conclusions, students' evaluation of their inquiry process, methods and conclusions can help them correct and improve their own methods and form correct inquiry strategies. On the one hand, students express their own thinking process, on the other hand, they also form the habit of listening carefully and being good at reflection.
It is also an effective way to cultivate students' reflective ability and guide students to participate in evaluation. In classroom teaching, students should be given full and independent interactive evaluation opportunities to reflect on the success or failure of learning. For example, when teaching "circumference", let students explore the measurement method of circumference independently. Sheng 1 Q: "Can the circumference of a circle be measured directly like a rectangle?" The second student immediately retorted: "No! Perimeter is a curve and cannot be measured directly. I think since the circle is surrounded by curves, it must be easy to roll. You can roll it on a ruler to measure the circumference of the circle. " Student 3 went on to speak: "We also found that it can be measured by winding a rope." Regarding the views of students 2 and 3, student 1 once again questioned: "I wonder, can the circumference of a big circle similar to the circular roof of a building be measured by winding rope and winding rope?" As a result, all students, including students 2 and 3, are immersed in the reflection on the universal significance of the measurement method ... In this case, when students 2 object to the "direct measurement" scheme published by students 1, when students 1 question the universality of the "rolling rope" measurement method discovered by students 2 and 3, students will undoubtedly reflect. These are all because teachers provide opportunities for students to fully participate in the evaluation.
As the guide of students' subjective reflection, teachers should rely on their keen eyes to capture resources in time and constantly improve the effect and value of subjective reflection. Paying attention to classroom reflection, encouraging students to reflect and skillfully using reflection will definitely make classroom teaching ups and downs, help stimulate students' interest in learning, improve learning efficiency, really make learning wonderful because of reflection, make students happy, smart and thoughtful, and truly become the masters of the classroom.