Reflection on fractional teaching 1 First, there are many mistakes in fractional operation.
Fraction addition and subtraction is mainly when the molecule is polynomial. If the whole molecule is not enclosed in brackets, it is easy to make mistakes in symbols and results. Therefore, when we teach the addition and subtraction of fractions, we should educate students that the parentheses cannot be omitted in the numerator part. Secondly, the conceptual operation of fractions should be calculated in the order of first power, then multiplication and division, and finally addition and subtraction. If there are brackets, the ones in brackets should be done first.
Second, the fractional equation is also the hardest hit by mistakes.
The definition of (1) root augmentation is rather vague. Let me briefly explain the concept of root augmentation.
(1) Incremental root is the root of the integral equation after naming the fractional equation, but it is not the root of the original equation;
(2) Finding the root can make the simplest common denominator equal to 0;
(2) The steps of solving the fractional equation are not standardized, and most students lack the important steps of "examination" and cannot jump out of the mode of solving the integral equation;
(3) The fractional equation is full of mistakes.
In view of the above problems, I will start with the basic knowledge and problems, and draw inferences to explain them. Like the integral equation, I first analyze the meaning of the question, accurately find out the equal relationship of quantitative problems in the application problem, set the unknowns appropriately, and list the equations; The difference is that the listed equations are fractional equations. Finally, we should check whether it is the solution of the listed fractional equation and whether it meets the meaning of the question.
In the chapter of fractions, we should use fractions to analogize teaching, so that students can clearly understand the differences and connections between fractions and algebraic expressions, understand the model idea of fractions, and further develop the sense of symbols, which will certainly get twice the result with half the effort.
Reflections on Fraction Teaching Part II "Fraction operation" teaching, students feel good in class, but they will make many mistakes when doing homework or testing, especially the mixed operation of fractions, which belongs to the problem of calculation ability. Therefore, we should pay special attention to this deep root in teaching and find corresponding countermeasures according to the actual situation of students.
In order to solve the problems of students' many mistakes in fractional operation and poor ability, the most important thing is the design of "intensity, depth and pertinence" in students' exercises. Because the basic way to form the ability of fractional operation is practice, and the biggest reason for students' poor ability of fractional operation is lack of practice or lack of targeted practice. We should be careful and practice more in teaching, and we should not substitute evaluation for practice. Secondly, we should adhere to the principle of excessive practice, ensure a certain amount of practice, not only stay at the level of "knowing how to do", but also strive to make most students reach the level of "proficiency and accuracy" through practice; Thirdly, the reasons why students make mistakes in fractional operation are different, so the exercises must be targeted. We should analyze the causes of students' mistakes from their past exercises and give individual counseling. In a word, to solve the problem of many mistakes in the operation of junior high school scores, we must "practice-correct-practice again"
The third part of this lesson is to further understand the fractional equation (the unknown is in the denominator) and discuss its solution on the basis of students' learning the integral equation, especially the linear equation with denominator. Reflecting on the teaching of this class, the following points are worthy of recognition:
1. The teaching design fully respects students and meets the requirements of the new curriculum concept and the "learning-based, classroom-up-to-standard" teaching model. When designing the teaching content and links of this course, students' cognitive rules and existing knowledge and experience are fully considered. Classroom teaching adopts the teaching mode of "reviewing old knowledge-creating situations-autonomous learning-exchange feedback-induction and promotion-application practice". Firstly, a linear equation with denominator is designed, so that students can review the basic steps of solving linear equation and the method of removing denominator on the basis of solving old knowledge. Then, two practical problems are given to arouse students' thinking. By establishing mathematical model and listing equations, students can feel the difference between fractional equation and integral equation, and guide them to learn the definition of fractional equation by themselves. After having a preliminary understanding of fractional equation, students are encouraged to learn the solution methods of fractional equation independently, exchange different methods in the process of showing feedback, and realize the role of transformation in solving equation. Through the test, it is found that some fractional equations will produce "roots", which makes the original fractional equations meaningless, which leads to thinking: Why? Organize students to discuss in groups, explain the reasons, and summarize the basic ideas and general steps of solving fractional equations. Next, do application exercises. The design of the whole class is compact and natural, which can arouse students' thinking and fully embody the concepts of "learning before teaching" and "learning as teaching"
2. In classroom teaching, students can be the main body to design questions, and when it is time to let go, let go and fully respect students. Whether it is the definition of score, the way of thinking to solve the score equation, or even the difficult problem of this course-the reason why the score equation has roots is that students complete it through independent learning or group communication and cooperation. Students are active in thinking and actively participate in the teaching activities of this class, and the class is full of vitality.
3. Pay attention to students with learning difficulties in classroom teaching and build a platform for them. When students are engaged in autonomous learning and exchange discussions, teachers can step down from the podium and walk into the middle of students, take the initiative to pay attention to students with learning difficulties, guide them to solve difficult problems or remind members of the same group to pay attention to the learning situation of students with learning difficulties. Moreover, in the process of applying new knowledge to solve problems, the No.5 students in each group are also invited to show them on the blackboard. When they encounter difficulties, other members of the same group are allowed to help, which creates opportunities for students with learning difficulties to show themselves and makes them feel the joy of success.
4. Pay attention to the improvement of students' abilities in all aspects and the timeliness of classroom teaching evaluation in classroom teaching. Before this class, the teacher wrote down the evaluation criteria on the blackboard, and guided the students to scientifically comment and evaluate the learning achievements of others according to the criteria in the teaching process. This not only fully mobilizes students' learning enthusiasm, but also guides students to evaluate others' learning from different levels, and also exercises the rigor and accuracy of students' language. While improving students' language expression ability, it also guides students to learn to listen, check, evaluate and even learn from each other.
Of course, "teaching is an art of regret", and even the most successful class has its flaws. This course
There are no exceptions. Because this course fully respects students in the process of communication, discussion, demonstration and feedback, it is difficult to grasp the time, which leads to some hasty application exercises and some students can't complete all the exercises on time. In addition, although the participation of students in this class is relatively high, there is still room for improvement.
In a word, the teaching effect of this class is good and the teaching goal has been achieved. It proves that my bold attempt in classroom teaching reform, especially the research on "learning-oriented, classroom standards" has made some progress. In the future, I will continue to work hard, actively explore and deeply study more scientific and effective teaching methods and means, so as to make the mathematics classroom wonderful.
Reflections on fractional teaching Part IV Fractional junior high school mathematics is an important chapter, which occupies a certain proportion in the senior high school entrance examination. Students have basically mastered the relevant knowledge of fractions (the concept of fractions, the basic properties of fractions, reduction, general fractions, the operation of fractions, the application problems of fractional equations, fractional equations that can be transformed into linear equations of one variable, etc.). ), and obtained the common methods of learning algebra knowledge, and felt the practical application value of algebra learning.
First, this chapter allows students to learn the arithmetic rules of fractions through observation, analogy, guessing and trying, and develop students' reasonable reasoning ability, so review should focus on the exploration process of rules. Students must be proactive. Through observation, analogy, guessing and trying, we should discover, understand and apply laws in a series of ideological activities. At the same time, we should pay attention to students' understanding of arithmetic and cultivate their algebraic expression ability, calculation ability and rational thinking ability. However, I didn't pay attention to the laws of exploration and analogy in the teaching of knowledge, but focused on the application of the four algorithms of fractions and the application of fractional equations, and didn't grasp the key links of teaching and choose the appropriate teaching methods. We should avoid similar things in the future.
Second, the reconstruction review
The operation of fractions (addition, subtraction, multiplication, division, multiplication and mixed operation) is one of the foundations of the deformation of algebraic identities, but we should not blindly increase the difficulty of calculation and problems, pay attention to the understanding of reasoning in the operation process and flexibly use the basic properties of fractions.
Moreover, we must pay attention to the specific questions about scores in textbooks, pay attention to the degree of students' investment in these specific activities, and see if they can actively participate. Secondly, we must look at the level of students' thinking development in these activities-can they think independently? Can you express your ideas in mathematical language? Can you reflect on your own thinking process? Then discover new problems and cultivate students' ability to solve problems! Improve students' interest in learning!
The fifth part of thinking about fraction teaching went to an experimental primary school for a class yesterday. The topic is the first lesson of fractional multiplication and division. First, Mr Qin introduced the rules of fractional multiplication and division by reviewing the operation of fractional multiplication and division. Then Mr. Qin asked the team leader to correct the group members' preview homework, and then the team leader reported the inspection and listed the mistakes in the calculation questions one by one. I looked at my watch. It's been 15 minutes. Then, taking the students' mistakes as an example, Mr Qin explained the multiplication and division operations of two questions whose numerator and denominator are monomials. At that time, I was thinking, the most important thing in a class is the first 20 minutes. Why haven't you explained the calculation of fractional multiplication and division with polynomial denominator? I think calculation is a weakness of students. Teachers should demonstrate solving problems first, and then learn to strengthen practice. Only when students do their own calculations will they find the shortcomings. The class lasted about 25 minutes, and Mr. Qin began to explain the fractional multiplication and division method in which the numerator and denominator are polynomials. Teacher Qin didn't explain it separately, but interacted with the students and wrote down the problem-solving process step by step, so that the students could tell the basis. Finally, Miss Qin invited four students to do exercises on the blackboard. Maybe the time allocation is not good, leaving an extra tail.
After that, we made a class evaluation. After listening to teacher Qin's brief introduction to the topic, I found that my class evaluation was in the wrong direction. Teacher Qin's topic is to study the mistakes that students will make in preview and discuss the types of wrong questions in preview. Finally, I think Mr. Qin's class is still excellent and worth learning.
Reflections on Fractional Teaching Part VI. Design Ideas;
As the first lesson of fractional equation, this course is conducted on the basis of students mastering the solution of linear equation and fractional elementary arithmetic. It not only deepens the content of the previous lesson, but also lays a good foundation for future teaching-"application", so it has an important position and role in teaching materials. The teaching focus of this section is to make students clearly realize that fractional equation is also one of the tools to solve practical problems, explore the concept of fractional equation, and clarify the difference and connection between fractional equation and integral equation.
Second, the teaching knowledge points:
In the teaching process of this course, I think we should start from the following aspects:
1, fully understand the meaning of the problem in the actual problem, find the equivalence relation, and list the equations according to the equivalence relation.
2. Difference between fractional equation and integral equation: To distinguish two conditions that a fractional equation must meet, there must be a fraction in the equation and an unknown number in the denominator. These two conditions are necessary and sufficient conditions for judging whether an equation is a fractional equation.
3. The connection between fractional equation and integral equation: Fractional equation can be converted into integral equation by multiplying both sides of the equation by the simplest common denominator, omitting the denominator, which should be fully reflected in the teaching of this reduction idea.
Third, overall reflection.
The first is how students can find the equivalence relation in the topic smoothly. It is difficult to give two examples in the book. According to the introduction of books, the classroom may give people a quiet thinking at the beginning, which is difficult to open and cannot effectively stimulate students' interest and passion in learning. Therefore, it is necessary to establish a ladder in the study plan to reduce the difficulty and let students experience the joy of success, so that students will be willing to continue to explore and learn. The difficulty of practical problems is set at different levels, and the problems are at different levels, which can make students at different levels have different experiences and feelings.
Secondly, in the teaching process, teachers should improve their ability to improvise and preset questions, so that students can be fully prepared before class. For example, we have learned the integral equation before, but we have only said the equation once before, and there is no systematic classification. This is an integral equation. If the word "integral equation" is not explained in detail in advance, cooperative inquiry II will not go smoothly.
Finally, we should let appropriate encouragement and evaluation run through the teaching process. Only in this way can students constantly enhance their self-confidence, explore new knowledge and solve problems in pleasure.
In short, there is no fixed method for teaching and no fixed method for learning. We should constantly enrich ourselves and improve ourselves on the road of educational reform.
Reflection on Fraction Teaching Part VII This section is the content after learning the basic properties of fractions, one of the basic operation contents of fractions, and the reflection on the teaching of addition and subtraction of fractions. Among them, the addition and subtraction of fractions is the focus of this lesson, and the addition and subtraction of fractions with different denominators is the difficulty of this lesson. Addition and subtraction of fractions with different denominators can be converted into addition and subtraction of fractions with the same denominator. Therefore, mastering the addition and subtraction of fractions with the same denominator is the key. I will think from the following aspects:
(1) succeeded
This lesson introduces practical problems, so that students can directly feel that they will encounter fractional addition and subtraction in real life, which requires mastering the method of fractional addition and subtraction, thus leading to the content of this section.
Because fractions and fractions have many similar properties, we start with intuitive addition and subtraction of fractions. Firstly, explore the law of addition and subtraction of fractions with the same denominator. By analogy, the operation law of the formula comes from the operation of numbers, which reflects the internal relationship between mathematical knowledge from concrete to abstract and from special to general, and conforms to the students' cognitive law. In the process of drawing a conclusion, discuss with students and pay attention to their participation. Students quickly integrate into the classroom, arouse their learning enthusiasm, and reflect on the teaching of addition and subtraction. Then, by analogy, we also arranged the addition and subtraction study of different denominator scores, which conforms to the development law of students' cognition and is helpful to the implementation and mastery of different levels of knowledge. Moreover, it pays attention to the connection between knowledge and embodies the thinking method of reduction in mathematics. The classroom atmosphere is active and students actively participate. Judging from the situation of classroom students doing problems,
(2) Disadvantages
This lesson has a beginning and a tail, and the echo before and after is not done well. The problem of how to calculate ""in the cited example has not been solved, which is one of the biggest regrets of this lesson. Classroom teaching is really a "flawed art". It is with such defects that we are more motivated to stride forward on the road of exploring tunnels.
A math class, after reflection, will find many places worthy of scrutiny, and many details need to be carefully designed. In reflection, we can enhance our understanding, accumulate valuable experience for future teaching, and make ourselves closer to students.
Reflection on Fraction Teaching In the first class of Chapter 8, the algebraic expressions listed in the cited examples are used for induction and comparison, and the concept of fraction is obtained. The most essential feature of the concept of fraction is that "the denominator contains letters", thus studying the conditions that the fraction is meaningful and meaningless, the value of the fraction is zero, and the value of the fraction is a positive integer or a negative integer, and solving various mathematical problems.
When solving the problems of zero fractional value, zero numerator and non-zero denominator, it is necessary to consider the choice of letter values. The method of reasoning with students on the blackboard is more effective than my original method. The student's method is: get x=2 and x=-2 from the numerator x2-4=0, and then substitute the letter values obtained into the denominator for calculation, so that the denominator is zero and the denominator is not zero, and make such a choice.
In the transformation solution, it is found that students are still unfamiliar with solving linear inequality problems. In order to improve students' learning effect in an all-round way, it is more effective to review under similar circumstances. The main body of learning is students, not showing off in class.
For -a2- 1, it must be negative, and teachers and students need to discuss and study together to ensure that all students understand and use it flexibly.
As for the topic: What is the value of integer X and the value of score 4/x- 1 is an integer, which is also a difficult point for students to understand and solve problems.
Because students don't have textbooks, our classroom learning plan should be designed to be more practical, and the expression of classroom knowledge content should be more convenient for students to understand and accept.
Reflections on Fraction Teaching 9 In this course, I mainly adopt the classroom teaching mode of "36 1" to let students deepen their knowledge on the basis of self-study. This learning mode meets the requirements of curriculum reform, but after teaching, it is found that it takes a long time for students to solve fractional equations in previous teaching, so it is difficult for students to complete teaching tasks in a limited time. But in this class, students can save class time by previewing before class.
In teaching, we should use analogy method and use fractions to teach, so that students can clearly understand the differences and relations between fractions and algebraic expressions, understand the model idea of fractions and further develop the sense of symbols, which will certainly get twice the result with half the effort. The basic idea of solving fractional equation is to transform fractional equation into integral equation. The solution can be transformed into a fractional equation of a linear equation with one variable, and it is also a solution based on the linear equation with one variable, but the fractional equation needs to be transformed into an integral equation, so we should pay attention to the connection and difference of old knowledge, pay attention to the idea of infiltration and transformation, and review the solution of the linear equation with one variable properly in teaching.
The solution can be transformed into a fractional equation of a linear equation with one variable, and it is also a solution based on the linear equation with one variable, but the fractional equation needs to be transformed into an integral equation, so we should pay attention to the connection and difference of old knowledge, pay attention to the idea of infiltration and transformation, and review the solution of the linear equation with one variable properly in teaching. As for the reason of adding roots when solving fractional equations, only students need to understand, and it is important for students to master the test method of roots.
To enable students to master the basic idea of solving fractional equation is to transform fractional equation into integral equation, and the specific method is "denominator", that is, both sides of the equation are collectively called the simplest common denominator.
In the teaching process, due to various reasons, there are many shortcomings.
1. Looking back, many topics were introduced. We should choose one or two simple and representative topics, step by step, in line with the laws of human cognition.
2. Not paying enough attention to teaching. I trust students' comprehension and digestion ability too much. The difficulty of fractional equation is the first step, which is to transform fractional equation into integral equation. It is especially necessary to strengthen this process here, and it needs special training or analysis. For example, analyze students' different practices and make them understand that this method of textbook is the simplest and most convenient.
3, the time is not very good. Students don't preview enough, which leads to too many emergencies and too hasty summary.
Reflections on fractional teaching 10 The following is my teaching experience:
First, the discovery of teaching
There are many operational errors in (1) score. Fraction addition and subtraction is mainly when the molecule is multiple. If the whole molecule is not enclosed in brackets, it is easy to cause errors in symbols and results. Therefore, when we teach the addition and subtraction of fractions, we should educate students that the parentheses cannot be omitted in the numerator part. Secondly, the conceptual operation of fractions should be calculated in the order of first power, then multiplication and division, and finally addition and subtraction. If there are brackets, the ones in brackets should be done first.
(2) Fractional equation is also the hardest hit area. First, the definition of increasing root is vague. In this regard, I explain the concept of adding roots in simple terms:
1. Increasing root is the root of the integral equation after removing the denominator of the fractional equation, but it is not the root of the original equation;
2. Finding the root can make the simplest common denominator equal to 0; Second, the steps of solving the fractional equation are not standardized, and most students lack the important steps of "examination" and cannot jump out of the mode of solving the integral equation;
(3) The fractional equation is full of mistakes.
In order to solve the above problems, I start with the basic knowledge and problems in class review, and draw inferences from others, with special emphasis on solving application problems with fractional equation, which is the same as column integral equation. First of all, I analyzed the meaning of the question, accurately found out the equivalent relationship of quantitative problems in the application question, set up the unknowns appropriately and listed the equations. The difference is that the listed equations are fractional equations. Finally, we should check whether it is the solution of the listed fractional equation and whether it meets the meaning of the question.
Second, reflection after teaching
Through the teaching of this class and the comments of several experts after class, the teaching purpose of this class is basically achieved, but the capacity of this class is large, and the teaching effect will be better if multimedia can be used. I will continue to work hard to improve my teaching level in the future.
Reflections on fractional teaching 1 1 The idea of solving fractional equations is to transform fractional equations into integral equations, and finding roots is an essential step in solving fractional equations. Fractional equation is one of the tools to solve practical problems.
Mathematical ideas and methods contained in teaching design: In the chapter of fractions, we should use fractions as analogy teaching, so that students can clearly understand the differences and connections between fractions and algebraic expressions, understand the model ideas of fractions, and further develop the sense of symbols, which will certainly get twice the result with half the effort. The basic idea of solving fractional equation is to transform fractional equation into integral equation. The solution can be transformed into a fractional equation of a linear equation with one variable, and it is also a solution based on the linear equation with one variable, but the fractional equation needs to be transformed into an integral equation, so we should pay attention to the connection and difference of old knowledge, pay attention to the idea of infiltration and transformation, and review the solution of the linear equation with one variable properly in teaching.
Teaching objectives:
1. Understand the concept of fractional equation and the reasons for the increase of roots.
2. Mastering the solution of the fractional equation, we can solve the fractional equation which can be transformed into a one-dimensional linear equation, and we will test whether a number is the root of the original equation.
Important and difficult
1. key point: I will solve the fractional equation that can be reduced to a linear equation with one variable, and I will test whether a number is the root of the original equation.
2. Difficulty: I will solve the fractional equation that can be transformed into a one-dimensional linear equation, and I will test whether a number is the root of the original equation.
3. Cognitive difficulties and breakthrough methods
The solution can be transformed into a fractional equation of a linear equation with one variable, and it is also a solution based on the linear equation with one variable, but the fractional equation needs to be transformed into an integral equation, so we should pay attention to the connection and difference of old knowledge, pay attention to the idea of infiltration and transformation, and review the solution of the linear equation with one variable properly in teaching. As for the reason of adding roots when solving fractional equations, only students need to understand, and it is important for students to master the test method of roots.
To enable students to master the basic idea of solving fractional equation is to transform fractional equation into integral equation, and the specific method is "denominator", that is, both sides of the equation are collectively called the simplest common denominator.
Reflections on fractional teaching 12 1. Introduce new teaching emphasis in review, review the equation knowledge learned in the past, and adopt the method of letting students say several linear equations and solve them themselves, so as to give full play to students' initiative and enliven the classroom atmosphere. A good start to this course.
2. Using a student's linear equation (x-1)/3+1= (2x-3)/6, take the opportunity to make it clear that the equation that can be transformed into ax=b(a is not equal to 0) is a linear equation. Naturally, students have made clever preparations for future study. It can also attract students' attention, make them feel interesting and listen to it step by step.
3. Through asking questions and activities, students can feel and experience themselves, ask questions, think and explore in the process of feeling and experience, and discover new knowledge through asking questions, thinking and exploring, which stimulates students' enthusiasm for participation, cultivates students' awareness of exploration, and enables students to learn independently in a happy atmosphere.
Through this lesson, I also realized that in the future teaching, we should do the following:
1, turn boring into interesting, and let students become the focus of the whole teaching.
Interest is the best teacher. Only by fully mobilizing students' learning enthusiasm can students really participate in learning and take the initiative to learn. Of course, this requires teachers to work harder, connect with reality and design more scenes, so that students feel that they are not in class, but playing a TV series, and he is the protagonist.
2. simplify the complex.
The simpler students want to learn, the more they can do, the more they want to do. Simplicity contains a great truth. Only by being simpler and more skilled can we do complex things. Of course, this requires various forms, not a single one.
3. Give students enough room to think, don't rush to give an answer, even if the students make a mistake, don't put it off, leave students room to think.
Reflection on Fraction Teaching 13 By reviewing the addition and subtraction of fractions with the same denominator but different denominators, we can learn the addition and subtraction of fractions by analogy, take the general fraction of fractions (with different denominators) as a preliminary knowledge test, and then we can learn the basic exercises and proficiency rules completed by students independently, and explain and discuss the problems (such as addition and subtraction of molecules, removal of brackets and simplification of fractions, etc.). ) appears after the calculation process. Finally, consolidate classroom exercises and summarize homework assignments.
At the end of the lecture, I found that students have a good grasp of the addition and subtraction of fractions with the same denominator, but they are not very good at the addition and subtraction of fractions with different denominators. Many students are not proficient in general fractions, and some students don't understand that the calculation result should be the simplest fraction and can never be reduced to the simplest form.
After the addition and subtraction of scores, list a mixed addition and subtraction operation problem, and review it in combination with the mixed addition and subtraction algorithm when explaining. The difference between the mixed operation of fractions is that if there is a denominator or numerator that can be factorized, it is necessary to factorize first, and then divide the fractions with different denominators into those with the same denominator for calculation, and division should be converted into multiplication. And the final result of calculation should be in the form of the simplest score. When calculating, we should first observe the characteristics of the score to analyze whether it can be calculated by the distribution law of multiplication, so as to simplify the complex.
Reflections on fraction teaching 14 first, we should use teaching materials creatively.
Textbooks only provide teachers with the most basic textbooks, and teachers can adjust them according to the actual situation of students. The fractional equation quoted in this textbook is complex, so it is difficult for students to explore its solution directly. I derive the fractional equation from the simple integral equation, and then guide the students to explore its solution. In this way, it is easy to find the breakthrough point of new knowledge: remove the denominator by using the properties of the equation, convert it into an integral equation and then solve it. Therefore, students learn better.
Second, trust students and provide them with opportunities to fully show themselves.
Students learned to explore the solution of fractional equation and the necessity of testing fractional equation once and for all.
Third, pay attention to improvement.
When talking about examples, it is better to talk about a problem of generating increasing roots first, which is convenient to explain why fractional equations sometimes have no solution, and also explains the necessity of testing fractional equations, which is the biggest difference between solving fractional equations and the whole equation, thus re-emphasizing that solving fractional equations must be tested and the step of not writing can not be omitted.