Reflection on the Significance of Fraction Teaching (1)? What is the meaning of the score? This part of the content is taught on the basis of students' learning "Preliminary Understanding of Fractions" in Grade Four. Before studying, I found that some students still can't walk out of the original frame when studying this part, just stay in? Divide an apple into two parts, each part is half of this apple. ? Under this understanding. Students only think that one is a unit? One? . I don't have a deep understanding of what a score is, but I have a superficial understanding. I was also confused about something that can be regarded as a unit for a while, which also made me confused about the teaching of this course. What should this class teach a child? What is the focus of this course and how to break through it?
With a series of puzzles, I carefully read the teaching reference again, and searched the classroom records and case design and analysis of this lesson through various channels. Finally clear? What is the meaning of the score? Is the teaching based on students' initial understanding of music score, and its teaching purpose is to let students know the unit correctly? 1? Understand the meaning of score and explain the meaning of score in specific situations. Students all know that when measuring, dividing things or calculating, integer results are often not obtained. This time is often expressed by scores, and the meaning of scores is an abstract concept for primary school students. How to make students understand the unit? 1? Meaning? Guiding students to gradually abstract the meaning of fractions from concrete examples is the key problem to be solved in this lesson. So I can firmly grasp the key points of this lesson and guide students to understand this unit from the following three aspects? 1? Understand the meaning of music score.
1, game import, breakthrough unit? 1? Understand.
In teaching, in order to help students break through the shackles of original cognition, we can regard multiple objects as a whole and recognize units. 1? . I started designing in teaching? Say nothing? Games. (Rules of the game:? Describe a given situation in an appropriate mathematical language, and only numbers are allowed when describing it. 1? , numbers other than 1 are not allowed. )
The specific operation links are as follows:
? Teacher: What's this? (Pointing) What is this? (5 fingers) wrong, the rules of the game can only be used? 1? To describe it, put it another way! 1 hand. This is? (a pair of hands)
Please 1 students stand up. (1 person, 1 student) (Please 1 student's deskmate stand up) What about this time? (1 students at the table, 1 students in the group)
There are 24 students in our class (1 class)
?
With help? Say nothing? This game not only enlivens the tense atmosphere in the classroom before class, but also makes students fully aware of it. Many times we can regard multiple objects as a whole, and this whole can also be used? 1? Show students' new understanding of natural number 1 At this time, let the students talk about it: What do you know about 1 through our little game today? Understand? 1 as we know it today is very special, so we should put quotation marks on it and call it: unit? 1。 Thus, to the unit? 1? Understand this teaching difficulty, so it is easy to break through.
2. Experience it yourself and know the score in the activity.
Mathematics curriculum standards regard practical activities as an important part of mathematics learning. Its requirements are: Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience? Teachers provide students with opportunities to fully participate in learning activities, and help students truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication? Get rich experience in mathematics activities. Therefore, in the teaching of this course, I designed it by combining students' practical experience and existing knowledge. Divide sugar? Activities.
The specific operation links are as follows:
Teacher: How to divide this 12 candy equally? Would you please use 12 in your hand to represent 12 candy?
Requirements for courseware display activities:
Create a score:
(1) Divide 12 pieces equally and swing.
(2) fill in the record sheet.
(3) the contents of the table talking to each other.
② Thinking Tips: (Learning Record Sheet)
I take () as a unit? 1? , put the unit? 1? The average score is () copies, of which 1 copy is the unit? 1? Yes, there are () pieces, and () pieces are units? 1? Yes, there is ().
In this mathematical activity, students can fully experience and understand the meaning of fractions by hands-on, and in the process of mutual communication and learning, they can independently summarize the meaning of fractions by combining their own personal experiences. It can be seen that through the design of this link, students feel the close connection between mathematics and real life in mathematics activities, and effectively improve their learning ability of independent inquiry.
3. Divide sugar and give back, and expand and extend in joy
The specific operation links are as follows:
Teacher: Today, the students did very well. The teacher decided to give this 12 piece of sugar to everyone? Please take the sugar according to the score given by the teacher, and take it away if you get it right.
Let a female classmate take out these sweets 1/4(3 pieces).
Teacher: The teacher is fair. This classmate took 3 yuan, and this male classmate can only take 3 yuan. How much leftover candy should he take? 1/3(3 pieces) 1/4 1/3. Why are they all three dollars?
(unit? 1? No, even if the scores are different, the specific figures may be the same)
(3) Ask a classmate to take 1/3 of the remaining sugar and ask: Did he get it right? Why did she only take the 1/3 with three dollars, but he took the 1/3 with two dollars?
(unit? 1? Different, even if the scores are the same, the numbers are not necessarily the same. )
Teacher: Teacher, there is still sugar here. There is still a lot of knowledge about grades waiting for us to discover and learn. I hope everyone can take the initiative to explore. Teacher, please take care of these sweets for me when you talk to me! ?
Mathematics teaching should not just stay in a class, but should be a process of stimulating and inducing students' enthusiasm for learning and desire for knowledge. So at the end of this class, I once again mobilized students' enthusiasm and infiltrated scores through this sugar sharing session? Whole and part? The understanding of the relationship between them has stimulated students' enthusiasm for exploring their academic achievements independently.
These are some of my own feelings about this class, but I can't ignore them at the same time. I still have many shortcomings, which should be improved in this class. For example, when students report, the teacher is too hasty to guide students to solve their own problems. When the students say that the meaning of the score is inaccurate and incomplete, the teacher is impatient. When the first student reports, he does not correct his language expression, which leads to many students' inaccurate language expression. In daily teaching, teachers say half a word when expressing questions, and the requirements for students to answer questions in complete language are not strict, all of which need to be improved in future teaching.
Pay attention to starting from students' existing knowledge and experience, grasp the growing point of new knowledge, and deepen the understanding of scores. At the beginning of the class, let the students express the meaning of 1/4 with the materials in their hands (group cooperation: divide a little, circle, paint and draw a picture). Through hands-on operation, thinking, observation and comparison, let the students understand that an object and some objects are averaged as a whole, and one or several of them are expressed by scores, thus revealing the meaning of scores and completing the evaluation of units? 1? Understand.
Pay attention to let students consolidate and deepen their understanding of the meaning of fractions in application. This lesson not only provides students with rich learning materials, but also summarizes the significance of scores through observation, comparison, analysis and discussion. Also pay attention to let students experience the process of applying scores in life, such as taking the class size as the overall average score, where each student accounts for a few points in the class and two people account for a few points. Contact the common scenes of dividing things in life, let the students talk about what scores are used to represent the results, and explain the meaning of the scores. In this way, students not only deepen their understanding of the meaning of fractions, but also raise their understanding of fractions to a new level, and at the same time lay a foundation for learning related knowledge of fractions in the future.
Reflections on the Teaching of Fractional Meaning
After reading teacher Liu Quanxiang's article, I was sweating like a pig. After the lesson "The Meaning of Fractions", I didn't sort it out carefully. Or is it Mr. Liu's incisive analysis and promotion? Interpretation? I have benefited a lot. Now, I summon up the courage to talk about some of my ideas in this class.
The meaning of score is a typical concept class, which has been concerned by experts and teachers. By reading various magazines and clicking on the website of primary school mathematics teaching, the case design and analysis of this course have their own characteristics. In particular, I read Mr. Zhang Dianzhou's "Primary School Teaching", the first issue of 20 10 on "? Scores? Some mathematical problems that need to be clarified in teaching have some feelings and some ideas.
First of all, how to define a score?
First of all, we have to ask, how to define the score? Generally, there are four types:
Definition 1 (definition of number of copies): the score is one or more copies after the average score of a unit.
Definition 2 (definition of quotient): A fraction is the quotient of the division of two numbers.
Definition 3 (ratio definition): the score is the ratio of q to p.
Definition 4 (axiomatic definition): ordered integer pair: (p, q), where p? 0.
The definition in our existing textbooks is: put the unit? 1? Divide into several parts on average, and the number indicating this part or parts is called a score. The advantage of this definition is that it is intuitive, easy to understand and emphasized? Average score? , especially right? What score? It is also of great value to understand fractional operation in the future.
However, there are some problems in defining the score by the number of copies. First of all, one or more statements are still very close to natural numbers, which does not mean that this is a new number. Secondly, it is often misunderstood that the average share of a moon cake is less than 1 (smaller than a moon cake). Finally, due to the fixed thinking of moon cakes or other direct pictures, it is impossible to choose the unit properly, forming a rigid thinking.
The real source of fraction lies in the popularization of division of natural numbers. A moon cake is divided into three parts on average to get a piece of a certain size. For this objective quantity, it should be regarded as 1 according to the meaning of division. 3 the quotient obtained. But this division with big divisor and small dividend will become an unsolvable problem if you use previous knowledge, then? Scores? This new friend will debut. In this way, the essence of number system expansion is highlighted. Therefore, the definition of score number can be used as the starting point of teaching, but it should not be overemphasized and should be quickly transferred to a more abstract definition of score.
At the beginning of preparing lessons, I tried to get rid of it? How many copies? Definition, trying to close to the meaning of division and ratio, but it seems to be in the process of marching? Forgot what was the purpose of the original departure? (Wei Bin's evaluation) Because of the relationship between scores and division and comparative value's understanding, special study was arranged for grades 5 and 6. So, I moderately returned to the teaching purpose, returned to? How many copies? The definition of "1" only emphasizes that students communicate the connection and difference between fractions and integers with the help of intuitive operation and line model, and deepen their understanding of the unit "1", so as to understand the meaning of fractions.
Secondly, how to interpret the definition of score?
What is the essence of fractions? In the book Mathematics and Mathematics Education by Professor Shi Ningzhong, a mathematics educator, there is a section devoted to the discussion? How to understand the meaning of fractions? Fraction, representing a part of a thing, is essentially dimensionless. The significance of fractional dimensionless is that many incomparable states of things can be changed into comparable states.
In the transition to the essential meaning of fractions, Mr. Zhang Dianzhou pointed out: Is fractions relative to the whole? 1? As far as ... Mark, etc. Counting the number of rays from 0 to 1 is a key step to know the score, and it is very important to do it as soon as possible. ? This is because the number line is a semi-abstract model. What is this? Circular model? Are there any other airplane models? More abstract? Can be used as a soundtrack? Do you like the copy number model? The quotient of division? Over-defined geometric carrier. Use the length of the line segment to indicate the size of the score. Whether it's one or some, it's all units. 1? . This expression has many advantages. First of all, its units are abstract? 1? . Although it is more abstract than disks, triangles, rectangles and other geometric figures, it still has geometric intuition and can help students perceive the meaning of fractions. Secondly, this is the prototype of the number axis, which students have been exposed to since they studied natural numbers, thus communicating the relationship between scores and natural numbers well.
In this lesson, I will start with a moon cake (natural number 1), and then start with a group of moon cakes (unit? 1? ) to highlight the relativity of the meaning of fractions. Then abstract it to the number line as the starting point, and the dimensionless meaning of the fraction is just a new number.
Finally, what is the effect?
As for the final teaching effect, it is up to the students to test it. Judging from the students' reaction after this class, perhaps it is because the students in the textbook of Jiangsu Education Edition have arranged two courses in front, and some objects have actually appeared as a whole, so they participate in the grading. How many copies? There should be no problem understanding the meaning. However, the advantages of using the number line to express the score (such as the nature of the score, the comparison of the size of the score, the abstraction of the score, and the infinity of the score between 0 and 1) have not been well understood by the students, especially in the last link, after showing the scores of the whole class on the number line, the teacher did not guide them well, which is deeply regrettable.
Reflections on the Teaching of Fractional Meaning
Today, I finished the teaching of "The Meaning of Fractions", which was originally used as an evaluation class. Because the research on the subject is for your reference, in just four days, everything from preparing lessons to making courseware and learning tools must be in place. Because I still have a lot of confusion in my heart, I always hesitate when preparing lessons and making courseware. Some places don't know how to deal with it. Although everyone gave a lot of opinions when editing, the opinions were not unified. Only after class can everyone give solutions according to actual problems.
Let's talk about the main confusion before class:
1, how to connect knowledge? There are many knowledge points in this lesson, including: the generation of score, the meaning of score, and the unit? 1? , musical score units, musical score development history, some of these knowledge are interrelated, some are interrelated, how to transition?
2. Is it necessary for students to operate by hand? Students have learned the initial understanding of scores in grade three and gained some experience. From the picture, we can also see the result after the average score, so should we do it?
3. How to import smoothly? From a difficult unit? 1? Start with the necessity of introducing this concept, or?
4. Do you want to deduce the concept word by word? What are the key words in the meaning of the score? An object? 、? Some objects? 、? A whole one? 、? Average score? 、? How many copies? 、? A share? 、? How many?
5. How to guide students to read textbooks? Students should also understand the concept of norms in textbooks. Reading is necessary. How to guide them?
6. What kind of materials are provided to students? Is it only for some objects, or all the materials for one object and some objects are for students?
7. To what extent have you expanded your knowledge? Students' understanding of the concept needs to go from initial understanding to in-depth understanding, so it also needs to be expanded to a certain extent. How to grasp this degree?
Mathematics is not only an interesting activity, just making mathematics interesting does not guarantee that mathematics learning will be successful, because the success of mathematics requires hard work.
Self-reflection after trial teaching;
1, about the use of media. In teaching, there are some students' operations, some courseware demonstrations and teachers' blackboard writing. It feels messy. How to deal with the timing of courseware playing?
2. How to become more organized. I am not proficient in this lesson, which leads to some circuitous words or playing courseware, giving people a sense of confusion.
3. How to make students talk, talk and want to talk? Concept teaching itself is rather boring. If students can obtain concepts through their own operations, observation, comparison and other activities, and can summarize concepts, how can they improve their interest in learning?
4. Stress strategy.
Problems that have arisen:
In the whole teaching, there is no standard definition of the meaning of fractions, and there is no perfect reading. Originally, I wanted to let students know whether there are more or less objects through operation, as long as they are divided into four parts on average, one of which can be represented by a quarter, and then the concept of the whole can be extended to a large number. But for the thinking after the operation, the guidance is not effective, which leads to the students' inability to say? Core? .
Comparison of seeking common ground while reserving differences:
Mainly two levels of comparison:
(1) is different. Why can everything be represented by a quarter?
(2) The number of objects divided into one object and multiple objects is obviously different. Why can everyone be represented by a quarter?
The contrast between the two layers highlights the essence of the quarter score: it has nothing to do with what is scored, and it has nothing to do with the number of things scored. Just divide these objects into four parts, one of which is a quarter of the total number of objects.
Difference comparison:
Because there is only one quarter example in the textbook before revealing the meaning of the score, I want the students to finish it first? Do it. Ask the students to think about how these scores were obtained. So what are the reasons for the different scores? The average number of copies is different, and the number of copies represented is also different.
In this comparison, make students realize that the number of representations varies from unit to unit? 1? Not the same; The reason why the scores are different is because the average number of copies is different-from the difference, these aspects of the score are more biased, and the denominator of the score indicates the unit. 1? How many are the average scores? Molecules indicate that there are so many.
It is precisely because of the method of seeking common ground while reserving differences and positive comparison that the concept of * * * is highlighted; Using the method of reserving differences, the essential attributes of concepts are emphasized from the opposite side. I think it is effective to grasp the essence of concepts and teach them.
5. Handle the teaching of independent students and teachers. I feel that teachers talk more in class and students talk less. There are some places where students need to talk more. If students don't talk, teachers will arrange them themselves.
Only after getting help and suggestions from peers as soon as possible can we make better improvement.
Teaching Reflection on the Meaning of Fractions (II) For the course The Meaning of Fractions I teach, I mainly reflect on it from three aspects: self-evaluation, question reflection and classroom reconstruction.
I. Self-evaluation:
1, reflect on the completion of teaching tasks
In this class, students fully participate in active inquiry activities such as examples, hands-on operation and self-creation, so that students can understand the unit. 1? And knowing the meaning of the score unit, the whole class's teaching focuses are prominent, and the difficulties are also well broken through, and the teaching tasks are successfully completed and the teaching objectives are basically achieved. During the whole class, students' ability of abstraction, generalization and practice has been well developed, and the actual teaching effect has basically reached the idea when preparing lessons. The actual teaching basically follows the original plan. It's just that when I introduce the generation of scores to students, when the related videos can't be played normally due to equipment reasons, I temporarily adjust them so that students can understand the generation of scores by reading 62 pages of small materials in the textbook. Knowledge transfer is effective.
2. Reflect on teaching methods.
The success of the teaching method lies in my comprehensive use of heuristic teaching, situational teaching and activity teaching, so that students can experience the process of obtaining scores and feel the significance of scores by giving examples, scoring and creating their own scores. Thereby promoting students' internalization and construction of new knowledge.
The existing problem is that I don't grasp enough reasonable space and time for students to practice, think and communicate in teaching.
3. Reflect on the guidance of learning methods.
In this class, my guidance on students' thinking training methods is in place, and students' mathematical transfer ability has been improved to a certain extent, but the guidance on students' cooperative learning is not enough, and the awareness and efficiency of students' group cooperative inquiry need to be improved.
Second, reflect on the problem.
1, reflecting on the shortcomings in teaching
The shortcomings in the teaching of this course are as follows:
(1), the schedule is too uniform and loose, so that there is a phenomenon that the front is loose and then the hall is delayed;
(2) Students have mastered some knowledge points, which can be expressed in language, but teachers are still worried about discussion and take up more time;
(3) It is not enough for the teacher to let go. When students make a report and the language expression is not very appropriate, the teacher is too hasty and adds more;
(4) insufficient guidance for students' group cooperative learning;
(5) There is no language to inspire teachers in the classroom, and the classroom atmosphere is not really mobilized; (6) The courseware is not fully debugged, and the multimedia resources are not fully utilized when the import score is generated.
Teaching advantages.
2. Reflect on the unexpected events in the classroom and their handling.
After teaching the meaning of fractional units, I found that students' attention and interest in learning decreased. I took the method of answering questions with scores as the unit in time to stimulate students' interest and enthusiasm in learning and make students' attention return to classroom teaching activities.
Third, classroom reconstruction.
1, my harvest and feeling
In this teaching practice, I not only gained a lot, but also realized some truth. Know the unit? 1? At first, students can regard some objects as a whole, and use the natural number 1 to represent a whole, which is the cognitive unit? 1? Break through the difficulties of this course and lay a good foundation. For fifth-grade students, mathematical concepts are still abstract. When they form mathematical concepts, they generally need to have corresponding perceptual experience as the basis, and gradually establish the general representation of things from many related materials through their own operation and thinking activities, thus separating the main essential characteristics of things.
2. Improvement strategies for shortcomings.
For the improvement strategies and ideas of the shortcomings of this lesson, I think we should improve and think from the following points:
(1), teachers should trust students, let go when it is time to let go, don't spend too much time and energy to emphasize what students have mastered, and put precious teaching time on the focus of teaching;
(2) Try to talk more and practice more in math class;
(3) Teachers should enrich their own motivation language, affirm students' good performance through various forms, encourage students, mobilize their learning enthusiasm, and create a relaxed and happy learning atmosphere.
3. Suggestions for improving some teaching links.
After hands-on operation, self-creation and other activities, this link can also be designed as follows: only give one score, for example, let students exchange its meaning with examples, then give students two scores, let students exchange their meaning again, and let students summarize the meaning of the score and understand it? How many shares? And then what? A number indicating such a number or numbers? These keywords.
The link of knowing the score unit can also be designed in this way, so that students can read the teaching materials first and then exchange their self-study results, and consolidate the effect of students' self-study in time through appropriate exercises, thus gradually cultivating students' self-study ability and confidence.