The purpose of teaching goal stratification is to set different learning goals for students at different levels according to their different knowledge in teaching activities, so as to teach different levels of knowledge to adapt to students' knowledge structure. Bloom, a famous contemporary American psychologist and educator, put forward the theory of mastering learning: "As long as appropriate materials and teaching are provided, and appropriate help and enough time are provided to each student, almost all students can complete their learning tasks or achieve the prescribed learning goals."
When making teaching objectives, teachers should not only pay attention to the unified standards in teaching and highlight the consistency of teaching requirements, but also pay attention to students' personality differences, highlight the hierarchy of teaching objectives and combine unity and hierarchy. On the one hand, according to the learning objectives of the curriculum standard and the actual situation of the students in the class, the classification design is carried out for all students, so that all students can meet certain requirements, which is the teaching goal of "guaranteeing the bottom". On the other hand, we should give consideration to the goal of "not capping the top", and put forward the goals flexibly and hierarchically in order to meet the knowledge needs of different students. As the saying goes, "jump up and pick peaches." This requires students to think through their own efforts and complete a higher level of knowledge than the existing level of knowledge. This level of knowledge can be achieved through the efforts of students.
Second, the teaching content is layered and gradual.
When designing the teaching content, we should consider the hierarchy, step by step, and take different measures according to the actual learning starting point of students. Teaching guidance for students with low starting point should be inclined, and the educational principle of "small steps and slow steps" should be adopted in design problems; The teaching problems of eugenic design should be flexible and difficult, and students should be encouraged to put forward their own problems and solve them through discussion. The design of exercise questions should have a certain gradient, from basic questions to variant questions to extended questions, and some mobile questions should be designed according to the specific situation in the classroom.
1, ask questions in layers
In the classroom teaching of stratified teaching, according to the students' reality, teaching materials and teaching objectives, the teaching is designed into different levels of problem scenarios, from shallow to deep, step by step, prompting students to actively explore, think positively, guess boldly and concise the law.
The first design is to ask questions to all students. The problem is too difficult, and the thinking of "students with learning difficulties" can't keep up, and even they are at a loss; If the question is too simple, gifted students will feel uninterested and lead to distraction. The principle of designing questions is to ensure that all kinds of students have the opportunity to answer in class. Therefore, teachers should be good at transforming established learning tasks into specific problems that students are easily interested in, and designing certain problem scenarios. Let gifted students play a leading role at critical moments to stimulate their enthusiasm for learning; Let "students with learning difficulties" answer some basic questions such as calculation problems and encourage them to learn math well. For example, it is also a lesson from Beautiful Pastoral. Created a "beautiful spring, the teacher led the students to the beautiful countryside and saw the scenes of various animals playing." Then ask the following questions for students to think about: (1) What mathematical information can you get from this thematic map? (2) According to these mathematical information, what mathematical questions can you ask? No matter what kind of students can answer these questions, there are some differences in the amount of information obtained and the originality of questions. Another example: before class, ask the students, "What did you learn in this class?" "What do you think we should pay attention to when observing things?" Wait a minute. This kind of problem embodies the principle of "guaranteeing the bottom without capping".
Secondly, it is aimed at middle and low grade students, mainly designing some declarative and procedural questions for them, guiding them to recall, understand and perceive, and learning declarative and procedural knowledge. It is also a lesson from Beautiful Pastoral. According to the students' conclusion, there are six Aries and four black sheep. How many sheep are there? (6+4= 10);
A * * * There are 10 sheep and 6 white sheep. How many black sheep are there? ( 10-6=4); A * * * There are 10 sheep and 4 black sheep. How many white sheep are there? ( 10-4=6)。 Then ask the middle and lower grade students: "Can you list three formulas according to the information of six yellow flowers and 13 red flowers?" This will give junior and middle school students enough opportunities to show off and experience the happiness of success. Of course, in the end, don't ignore the upper middle school students, but design problems to satisfy their desires. For example, the number "9", what can it stand for? It can be said that it is less than10; It can be expressed as 1 less than10; It can mean 1 1 minus 2 equals 9 and so on. It has many manifestations. Can you say it? Who is the most representative? What can "8" also mean? This kind of problem provides a broad space for senior high school students to think.
According to students of different levels, some targeted questions are designed to give each type of students flexible learning tasks to complete, so that every student has a successful experience and increases the interest of gifted students, especially "students with learning difficulties" in learning mathematics.
2, layered practice
Practice is the process of forming and consolidating students' mathematical cognitive structure, an important means for students to master knowledge, form skills and develop abilities, and a basic activity form for cultivating students' mathematical abilities. Designing targeted exercises suitable for classroom teaching content and students' cognitive level is of great significance for improving the quality of mathematics teaching and cultivating students' mathematics learning ability.
(1) Same exercise, layered requirements
Change the unified level of classroom practice into multi-level training, so that students at different levels have their own training goals, fully mobilize the potential of all kinds of students, so as to achieve "you arrive at the destination, I also arrive at the destination", so that every student has the opportunity of self-development and a successful experience. Then stimulate students' subjective initiative and improve teaching effect. Both of them are "beautiful pastoral". When practicing different representations of "9", I designed it like this: "9" can be said to be "1 less than 10", "4 is greater than 5",1-2 = 9 "and" three books and six books ". Another example is: according to "Hua Hua kicks 5, Dong Dong kicks 7, Liang Liang kicks 13", students in middle and lower grades get a "smart dog" every 2 questions, and other students get a "smart dog" every 4 questions. In this way, every student has a chance to win the prize, which truly embodies the teaching concept of "jumping to pick peaches".
(2) Different students have different exercises.
Because of the multi-level teaching objectives, design exercises should also be multi-level, which is the continuation of classroom teaching and an important link of hierarchical teaching. Let students with different foundations practice "free choice" in order to carry out targeted training. First of all, the exercises should be designed as basic exercises, comprehensive exercises and extended exercises. One is the basic problems related to the teaching content, as well as the exercises that are slightly more difficult to decompose or give specific hints in the teaching materials and the exercises in the supporting exercise books, so that students with learning difficulties can complete as much as possible and gradually achieve their learning goals in practice. One is designed according to the media requirements of teaching content, which is designed for most students to practice for middle school students, so that they can understand and consolidate what they have learned in practice. The other is to educate top students according to their learning level and the requirements of teaching content design. The exercises with a little difficulty will make them develop and improve in exploration.
In stratified practice, on the basis of ensuring a certain amount of questions for each student, students are allowed to choose freely, and at the same time, students are encouraged to break through to a higher level to arouse their enthusiasm for knowledge. For example, the teaching goal of the course "Knowing Clocks and Watches" is to know the hour and the half hour by combining life experience. According to the pre-class survey, 30% of the students already know the whole hour and time, so they consider the knowledge level of each kind of students when designing exercises and design a series of questions to encourage each student to climb to a higher level. (1) Name the following time on the clock face (the courseware shows the following time on the clock face: 9: 00, 12: 00, 10: 30, 5: 30, 1: 00,1/kloc. (2) Write the time of the clock face on the homework paper. Although the above exercises provide the same condition information, the requirements of the two questions are different. The writing time of the second question is longer than that of the first question. Through feedback and communication, students who only did the first question also learned the writing method of the second question, and also learned the current writing method by listening to the speeches of their peers. Then design a second set of questions for students to choose from: ① Set aside the following time as required: 7: 30, 8: 00, 4: 30 and 6: 30; (2) deskmate cooperation, one student dials his favorite moment, and the other student writes the moment (two roles are free to choose, and partners are free to choose).
Multi-level and multi-angle practical activities provide students with a broad thinking space for innovative learning, meet the needs of students at all levels, make each student gain the desire for knowledge and the joy of learning success, realize their own freedom, achieve the goal of multi-level learning optimization, and truly embody people-oriented.
Third, the hierarchical implementation of teaching evaluation
The new curriculum emphasizes that the evaluation of students should vary from person to person. Different evaluation criteria should be adopted for students of different levels. Use the praise and evaluation of "students with learning difficulties" to find their bright spots, affirm their little progress in time, and mobilize their learning enthusiasm; Encouraging evaluation of middle school students not only reveals the shortcomings, but also points out the direction of efforts and promotes their positive progress; Take a competitive evaluation of top students, adhere to high standards and strict requirements, and urge them to constantly surpass themselves. At the same time, in the evaluation process, we should not only evaluate the results, but also track and evaluate the process. For some students who sometimes find it difficult to achieve ideal results in the process of inquiry, it is also necessary to evaluate their inquiry process in layers and dig out valuable components, especially to fully affirm their inquiry spirit.