The knowledge points related to light reflection in mathematics were mainly based on the geometric application of the law of light reflection. 1. ** Mathematical expression of the law of reflection ** - When light is reflected, the reflected ray, the incident ray, and the normal are all in the same plane (this is reflected in the planar relationship in geometry problems, which can be used to construct planar geometry). - The reflected light and the incident light were on two sides of the normal. - The reflection angle was equal to the incident angle. This equality was the key to solving many geometric problems. In mathematics, when it came to the calculation of the angle of light reflection or the derivation of the angle relationship in a geometric figure, this equality relationship could be used to establish an equation. For example, in a triangle, if a ray of light is reflected on the boundary surface of the triangle, the relationship between the internal angles of the triangle can be determined by the relationship between the reflection angle and the incident angle. 2. ** Reflection of Reversibility of Light Path in Mathematics ** - Light had reversibility. In mathematical geometry, this meant that if one knew the incident and reflection paths of a ray, then according to the principle of reversibility, the reflected ray could be regarded as an incident ray, and its reverse extension was symmetrical to the original incident ray. This feature could be used to simplify some complex optical path geometry problems. For example, in the case of multiple reflections, reversibility could be used to transform complex optical paths into a form that was easier to analyze. 3. ** The relationship between reflected light and geometric figures ** - In some geometric shapes (such as a hexagon, a circle, etc.), when light is reflected at the boundary, a specific angle will be formed. For example, in a circular mirror, light rays were incident from a point. After reflection, the path of the reflected light rays formed a specific geometric relationship with the center of the circle, the incident point, and other elements. One could use the properties of the circle (such as the tangency property, the circular angle theorem, etc.) and the law of light reflection to solve the relevant geometric quantities (such as the angle between the reflected light rays and a certain diameter, etc.). - In a hexagon, if a ray of light was reflected on the boundary surface of the hexagon, the path of the ray after multiple reflections and the angle relationship between the edges of the hexagon could be analyzed according to the relationship between the reflection angle and the incident angle, combined with the inner angle theorem and the outer angle theorem of the hexagon. 4. ** Reflection classification and mathematical model ** - Mirror reflection: When parallel rays hit a smooth surface, the reflected rays are also parallel. From a mathematical point of view, this was a regular reflection model. When dealing with geometric problems involving parallel rays and planar reflective surfaces, the parallel relationship could be used to perform parallel transmission and equivalent substitution of angles. For example, when calculating the distribution of light rays reflected by multiple parallel reflective surfaces, a series of parallel angle relationships could be established to solve the problem. - Diffuse reflection: When parallel light rays hit an uneven surface, the reflected light rays shoot in all directions. In mathematical modeling, diffuse reflection was relatively complicated. Advanced mathematical methods such as probability statistics or integral might be needed to describe the overall reflection effect of light. For example, when studying the energy distribution of light on a rough surface. - Directional reflection (between diffuse reflection and mirror reflection): It is reflected in all directions, and the intensity of reflection in all directions is not uniform. In mathematics, it might be necessary to describe the direction and intensity distribution of the reflected light by using a function or a function, and then analyze the transmission characteristics of the light under such reflection. Read more exciting novels for free
1. First, determine the reflective surface, which is represented by a straight line. For example, the reflective surface of a flat mirror can be drawn as a horizontal straight line. 2. Draw the incident light. This is a straight line with an arrow, indicating the direction of light transmission. The arrow points to the reflective surface. 3. The incident point was determined, which was the intersection point of the incident light ray and the reflective surface. 4. The normal line of the reflective surface is a straight line that is normal to the reflective surface and is usually represented by a dotted line. 5. According to the law of reflection, the angle of reflection was equal to the angle of incidence. The angle of incidence was measured, and the normal line was used as the axis of refraction to draw the reflected light. The reflected light was also a straight line with an arrow, and the direction of the arrow indicated the direction of the reflected light. For example, in the book " Reflection Optics " written by Eugene, the images on flat surfaces and concave mirrors were discussed. The theory of reflecting light was involved, and these theories helped to accurately draw the reflection image of light. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
In mathematics, the direction of light reflection was determined by the law of light reflection: the reflected light ray, the incident light ray, and the normal line were on the same plane; the reflected light ray and the incident light ray were separated on both sides of the normal line; and the reflection angle was equal to the incident angle. Specifically, when the light is directed to a plane, the normal line of the plane is drawn through the point of incidence. The angle between the incident light and the normal line (the angle of incidence) is equal to the angle between the reflected light and the normal line (the angle of reflection). According to this relationship, the direction of the reflected light can be determined. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The following is a reflection on the teaching of first-year mathematics: - ** Success ** - ** Situation and interest cultivation **: integrate the concept of "efficient classroom group cooperative learning" into the teaching. By creating vivid and specific situations (such as animal sports prizes, calculation of the number of notebooks, etc.) to attract the students 'attention, students can learn to calculate in the situation, avoid boredom, enhance learning interest, and easily achieve learning goals. - ** Group Cooperation and Exchange **: Use group exchange and learning activities, and report individually within the group to create a warm and active learning atmosphere, which helps students understand and master calculation methods and theories. - ** Arithmetic Ability Cultivation **: Pay attention to the training of mathematical ability. Take 10 + 20 as an example. Students will have a variety of algorithms, such as placing small sticks (1 bundle plus 2 bundles, 3 bundles, or 30), using counters (1 plus 2 beads on the 10 digits, 3 tens, or 30), number composition (1 plus 2 tens, 3 tens, or 30), and adding the same digits (1 plus 1, 10 plus 10, 10 plus 10, 30). This will reflect the variety of algorithms and allow students to understand mathematical theory and broaden their minds during communication. - Knowledge comparison and pattern discovery: Guide students to compare knowledge, such as distinguishing between a few ones and a few tens, so that they can better grasp the calculation method and theory of adding and deducting a whole ten. They can quickly and accurately do mental arithmetic. - ** Inadequacies ** - ** Time allocation and ability to ask questions **: Although the teaching process is smooth and most students can calculate correctly, there is an uneven time allocation (first loose and then tight), and the students 'ability to ask questions is relatively weak. - ** Students 'ability to express themselves **: Many students can calculate the results, but when they are asked about the calculation ideas, they will not express themselves. This reflects the lack of expression training. Students should be allowed to speak more. - ** Practice design **: Practice forms, methods of guidance, and other aspects need to be carefully designed. Practice is an important means to consolidate new knowledge. It should be designed according to the physical and mental characteristics of the lower grade students, so that all students can actively participate in learning and consolidate new knowledge. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The following are some possible reflections on the fifth grade mathematics teaching of the People's Education Press: ** 1. Number and algebra ** 1. ** Elements and Multipliers ** - As for the teaching of the concepts of factor and multiple, students might have difficulties in understanding the concept of " In integral division, if the quotient is an integral number without a remainder, the dividends are the multiple of the dividends, and the dividends are the factors of the dividends." Teachers needed more examples to help students understand. For example, through specific integral division formulas, such as 12 div3 = 4, it was explained that 12 was a multiple of 3, and 3 was a factor of 12. - When teaching the features of 2, 5, and 3, although the rules were relatively clear, students might be confused when using these features to solve complex problems. For example, to determine whether a large number is a multiple of 2, 3, or 5 at the same time, teachers need to strengthen the teaching of the connections and differences between different characteristics. - The concepts of prime numbers and composite numbers were more abstract, and students might find it difficult to distinguish the relationship between prime numbers, composite numbers, and 1. The teacher had to guide the students to understand these concepts from the perspective of the number of factors, and let the students list the prime numbers and composite numbers within a certain range to deepen their memory. 2. ** The meaning and nature of scores, addition and deduction of scores ** - The meaning of a score was a difficult problem for students. Take a whole as a unit " 1 ", then divide the unit " 1 " evenly into a number of parts. The number that represented such a part or parts was the score. Teachers could use more physical demonstration or graphic display in teaching, such as taking a circle or a rectangular as the unit " 1 ", and then dividing it to represent the score, helping students understand the meaning of the score from intuitive to abstract. - In the teaching of fraction addition and substitution, students were prone to making mistakes in addition and substitution of different decimators, especially in the process of general fraction. Teachers needed to emphasize that the basis of general scores was the basic nature of scores, and through a large number of exercises, students should be familiar with the methods of general scores and reduction scores to improve the accuracy of the calculation of scores. ** 2. Spatial and graphic aspects ** 1. ** Observing objects ** - Students might find it hard to imagine different shapes when they put together a geometric object according to the shape seen from one direction. The teacher could let the students use the small cubes to observe from different angles, so as to cultivate the students 'spatial imagination and concept. 2. ** Cuboids and cubes ** - When teaching the characteristics of cuboids and cubes, students might not have a deep understanding of the concepts of edges, surfaces, and vertexes. Teachers could use physical models to let students count the number of edges and faces, measure the length of the edges, and better grasp the characteristics of cuboids and cubes. - As for the derivation and application of the formulas for the volume and surface area of cuboids and cubes, students might not be able to correctly judge whether to calculate the volume or the surface area when solving practical problems, or make calculation errors when using the formulas. Teachers should strengthen the analysis of practical problems, guide students to correctly distinguish the concept of volume and surface area, and carry out more targeted exercises. ** 3. In terms of statistics ** When teaching single-line and double-line charts, students might have problems reading the data in the chart, analyzing the trend of the data, and making predictions based on the chart. Teachers could ask students to collect data and create a line chart by themselves. In this process, they could understand the elements and significance of the chart and improve their ability to analyze and interpret the data. ** 4. Comprehensive applications ** In the comprehensive application of mathematics activities, students might not have a clear division of labor and lack the spirit of cooperation when working in a group. Or when solving practical problems, they could not effectively apply the mathematical knowledge they had learned to practical situations. Teachers should clarify the rules of group division before the activity, strengthen guidance during the activity, help students connect mathematical knowledge with practical problems, and improve students 'mathematical application ability. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The law of light reflection belonged to physics, not mathematics. The knowledge points of the law of light reflection were as follows: 1. The three lines are in the same plane: the reflected light, the incident light, and the normal line are in the same plane. 2. Separation of two lines: Reflected light and incident light are separated on both sides of the normal. 3. The two angles are equal: the reflection angle is equal to the incident angle. 4. Reversible Light Path: In the reflection phenomenon, the light path is reversed. 5. [Special situation: When the light is incident vertically on the mirror, the three lines will be combined, that is, the incident light, normal, and reflected light will overlap.] 6. Reflection classification: The reflection of light mainly includes mirror reflection, diffuse reflection, and directional reflection (non-Lambertian reflection) between the two. 7. Reflection applications: such as periscope, bicycle reflective lights, car rearview mirrors, mirrors, solar stoves, flashlights, etc., and we can see objects that do not emit light because the light reflected by the object enters our eyes. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
In the teaching reflection of the mathematics activity Clouds and Raindrops, there were the following reflections: - ** Teaching segment design ** - In the introduction stage, the raindrops were defined as the tears of the clouds. When comparing which cloud had the most tears (i.e., the number of raindrops was the most), the children would first observe and find out which cloud had more raindrops and explain the reason. Then they would verify it together. This method would help deepen the impression of the children. - In the process of counting raindrops, the children were not directly told how to count. Instead, they used their peers 'strength and let the children share different counting methods, such as five plus five, counting from the right row by row, counting from the top vertically, etc. This process developed the children's observation ability and language expression ability. - ** Teaching effectiveness and enlightenment ** - Judging from the children's homework, most of the children had a good grasp of the knowledge points, but there were some children who had messy connections. - Realizing that children's ability and imagination were stronger than imagined, they should pay more attention to the initiative of children in future teaching activities and let children become the masters of activities. And in the Chinese text "Raindrops" related teaching reflection: - ** Teaching effectiveness ** - The students showed a spirit of autonomy in learning new words and reading aloud. There were many ways to recognize and remember new words. The teacher encouraged the students 'success to make them happy. - Using autonomous and cooperative learning methods, through a variety of reading methods, students can understand the text, learn to read aloud, cooperate, feel emotions, understand the truth, and obtain methods. - The design of open-ended questions could stimulate the students 'desire to explore, let them imagine reasonably, explore in many ways, and use language in a creative way. - ** Inadequacies ** - Some students had difficulty reading aloud, especially the erhua sound. Although the teacher had demonstrated it many times, the effect of reading the erhua sound in the sentence was still not ideal. - ** In terms of improvement measures ** - More students should be given the opportunity to showcase themselves. It should be open to all and allow more students to actively answer questions. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The following is a summary and reflection on the primary school mathematics lesson: ** I. Basic teaching skills and classroom control ** 1. ** Solid teaching foundation ** - In primary school mathematics teaching, a teacher's basic skills were very important. For example, in some high-quality class evaluation activities, excellent teachers showed strong organizational and control skills in the classroom. They had a high theoretical level. Especially in terms of mathematical language, the teacher's language was concise and concise, which helped to cultivate the students 'rigorous mathematical language expression habits. Moreover, these teachers paid attention to practical results in their lessons. They did not pursue superficial tricks, but from the student's point of view. They understood the student's starting point and taught according to the student's actual situation. 2. ** Enlightenment and Reflection ** - This reminded the majority of primary school mathematics teachers to constantly improve their basic skills, including in-depth understanding of the teaching materials and control of the classroom rhythm. In his own teaching, he should pay attention to using concise and accurate language to guide students, avoiding long and complicated expressions that would confuse students. Moreover, they had to think about the teaching content and methods from the student's point of view. They could not be separated from the student's actual learning situation. ** 2. Students 'emotional attention and knowledge formation ** 1. ** Pay attention to students 'emotions and knowledge formation ** - In the classroom, excellent teachers would let students solve problems independently and encourage students to actively participate in the learning process. For complex problems, the students were guided to explore them by using their mouths, hands, and brains. Every student had the opportunity to think and express their opinions, and truly become the master of learning. Even if the students encountered difficulties, the teachers would patiently enlighten and guide them, reflecting the teaching philosophy of teacher-led and student-centered. However, there were also cases where some teachers gave too much guidance and explained too much. 2. ** Enlightenment and Reflection ** - Teachers should give students more space to think and explore independently and believe in their abilities. For example, when teaching mathematical concepts or solving mathematical problems, students could first try to understand or solve them themselves, and then carry out the necessary guidance and summary. At the same time, they should pay attention to the degree of guidance to avoid excessive guidance, so that students would lose the opportunity to explore independently. ** 3. Group learning ** 1. ** The effectiveness of group cooperation ** - Many teachers pay attention to the effectiveness of group cooperative learning in primary school mathematics teaching. The teacher would ask valuable questions for the group to cooperate and explore. Before the activity, the teacher would make clear the requirements and use teaching aids or learning tools to let the students operate, such as putting, cutting, painting, etc., so that the teaching content could be visualized. During the activity, the teacher would patrol and guide, and after the activity, the group would display and communicate. This could effectively cultivate the students 'hands-on ability. 2. ** Enlightenment and Reflection ** - In daily teaching, teachers should carefully design the content and form of group cooperation to ensure that group cooperation is not just a formality. According to the teaching content, the group cooperation tasks should be arranged reasonably, so that every member of the group could actively participate, and in the process of cooperation, the students 'mathematical thinking ability and cooperative communication ability should be improved. ** 4. Teaching Concept and Purpose ** 1. ** Renew education concepts and clarify education goals ** - Primary school mathematics teachers should update their educational concepts and understand that they should not only teach basic mathematics knowledge and skills, but also pay attention to cultivating students 'thinking ability, spatial concept, stimulate learning interest, establish learning confidence, and carry out moral education. Every class should be viewed from the perspective of cultivating high-quality talents. 2. ** Enlightenment and Reflection ** - In actual teaching, teachers should integrate the goal of educating people into every teaching link. For example, when explaining mathematical examples, he could infiltrate the cultivation of mathematical thinking methods. At the same time, he could use mathematical knowledge to tell stories about mathematicians to encourage students to actively explore and cultivate students 'perseverance in learning. ** 5. Cultivation of learning interest ** 1. ** Maintain and improve interest in learning ** - The interest plays an important role in primary school mathematics learning. Teachers should pay attention to cultivating students 'correct learning motivation and good psychological quality. Through the creation of learning situations, starting from the things that students are familiar with, and other ways to stimulate students 'interest in learning. This was because students were more willing to take the initiative to think and explore when the learning content was close to the actual life of the students. 2. ** Enlightenment and Reflection ** - Teachers should be good at digging out mathematics materials from their daily lives and integrating them into their teaching content. For example, when teaching mathematical operations, he could use daily life scenes such as shopping and changing money as examples to let students feel the practicality of mathematics, thereby increasing their interest in learning. ** 6. Mathematical Thinking Method Penetration ** 1. ** Mathematical thinking methods are not enough ** - In primary school mathematics teaching, the infiltration of mathematical thinking methods was not in place. However, mathematical thinking was the soul of mathematics, and it was of great significance to cultivate students 'abstract thinking ability. 2. ** Enlightenment and Reflection ** - Teachers should consciously permeate mathematical thinking methods in the teaching process. For example, when teaching the four arithmetic operations, he could permeate the function thinking, model thinking, etc., so that students could gradually improve their mathematical thinking ability while learning the basic knowledge. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The following is a reflection on the fourth grade mathematics essay from different aspects: ** 1. Regarding the difficulty of the teaching content ** 1. ** The measurement of angles ** - This was the most difficult part of elementary school mathematics. There were many problems with the protractor for fourth-years. For example, the placement of the protractor and the correct reading of the degree of the angle. The common problems that students had were that they were used to looking at the degree of the outer circle no matter which circle the "0" mark was on one side of the angle. When reading the scale, there would be reading errors, such as reading 40 to 50, and the direction of reading the scale was blurry in their minds. This reflected that although the teacher emphasized the steps of "point coincidence, edge coincidence, and reading the scale" during teaching, the students might not really understand the principle. Teachers might need to think more from the student's point of view and consider how to let the student understand the nature of measurement more intuitively, rather than simply training skills. 2. ** Knowledge of big numbers ** - This unit involves a large number of students, and students have less contact with them in their lives. Even though students nowadays were willing to accept challenges, some abstract concepts, such as the understanding of numbers within a hundred million, reading and writing, the rewrite of large numbers, and the understanding of approximate numbers, were still difficult. Teachers used the methods of creating situations and cooperative communication, using data such as population censuses, land area, and gross domestic product to stimulate students 'interest in learning. However, in the teaching process, they might need to guide students to understand the meaning of these large numbers in more detail to enhance students' sense of numbers. ** II. Teaching aid and demonstration ** 1. ** The measurement of angles ** - When teaching the measurement of angles, there was a difference between the protractor of the teaching aid and the protractor of the students. For example, the teaching aid was made of wood, and the center point and the zero scale line were not clearly displayed on the blackboard, which could not give the students a good demonstration. This may affect the students 'understanding of the correct use of the protractor. Teachers should consider using clearer and more observable teaching aids or modern educational technology (such as a projector) to demonstrate the correct use of the protractor. ** 3. Regarding the Awareness of Students ** 1. ** The measurement of angles ** - The fourth-year student saw only a static, complete angle, and did not realize that an angle was formed by a ray rotating around the end. This made it difficult for students to understand the principle of angle measurement, such as "the center to the apex, the zero line to one side, and the other side to look at the scale." They did not understand why they had to do this, and they were at a loss when actually measuring the angle. Teachers could add some dynamic demonstration in the teaching to help students establish the image of the dynamic formation process of the angle, so as to better understand the method of measuring the angle. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The following is a detailed reflection on the classification of mathematics activities in small classes: ** 1. Achievement of the event objective ** 1. ** Knowledge and Skill Target ** - In the classification activity, if the goal is to let the child learn to classify according to a certain feature, such as color or shape. During the activity, it was necessary to observe whether the child could accurately classify the items according to the given standards. For example, in an activity that used color as a classification standard, whether the child could put red items together and blue items together. If most of the children could operate it correctly, it meant that the goal was achieved. However, if some children were confused, such as grouping red and similar colors such as orange, this might indicate that the guidance of color distinction in the teaching process was not clear enough, or the color contrast of the teaching materials chosen was not obvious enough. - If the goal of the activity involves letting the child understand the concept of classification, such as saying,"Putting the same things together is classification." Teachers should guide children to understand this abstract concept through a variety of examples. In the process of reflection, review the child's answers. If the child can express similar concepts in his own language, it means that the concept transmission is successful. On the contrary, he needs to consider whether there are problems in the teaching method or the choice of examples, such as whether the use of overly complicated language or not vivid examples to explain the concept. 2. ** Course, Method, and Target ** - When the goal was to cultivate the child's observation ability and operation ability, it was necessary to consider whether the activity process gave the child enough opportunities to observe and operate. For example, in an activity that categorized objects by shape, the child needed to observe the objects of different shapes before operating them. If the teacher explained too much during the activity and the child had too little time to observe and operate independently, it might affect the development of these abilities of the child. Teachers could reflect on whether there was enough time for children to explore and discover the rules themselves, and whether they gave appropriate guidance during the operation of the children, without too much intervention and correcting mistakes in time. 3. ** Emotions, attitudes, goals ** - It was important for the children to develop their interest in mathematics activities. In the activity, you can create interesting situations, such as small animals sharing food, to attract children to participate. When reflecting, you should consider the enthusiasm of the child in the activity and whether he actively participated in the classification activities. If the child showed a negative or disinterested attitude, it might be that the situation was not attractive enough, or the difficulty of the activity was too high or too low, causing the child to lose the challenge or sense of accomplishment. ** 2. Event content design ** 1. ** The rationality of the classification criteria ** - The classification criteria chosen should be in line with the cognitive level of the children in the small class. For example, classification by size, color, simple shape, etc. was more suitable for small children. However, overly complicated classification criteria, such as classification by function or material (materials that were difficult for small children to understand), might cause difficulties for children. If it is found that the child has difficulty understanding the classification criteria during the activity, it is necessary to re-evaluate whether the selection of the classification criteria is appropriate. 2. ** Selection and Use of Teaching Aids ** - The choice of teaching aids should be intuitive, vivid, and colorful to attract the attention of children. For example, using colored blocks, small animal cards, etc. as teaching aids for classification. In the process of reflection, he had to consider whether the teaching aid had played its proper supporting role. If there were too many or too few teaching aids, it might affect the child's operating experience. Too many teaching materials may confuse the child, and too few may not fully demonstrate the variety of categories. At the same time, the presentation method of the teaching aid was also very important. Whether it could clearly display the characteristics of the classification, such as whether the color distinction was obvious when it was classified by color. ** 3. Event organization and implementation ** 1. ** Connection of activity segments ** - The transition between activities should be smooth and natural. For example, from the introduction stage to the main body's classification operation stage, to the final summary stage, there must be a logical connection between each stage. If the transition between the activities was found to be stiff, the child might be distracted. This required a re-adjustment of the transition between the segments. For example, the continuation of the story, questions, and guidance could be used to make the connection between the segments more natural. 2. ** Teacher's guidance and interaction ** - When the child was performing the classification operation, the teacher's guidance should be timely and appropriate. If the teacher pointed out the child's mistakes too early or interfered too much with the child's operational thinking, it might affect the child's independent exploration ability. Teachers should give appropriate guidance when children encounter difficulties or misconceptions. At the same time, the interaction between teachers and children was also very important. Children should be encouraged to actively express their thoughts and give positive feedback in a timely manner, such as praise and encouragement, to enhance children's self-confidence and participation. ** 4. Event Extension ** 1. ** Contact between family and kindergarten ** - You can think about how to extend the classification activities to the family, such as assigning small family tasks and letting the children sort their toys when they go home. If you don't connect well with your family in the extension of activities, you may miss some opportunities to consolidate the knowledge and skills that children have learned. They could consider informing parents of the content of the activities through parent groups and providing some simple suggestions for family activities to promote children's learning and development in the family environment. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Mathematics Reflection My sixth grade mathematics study was very rewarding, but it also made me realize that I had many problems. In the process of learning, I realized that my understanding of some concepts was not deep enough. For example, in the application of scores, although he knew the basic calculation method, it was easy to make mistakes when he encountered more complicated questions, such as the conversion of the unit " 1 ". This reflected that I had only memorized the formula mechanically, but had not truly understood the essence of the concept. I'm lacking in solving problems. For example, if there was a problem where there was a relationship between four numbers, I would often only use the most basic method and not grasp the simpler and more effective solution. If one could learn to assume an intermediate quantity and convert multiple unknowns into an equation expressed by this intermediate quantity, solving problems would be much easier. Carelessness during exams was also a big problem. Many of the questions that he had done before were wrong because he did not read the questions carefully and ignored the key information. This is because I am not strict enough with myself and have not developed a good habit of seriously examining questions. In my future studies, I will pay more attention to the deep understanding of concepts and do more practice in identifying concepts. Learn all kinds of problem solving techniques and ask teachers and classmates for advice. Moreover, he had to constantly remind himself to carefully examine the questions and reduce unnecessary mistakes. Only then could he improve his mathematics results. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>