Keywords: teaching students in accordance with their aptitude, flexible math homework
First of all, school teaching should overcome the shackles of conventional thinking.
Due to the influence of heredity, environment and education, there are individual differences in physical and mental development. In the school environment, students' individual differences are mainly manifested in their family cultural background, previous knowledge, ambition level (that is, learning motivation), intelligence, ability tendency (quality), learning methods and learning differences between boys and girls. Therefore, in school teaching, it is necessary to understand the individual differences of students' psychological development and teach according to the characteristics of different students, that is, to teach students in accordance with their aptitude, so as to improve the teaching quality, enhance students' learning confidence and achieve the expected results. So how should we practice teaching students in accordance with their aptitude in teaching? This is an important question worth pondering. First of all, we teachers must overcome the bondage of conventional thinking. Judging from the development of education, at first, it was a very formal process for adults to pass on their own experience, skills, cultural background and cultural values to their children. Later, schools and teachers appeared, and they all practiced the principle of teaching students in accordance with their aptitude to varying degrees. They knew every student's personality, talents, interests and specialties like the palm of their hand, and had different requirements for everyone, and often gave different answers to the same question raised by different students. However, since the spread of 17 and 18 centuries, many educators have made great efforts to improve the effect of collective teaching, which has led to a tendency to ignore the personality differences in classes. In our educational work, for a long time, we have paid more attention to * * * and unified requirements, but not enough attention to the development of students' respective characteristics and specialties. That is to say, we always focus on training students to be * * * with the same goal. Constrained by conventional thinking, we always focus on the place where students are far from the * * * with the same goal, rather than developing beyond it. Admittedly, students' weaknesses can't be ignored, but as a teacher, we should pay attention to both their weaknesses and their strengths, which vary from person to person. Therefore, as a teacher, we should teach in a targeted way, instead of pursuing the same goal in a uniform or one-size-fits-all way. We should overcome the shackles of conventional thinking and teach students in accordance with their aptitude. As a math teacher in a normal school, I am deeply touched by the teaching of math. Aside from other aspects, it is very skillful and creative as far as the assignment of mathematics is concerned. Now, when I assign homework to students, I put aside the shackles of traditional homework thinking, and reasonably assign math homework to students at different levels according to their hobbies and different learning levels, so that they can play, consolidate and extend their knowledge more effectively. Putting forward different requirements for different students not only makes them frustrated, but also makes them see hope, experience the fun of learning and enhance their confidence in learning mathematics.
Second, think about flexible math homework.
The new educational concept emphasizes teaching students in accordance with their aptitude, and teaching cannot develop into a fixed model. Therefore, the teaching mode is constantly updated and the teaching methods are constantly changing. 2 1 century is a century with consumption as the main body and people as the center. In this century, consumers are the main body of social activities. For education, education is the first task, and the main consumer of education is students. Students' willingness to consume should become the dominant trend of our education development, and meeting students' learning needs is the fundamental purpose of our education.
But for a long time, finishing homework seems to be the fundamental task of students in class. Homework is to complete homework, homework is to satisfy parents, and homework is to get a good grade. These three are connected by a greater than sign, and homework and students' burden are almost connected by an equal sign. The single homework form, boring homework content and large proportion of homework capacity make homework a "supplement" and "reinforcement" for teachers, which not only loses the educational significance of homework, but also obliterates students' interest in learning, inhibits the development of students' diversified thinking and affects the cultivation of students' imagination and creativity.
The new situation and new ideas have put forward new tasks for us. What kind of work concept should we have in the process of teacher allocation? How to give consideration to the consolidation of basic knowledge and the development of ability in the design of homework? How to correctly handle the relationship between all-round development and teaching students in accordance with their aptitude in homework design and layout? These are all worth thinking about. We must highlight the new curriculum concept, strengthen the homework reform, give new life and vitality to homework, and break the traditional "one size fits all" situation to meet the requirements of students' development.
How to reform the traditional math homework? The key is to get rid of the old and innovate, break the single boring operation mode, and rebuild an operation mode that combines knowledge and ability, theory and practice, which is acceptable to students and meets the requirements of quality education. This operation mode is conducive to the implementation of quality education, conforms to the requirements of the syllabus, and is conducive to the development of students' personality and the improvement of comprehensive ability and quality. Specifically, we should grasp the following points.
1. Refine the job content
Teaching practice shows that the enemy of implementing quality education is students' heavy academic burden, and one of the direct factors of the heavy academic burden is the flood of "sea of questions". The fundamental reason for this situation lies in the low efficiency, poor quality, large quantity and lack of typicality of the classroom.
First of all, pay attention to the quality of homework. Homework should be carefully selected in combination with the content in class, taking into account the typicality, systematicness and comprehensiveness of homework as far as possible. When selecting homework, we should not only consider the principle of easy before difficult, step by step, but also pay attention to the principle of inspiration and consolidation to avoid assigning homework that is easy to get. Secondly, we should also pay attention to the workload. Generally speaking, it is more appropriate to arrange homework for about 20 minutes after class. Of course, the determination of the amount of homework is also restricted by factors such as students' quality, age characteristics and specific teaching content, and cannot be generalized. Reduce unnecessary repetitive exercises, carefully select counseling materials, and assign high-quality and typical homework problems to students, so as to achieve the effect of practicing one problem at a time.
2. Diversified business forms
Traditional homework is mandatory, and monotonous homework makes students feel boring, which reduces their enthusiasm for doing homework and is not conducive to training and cultivating students' various skills. Therefore, we should pay attention to the change of homework forms, realize the diversification of homework forms, let students experience fun in various forms of homework, and thus cultivate students' interest in homework.
3. Hierarchical (elastic) distribution
Quality education has the basic elements of subjectivity, individuality, foundation and development. Among them, subjectivity and development require that homework must be hierarchical, that is, flexible, so as to suit all students and meet the needs of every student with different knowledge base and intelligence factors.
In mathematics teaching, the overall teaching goal and the required scale of homework in each class should be the same for all students, but it has been proved that assigning the same amount of homework content to all kinds of students is not suitable for the actual satisfaction ability of different students. Therefore, when preparing lessons, teachers should take out the required questions and multiple-choice questions of homework and mark them with different scores. There is no uniform requirement for multiple-choice questions and problem-solving. In this way, we can change the quantitative type into the elastic type in quantity, reasonably control the difficulty and quantity, and hang the "peach" in the position where each student jumps up and picks it, so that the underachievers can relieve their original psychological pressure, see hope and light, and enhance their self-confidence in learning. It can also improve the inquiry ability of top students and let all students develop a calm and consistent homework mentality.
Ask the same question from as many angles as possible, and the gradient of asking questions is from easy to difficult, so that students can explore step by step, and each student can get different degrees of successful attempts. The gradient of questioning can help students explore all aspects of the problem, reach a deep understanding of the nature of the problem, and thus cultivate the profundity of thinking.
Step-by-step problem groups are designed, different levels of topics are selected according to the requirements of teaching content, and problem groups are organized according to the requirements of different abilities, and the nearest development areas of knowledge, methods and abilities are set in a targeted manner, so that the students' thinking gradient is gradual and just right. Every time students solve a problem, they can understand the law contained in it and realize the artistic conception and proposition conception of solving the problem. It is practical and effective to stratify homework through these methods and improve students' enthusiasm for doing homework.
For example, the following assignments can be arranged after the first class in Chapter 8 of the second volume of junior high school textbooks:
A: Preview homework (preview homework).
Read the textbook and understand the following questions:
The meaning of (1) score.
(2) The concept of rational expression.
(3) The condition that the score is meaningful.
(4) The condition that the value of the score is zero.
This kind of preview homework can make students get the most benefit from the follow-up courses. In order to play a role, the content of this kind of homework must be started immediately in class. This kind of homework can make more class time for class discussion. Cultivate students' self-study ability and the spirit of independent thinking.
B: Practical homework (written homework)
(1) When _ _ _ _ _ _ _, the score 1/x is meaningful; _ _ _ _ _ _ _ _, the score 2x/(x+2) is significant; When _ _ _ _ _ _ _, the score (x+ 1)/(2x-5) is meaningful.
(2) When x takes what value, the value of the following score is zero?
5x/(x+ 1)； (3x-5)/( 10x+ 1)
(3) (Optional) When what value does X take, does the formula make sense? The value is zero?
x/(x+ 1)； (x-5)/2x； (2x- 10)/(x-5)
Practical homework is the simplest kind of homework, which can be used to help students master some skills, but it is easy to be copied by other students. Research shows that this kind of homework must be closely related to the previous learning materials in order to play a role. The above three small questions are carried out in different levels and steps, which conforms to the principle of homework design.
C: Expansive and creative homework (thinking homework after class)
(1) textbook example 2 If A = 5 and B = 5, what will the score b/(a-b) look like? What is the actual situation? Attachment 2: Two people, A and B, start from a certain place on an expressway and drive in the same direction. It is known that A walks one kilometer per hour and B walks b kilometers per hour, where A > B. If B starts from 1, how long will it take for A to catch up with B? When a = 6 and b = 5, how long does it take for A to catch up with B? (2) What is the value of X, and the value of the score (x-2)/(2x-5x+6) is zero?
Extensible and creative assignments are mainly used to examine whether students can apply familiar skills and concepts to new situations. The first question here is a variant of an example in the textbook that closely connects with the actual situation, so that students can connect with the actual situation and understand the meaning of mathematical knowledge. The answer of most students to the second question may be: x-2=0, so when x=2, the score is zero. However, although the numerator of x=2 is zero, the denominator 2x-5x+6 is also zero. In this case, the score is meaningless. So after solving x=2, we can test whether the conclusion is reasonable according to the condition that the value of the fraction is zero (the numerator of the fraction is zero and the denominator is not zero). Students' critical thinking can be cultivated in solutions. Creative homework goes further than extended homework, which requires students to incorporate some skills and concepts in the process of answering questions.
Generally, the above three types of homework can be arranged in the new class, and students can choose to complete them according to their actual situation. The arrangement of this kind of homework is diversified and hierarchical, which conforms to the typical principle. The quantity and difficulty of homework can be suitable for students of different levels, which can give full play to students' initiative and creativity, help students' autonomous learning ability and serious learning attitude, and at the same time, give timely feedback to the teaching effect.
In short, the traditional "one-size-fits-all" homework often does not take into account the cognitive requirements of students at all levels, which hinders the development of students' personality, and the homework is too difficult, which inhibits students' enthusiasm for learning. Modern psychology believes that achievement motivation is a universal and effective motivation among all kinds of motivations that stimulate students' learning motivation. Therefore, it is necessary to carefully arrange flexible homework for students, let students at different levels choose independently, give students the right of flexibility in homework, and realize "everyone can practice" and "everyone can succeed" so that students at all levels can be completely successful.
References:
[1] Xia Minghua. Compulsory education junior high school textbooks (discussion edition). Zhejiang Education Press, 1997.
[2] Guo Jianming. Exploration and practice of mathematics homework mode in junior middle school. Zhejiang Education Press, 1997.
[3] Tang Shaoyou. Infiltration of quality education in mathematics homework. Journal of Beijing Institute of Education, 16 No.3, 2002, (9).
[4], Liu rude. Contemporary Educational Psychology (Chapter 14). Beijing Normal University Press.