Reflections on parallelogram teaching +0

The arrangement of geometry knowledge in primary school mathematics is in the order from easy to difficult. This textbook undertakes the task of making students learn to calculate the area of parallelogram, triangle and trapezoid. The calculation of parallelogram area is taught on the basis that students have mastered and can flexibly use the rectangular area calculation formula and understand the characteristics of parallelogram. This lesson mainly allows students to derive the parallelogram area formula by transformation, transform the parallelogram into a rectangle, and analyze the relationship between the rectangle area and the parallelogram area, and then derive the parallelogram area calculation formula from the rectangle area calculation formula, and then verify it with examples, so that students can understand the derivation process of the parallelogram area calculation formula and master the formula on the basis of understanding. At the same time, it is also helpful for students to understand the derivation method and prepare for the derivation of triangular and trapezoidal area formulas.

The focus of this lesson is to understand the equal product transformation of parallelogram and rectangle. Through "cutting, moving and spelling", the relationship between the base and height of parallelogram and the length and width of rectangle, as well as the characteristic that the area is always equal, is found, and the conclusion that the equal product of parallelogram is transformed into rectangle is drawn.

Psychologist Piaget pointed out: "Activity is the basis of cognition, and wisdom begins with action". The process of hands-on operation is the process of students exploring and learning step by step. Therefore, I mainly adopt the learning methods of hands-on, independent exploration and cooperative communication, and stimulate students' interest in learning and arouse their enthusiasm for learning through courseware demonstration and practical operation. Through students' hands-on operation, observation and experiment, the conclusion is drawn, which embodies the teaching principle of taking students as the main body and teachers as the leading factor.

I asked the students to do the operation and try to turn the parallelogram into a rectangle. Report after the operation and exchange your own verification process. When reporting, there are many ways to cut and paste. At this time, I threw a question to the students in time: "Why do you want to cut along the height?" Stimulate students to think positively. Then I guide the students to observe and compare these two figures, and then discuss: What changes have taken place between the spelled rectangle and the original parallelogram, and what has not? What is the relationship between the length and width of the rectangle and the base and height of the original parallelogram? Through the thinking of the above questions, students have a deeper understanding of the derivation of parallelogram formula. At this time, I guide students to draw the derivation process: a parallelogram is converted into a rectangle after cutting and splicing, the length of the spliced rectangle is equivalent to the bottom of the original parallelogram, the width of the spliced rectangle is equivalent to the height of the original parallelogram, and the area of the parallelogram is equal to the area of the rectangle. Because the area of a rectangle is equal to length × width, the area of a parallelogram is equal to base ×. Then I asked my classmates at the same table to communicate with each other about the whole operation process, so that they could really understand the process of parallelogram changing into rectangle.

Students should be organized in time to consolidate and apply new knowledge in order to understand and internalize it. Based on the principle of "emphasizing the foundation, testing ability and expanding thinking", I designed four levels of exercises:

First floor: Basic exercise: Book p82, Question 1.

It is helpful for students to deepen their understanding of graphics and correctly distinguish the relationship between the base and height of parallelogram.

Layer 2: Comprehensive exercises:

1, can you find a way to find out the areas of the following two parallelograms? What must I do first to ask for the area of these two parallelograms?

Let the students make their own heights, measure the base and height of the parallelogram, and then calculate the area. This process also embodies the concept of "emphasizing practice".

2. Can you find the area of this parallelogram?

Students are confused by different heights. In the calculation, students should clearly find out the corresponding height when calculating the parallelogram area, so as to accurately calculate the parallelogram area. And according to the obtained area and another height, find the bottom corresponding to this height.

Layer 3: Extended Exercise:

1. Are the areas of the following two parallelograms equal? Why? Can you still draw a parallelogram with the same area as these two? How many can you draw? (The picture is in the courseware)

Students comprehensively use knowledge and make logical reasoning, and understand that the area of parallelogram is only related to the base and height, and the area of parallelogram with equal base and height is equal.

The whole exercise design part covers all the knowledge points of this lesson, although the amount of questions is not large. The diversity of problem presentation methods has attracted students' attention, filled them with confidence in facing challenges, stimulated students' interest, triggered thinking and developed thinking. At the same time, the arrangement of exercises follows the principle of easy first and then difficult, and goes deep at different levels, which also effectively cultivates students' innovative consciousness and problem-solving ability.

Teaching is an art with eternal regret. Although I tried my best to teach this class well, there are many problems in teaching. The following is what I need to improve in the future:

Mathematics class should not only teach students knowledge, but also bring children mathematical thinking methods when reviewing mathematics. There are two important points in this course. First, the translation of mathematical thinking. This class is not reflected. Second, the most important way of thinking in this course, "transformation" is not prominent enough, which means that students have not really realized the importance of this kind of thinking.

The previous link is too time-consuming. In the future, we must find ways to optimize them, not only this class, but also all classes. Every link in the classroom should be set around the core goal, and everything that is not important to the core goal should be abandoned to ensure that the core goal can be solved in the prime time in the classroom.

Through teaching, it is found that practice setting should be carried out according to students' learning situation and knowledge mastery, and should not be overstepped. This course should focus on the consolidation of basic exercises.

Reflection on parallelogram teaching (Ⅱ)

20xx 10 year124 October participated in the Basic Mathematics Competition of Economic Development Zone and taught the course "parallelogram area". After the implementation of teaching, some problems made me think. Let me talk about my lesson preparation and teaching experience.

First of all, I have explained the analysis of the content in the teaching design, so I won't go into details. Regarding the academic situation, I took the fifth-grade students in our school as a reference, and investigated the students' thoughts on this knowledge. According to the answers to the students' questionnaires, I found such a question:

1, the area formula of the rectangle can be written correctly, but it is confused with the calculated perimeter, and I don't remember that the area of the rectangle is derived from several squares.

2. There are several ways to find the area of parallelogram.

(1) calculated by perimeter, accounting for15%;

(2) 35% calculated by adjacent edge multiplication;

(3) 23% people know that it is transformed into a rectangle, but they can't calculate it correctly;

(4) Others (including not counting), accounting for 27%.

Although I know the importance of reading textbooks and students, my understanding is limited. In the process of design and teaching, the following three problems are reflected.

First, the ability to analyze the learning situation is insufficient.

Although I made an analysis of my study, I didn't realize that students didn't actually understand the equivalent relationship between the original parallelogram and the transformed rectangle because of my limited understanding ability. This is a difficult point, which led me to focus on how to infiltrate and transform my thoughts to students.

Second, the classroom control ability is limited.

In the implementation of teaching, the students in the teaching class basically know that the area of parallelogram is equal to the bottom multiplied by the height, but my field control ability is limited, which can't keep up with the students' thinking, resulting in the phenomenon of being acclimatized to my original design intention. But then I carefully recalled the performance of some students in the teaching process. Just because the top students know the formula does not mean that all students know it. I should have some control ability to let all students go through the verification process, but it also means that I missed it.

Another problem is that, due to time constraints, I took the place of students' observation, led students to directly demonstrate the relationship between the original parallelogram and the transformed rectangle, and deduced the formula, which is quite regrettable.

Third, mathematical language is not rigorous.

In this teaching, my mathematics language is not rigorous enough, such as the technical term "translation" in mathematics is not standardized enough.

In view of the above problems, I think the teacher's ability to control these things is not a day's work. In the future classroom teaching, I will try my best to record my own problems and language, constantly reflect, and gradually improve and enhance my on-site class experience.

What I didn't realize about the design of "parallelogram area" is that the process of finding equivalence relation is a difficult point for students, and my ideas to break through this difficulty are as follows.

Default teaching clip:

Teacher: Students, turn our rectangle into a parallelogram. Can you mark the base and the corresponding height of the parallelogram? Please start bidding.

Teacher: Students, can you find out the equivalence between the original parallelogram and the transformed rectangle by transforming it into a rectangle? Discuss in groups and talk about your findings with each other.

Of course, this is my initial idea. Actually, I haven't taught it yet, so I don't know if these can break through the difficulties.

Through this lecture, what makes me really happy is to keep thinking about the class and discover the mystery of the class, with regret, confusion and thinking ... I think these are all growth, teaching time is so long, I want to know the teaching materials and students, and this difficult thing will always be sorted out slowly, and then I will continue to grow!

Reflection on parallelogram teaching (III)

? The teaching goal of parallelogram area is that managers can deduce the calculation formula of parallelogram area through operation activities, and can use the parallelogram area formula to calculate the area of related graphics and solve some practical problems.

The textbook is to show a parallelogram open space directly and calculate the area. The purpose of this arrangement is to let students deal with a new problem and think about how to solve it. This arrangement of teaching materials provides good materials for students to think independently, but it has higher requirements for students. In view of the situation of students in this class, some middle and junior students may not be able to participate in it, so I designed the teaching flexibly according to the actual situation of this class. I designed it like this:

1, first show two irregular figures, let the students say the area. These two irregular graphics students have learned in the last class. You can calculate the area by calculating the grid, or you can convert it into regular graphics to calculate it. Many students in the class use method of substitution to solve the problem, which lays the foundation for the new lesson.

2. After converting the irregular figures in the previous link into squares and rectangles, review the area formulas of squares and rectangles there.

3. Who has the larger area, a parallelogram or a rectangle with equal base and equal height? Show it graphically. Students discuss and come to the conclusion that the parallelogram can be transformed into a rectangle, so that the area can be calculated by the bottom x height.

4. Complement other transformation strategies, and make it clear that parallelogram area = bottom x height.

5. Practice consolidation.

Show irregular figures first, let students think of transforming into familiar regular figures to calculate the area, which is the transformation idea that needs to be mastered in class. With the preparation before class, the following exploration activities are logical, and the truth is clear to students, including middle and junior students, which changes the way of directly presenting formulas in the past and allows students to set formulas for scientific calculation.

Reflections on parallelogram teaching (IV)

First, with the help of games, transform students' perception.

Reduction is a very important learning method and idea in mathematics learning, and it also plays a very important role in the learning of triangle and trapezoid areas. Before class, use passwords first, and then use numbers instead of passwords, so that students can change their perception and knowledge in the game. It not only prepares for learning new knowledge, but also mobilizes students' enthusiasm, and students are willing to participate.

Second, contact students' life and create a situation

Combined with the students' original cognitive level, the situation is created by guessing the clean areas of Class 2 and Class 4 in five years, and the life problem is turned into a mathematical problem. By guessing, stimulate students' interest in learning and let them feel that knowledge comes from life.

3. Derive the parallelogram area formula by transformation.

On the basis of students' understanding of transformation, the author puts forward "Can a parallelogram be transformed into a graph we have learned?" At the same time, let the students discuss with each other, and through cutting and spelling, turn them into figures that can calculate their own area. Through practical operation, students transform parallelogram into rectangle in different ways, and through the internal relationship between parallelogram and rectangle, the calculation formula of its area is deduced.

To be strengthened:

First, I think the whole teaching process has not been "relaxed". As a guide for students, the role of teachers is not good. The derivation process of the formula allows students to discover it slowly and guide it appropriately. I'm afraid I can't finish my education.

Learning task, draw a formula according to the characteristics of students comparing two graphs. In fact, when preparing lessons, I still intend to let students talk more and get formulas through discovery and comparison. Dare not let go, students' subjectivity has not been fully exerted.

Secondly, students should standardize their own operation process when demonstrating the process of splicing and cutting. For example, students say that cutting along the height, first take students to do the height of the parallelogram, so that students can make it clear that the parallelogram has countless heights, then cutting along any height of the parallelogram can get a rectangle. Because it is a competition lecture, I am afraid of making mistakes, so the course basically follows the preparatory class. This is because my adaptability is poor, so I need to study more textbooks, prepare students when preparing lessons, and have a correct estimate of all possible situations in class.

Reflections on parallelogram teaching (5)

In teaching design, I create a situation, turn a rectangle into a parallelogram, guess whether the area changes, and stimulate students' desire to explore. Students will naturally think of counting squares to find the area according to the knowledge they have learned before, but I didn't expect students to have some difficulty in counting the base and height of parallelogram. At this time, I gave appropriate guidance, which reflected the leading role of teachers.

The new curriculum standard points out that "effective mathematics activities can not only rely on imitation and memory, but teachers should guide students to truly understand and master basic mathematics knowledge, skills, ideas and methods through hands-on practice, independent exploration and cooperative communication." The teaching focus of this course is "the exploration of parallelogram area formula", and the difficulty is "the understanding of the derivation process of equilateral quadrilateral area calculation formula". In order to highlight key points and break through difficulties, I first guide students to explore independently, and then let them communicate. For the relationship between parallelogram and rectangle that students can't understand, I use courseware to demonstrate and let students exchange comments on the basis of observation. Finally, the students are divided into groups to cut and paste, and talk about the derivation process of parallelogram area formula. In this way, students can experience the operation process personally, understand and master the solution of parallelogram area in communication demonstration, and exercise their language expression ability in language description. In this link, I pay attention to let students practice and explore the law independently, let students experience the formation process of knowledge and further develop the concept of space. This not only makes students learn knowledge, but more importantly, it permeates the mathematical thinking method of translation and transformation, and cultivates students' ability of observation, analysis and generalization.

I think the shortcomings of this lesson are:

(1) When students convert a parallelogram into a rectangle, they are not given enough time to show different cutting and mending methods, which limits their thinking. Students should be fully shown that different cutting and repairing methods have the same results. Three cutting methods.

(2) When the students report, when the students' language is verbose, I am a little too hasty. I often interrupt the students' words, let them express in their own language, or let them modify their own language.

(3) Not doing enough to consolidate and apply knowledge. This plan is to let students explore what has changed and what has not changed after drawing a rectangular box into a parallelogram after basic exercises, thus expanding students' ability. However, when calculating the grid area, teachers' adaptability is not strong, which delays the time, so they have not done the problem before, and teachers' own ability needs more exercise.