How to write the lecture note of the image of a linear function of one variable in junior middle school mathematics? Below I collected a model essay for your reference! I hope you like it!

Draft of "Image of a Linear Function" in Junior Middle School Mathematics Lecture

According to the concept of the new curriculum standard, I will explain this lesson from six aspects: teaching material analysis, academic situation analysis, teaching objective analysis, teaching method analysis, teaching process analysis and teaching evaluation.

I. teaching material analysis

1. The position and function of teaching materials

This textbook is the content of the second lesson of the third section of the eighth grade mathematics chapter 18 in junior high school. Function is one of the important basic concepts in mathematics, and it is also one of the important contents of junior high school mathematics. It reveals the nature of interdependence and change between quantitative relations in the real world, and is an important model to describe and study the changing law of the real world. 18 is not only an introduction to student functions, but also the basis for further study.

As the content of this section, on the one hand, on the basis of studying variables, functions and images of functions, the meaning of functions is further deepened and expanded; On the other hand, it lays a foundation for learning the properties of linear functions and is a tool for further studying the quantitative relationship in the real world. In view of this understanding, I think this lesson not only has a wide range of practical applications, but also has the role of connecting the past with the future.

2. Emphasis and difficulty in teaching

According to the above position and function of the textbook, and the analysis of the learning situation, combined with the requirements of the new curriculum standard for this lesson, I will determine the focus of this lesson as follows: (1) Understand the concepts and images of linear function and proportional function; The difficulty lies in determining the relationship between the values of k and b and the position of the linear function image.

2. Analysis of learning situation

From the psychological characteristics, junior high school students' logical thinking gradually develops from empirical to theoretical, and their observation ability, memory ability and imagination ability also develop rapidly. But at the same time, students at this stage are active and easily distracted, and love to express their opinions, hoping to get the attention or praise of teachers. Therefore, we should grasp these characteristics in teaching, on the one hand, arouse students' interest with intuitive and vivid images, so that their attention is always focused on the classroom; On the other hand, we should create conditions and opportunities for students to express their opinions and give full play to their initiative in learning.

From the cognitive situation, students have learned variables, functions and images of functions before, and have a preliminary understanding of the meaning of functions, which lays the foundation for successfully completing the teaching tasks of this course. However, due to the high abstraction of function images, students may have some difficulties in understanding, so we should pay attention to cultivating students' idea of combining numbers with shapes in teaching.

Three. Analysis of teaching objectives

The new curriculum standard points out that teaching objectives should include knowledge and skill objectives, process and method objectives, emotion, attitude and values objectives, which should be closely related and become an organic whole. The process of students learning knowledge and skills is also the process of students learning to learn and forming correct values, which tells us that knowledge and skills should be the main line in teaching, and emotional attitudes and values should be infiltrated, both of which should be fully reflected in the process and methods.

1. Knowledge and skills

Understand that the image of linear function and proportional function is a straight line, skillfully make the image of linear function and proportional function, and master the influence of the values of k and b on the position of the straight line.

2. Process and method

Go through the drawing process of linear function and explore the similarities and differences of some linear function images;

3. Emotional attitudes and values

Experience the common methods of learning functions and studying mathematical problems by analogy: from special to general, from simple to complex.

Four. Analysis of teaching methods

Modern teaching theory holds that in the teaching process, students are the main body of learning, teachers are the organizers and guides of learning, and all teaching activities must be centered on students' initiative and enthusiasm. According to this teaching concept, combined with the characteristics of this class and the age of students, I adopt heuristic, discussion and teaching and practice teaching methods in this class, paying attention to the question raising and problem solving, and always taking the knowledge of students as the center. The nearest development zone? Set questions, encourage students to actively participate in teaching practice, discover, analyze and solve problems with teachers' knowledge in the form of independent thinking and mutual communication, and give students enough thinking time and space to associate and explore when guiding analysis, so as to complete the real knowledge self-construction.

An analysis of the teaching process of verbs (abbreviation of verb)

The new curriculum standard points out that the process of mathematics teaching is the process of teachers guiding students to carry out learning activities, the process of interaction between teachers and students and the process of common development between teachers and students. In order to teach in an orderly and effective way, I mainly arranged the following teaching links in this class:

(A) create a situation

Earlier, we learned to draw the image of the function by tracing points. Now, please follow the drawing steps and draw the images of the following functions in the same plane rectangular coordinate system: list, tracing points and connecting lines.

( 1)y =- 1/2x； (2)y =- 1/2x+2； (3)y = 3x； y=3x+2 .

Teaching instructions:

In the first step, the function (1) should be explained in detail in combination with the method of the previous function image. Pay special attention to the error-prone points of students' drawing, such as the values in the list, the positive direction and unit length of the plane rectangular coordinate system, and the correctness of the drawing points.

Step 2: Students independently complete the image of the function (2).

Step 3, students observe and discuss with each other, and answer: What shape is the image you draw?

The linear function y=kx+b(k? 0) is a straight line, usually called straight line y=kx+b(k? 0). And because two points can determine a straight line, when drawing a function diagram in the future, just take two points and draw a straight line after two points.

Step 4: Students use the two-point method to make images of functions (3) and (4).

Observing the images of the above four functions, we find that they are all straight lines. Please give examples to prove their findings.

Design intention: Teaching should start from the students' existing knowledge system, and making function images is the key to the function y=kx+b(k? 0) the cognitive basis of image, so the design is conducive to guiding students to enter the learning situation smoothly.

(2) Exploration and induction

Then observe the images of the above four functions, that is, the relationship between the values of k and b and the image positions of linear functions:

(1) y=- 1/2x+2 is obtained by moving the straight line y=- 1/2x up by 2 units; The straight line y=3x+2 is obtained by moving the straight line y=3x upward by 2 units respectively.

(2) The intersection of y =-1/2x+2 and y=3x+2 is at the same point because the b of the two straight lines are the same; That is to say, the ordinate of the intersection of a straight line and the y axis depends on B.

It is concluded that two linear functions have * * similarities when k is the same and b is different: straight lines are parallel, both of which are made up of straight lines y=kx(k? 0) Move up or down;

Difference: They are different from the intersection of the Y axis.

But when two linear functions, b is the same and k is different, they have one thing in common: they intersect with the Y axis at the same point (0, b); Difference: Straight lines are not parallel.

Supplementary note: Because the above function is only b>0, it can't reflect the downward translation of the proportional function, so I let the students complete B.

Design intention: Modern mathematics teaching theory holds that teaching must be obtained on the basis of students' independent exploration and experience induction, and the process of thinking must be displayed in teaching. Here, through observation and analysis, independent thinking, group communication and other activities, students are guided to summarize, so that students have a complete process of knowledge formation.

(3) Practical application

1. Complete the textbook example 1

Pay attention to guide students to discuss and communicate, and feedback the application of knowledge in practice in time.

2. Finish the exercises after class

Design intention: Several examples and exercises are from easy to deep, from easy to difficult, and each has its own emphasis, which embodies the teaching concept that the new curriculum standard puts forward to let more students get different development in mathematics. The overall design intention of this link is to feedback teaching and internalize knowledge.

(D) Summary, expansion and deepening

My understanding is that summary should not only be a simple list of knowledge, but also an effective means to optimize the cognitive structure and improve the knowledge system. In order to give full play to the main role of students, we should sum up the knowledge, methods and experience of learning. I designed three questions:

(1) What knowledge have you learned through this lesson?

② What is your greatest experience from the study of this lesson?

(3) What methods of learning mathematics have you mastered through this lesson?

(E) assignments, improve sublimation

Based on the consolidation and development of homework, I designed mandatory questions and multiple-choice questions. Mandatory questions are feedback to the content of this lesson, and multiple-choice questions are an extension of the knowledge of this lesson. The overall design intention is to feedback teaching, consolidate and improve.

The above-mentioned links are interlocking and in-depth, which fully embodies the communication and interaction between teachers and students. Under the overall control of teachers, students gradually deepen their understanding of knowledge through thinking and step by step, so that classroom benefits can reach the best state.

Teaching evaluation of intransitive verbs

The teaching of this course pays attention to excavating teaching materials and embodies students' dominant position; At the same time, taking questions as the carrier and inquiry as the main line, we consciously leave students with moderate thinking space, show the learning level of students at different levels from different perspectives, and integrate imparting knowledge with cultivating ability. Talking about the class is still a new thing for me, and I will talk about it further in the future. I hope that experts and leaders will give valuable opinions on this class. Thank you!

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