[Keywords:] junior high school mathematics; Hierarchical teaching; explore
The new curriculum standard requires that "different people get different development in mathematics", that is to say, the new curriculum standard recognizes that there are individual differences among students, such as intelligence differences, basic differences and learning quality differences. The existence of these differences makes students' mathematics learning prone to polarization. Therefore, it is necessary to teach students at different levels to keep their enthusiasm and confidence in learning mathematics, so that students at different levels can develop correspondingly in their study. At present, junior middle schools are not allowed to stratify students in the form of administrative classes, so the practical exploration of class stratification teaching is becoming more and more important.
First, the basis for the implementation of student stratification
Generally speaking, students should be stratified, because they are stratified in the class, and there should not be too many layers, otherwise it will be difficult to take into account the multi-level needs in the classroom. Students' stratification is based on students' mathematics academic performance, learning foundation and learning ability. For example, the author took over a ninth-grade teaching class on 20 1 1, with 44 students, with an average score of 70 points (full score 120 points). According to the results, students whose initial math scores are above 75 are classified as eugenics classes, and the rest are basic classes. After preliminary stratification, gifted students with quick thinking and strong learning ability are divided into excellent layer A, and the rest are excellent layer B; Students at the basic level are divided into basic B level and the rest are basic A level. Generally speaking, the eugenics layer and the basic layer can be considered in the teaching design, while the four layers are subdivided, which is convenient for arrangement in some cases (such as after-school counseling, etc.). ). Specifically, the number of people at different levels is: 8 in excellent A-level, 6 in excellent B-level 14 in basic A-level, and 6 in basic B-level.
Second, let students know their learning goals.
After the completion of stratification, students at all levels should be guided to learn the rules first, because students at different levels must understand what they want to do in class and after class in order to arrange their own learning according to their own level at the same time. For outstanding students, guide them to reflect, summarize and explore actively in the learning process, and cultivate good mathematical literacy in the learning process; For students with poor level, they can be asked to make appropriate induction and summary in class according to the teacher's teaching process and under the guidance of the teacher. The above content is to let students know the big goals, and in terms of the specific goals of each class, teachers can let students at all levels know their learning goals in this class first in combination with specific situations. For example, in the lesson of "Tangent Judgment", students at the basic level aim to master the tangent judgment theorem and the concepts of inscribed circle and center of triangle; The goal of the eugenics layer is to think about the method of judging the tangent of a circle and what is the core basic knowledge of the triangle center (angle bisector theorem and inverse theorem) after completing the above basic goals.
Third, the classroom organization of hierarchical teaching
The classroom of hierarchical teaching is divided into five links: listening, practicing, autonomous learning, summarizing and assigning homework.
1. The review, introduction and learning of new lessons are the listening part, and all students participate in this part. Students of different levels learn the same content in class, which involves how to keep students' attention in class and how to improve the interaction effect with students. As an important means of teacher-student interaction, classroom questioning should be targeted, and students of different levels should be selected to answer according to the difficulty of the question, so that students of different levels have the opportunity to answer. Generally speaking, recalling the concepts and properties of the previous section, calculus process or conventional reasoning process (such as proving the congruence of two triangles) are all basic answers to strengthen the expression ability; Ask eugenics questions about the direction, examples and problems of solving problems.
2. The practice part adopts the method of layered practice. If students at the basic level are frustrated repeatedly in the face of difficult problems, they will have doubts about their classroom learning and gradually give up learning, while gifted students will feel bored if they always do a lot of imitative basic problems. Therefore, it is beneficial to maintain and improve students' enthusiasm for learning mathematics to arrange stratified classroom exercises and homework.
For example, in the lesson "Determination of Tangents", the arrangement of eugenic layers:
(1) As shown in the figure, it is known that the straight line AB passes through the point C, OA=OB and CA = CB on ⊙O, so is the straight line AB tangent to ⊙O? Why?
(2) Given a point P outside ⊙O, can a ruler cross point P as the tangent of ⊙O?
(3) As shown in the figure, in △ABC, AB=AC, O is the midpoint of BC, with O as the center, let ⊙ O be tangent to AB at point M, which proves that AC is tangent to ⊙ O. ..
Basic layer practice layout:
(1) As shown in the figure, the condition of _ _ _ _ _ _ _ can be supplemented when the straight line L passes through a point m on ⊙O, so it can be seen that the straight line L is tangent to ⊙O;
(2) In RT △ ABC, ∠ c = 90. Please judge the position relationship between B as the center, BC as the radius ⊙B and straight line AC, and explain the reasons.
(3) If the straight line L is perpendicular to the radius OM of ⊙O, is the straight line L tangent to ⊙O? Why?
It is worth noting that students' practice in the basic stage should not be too simple. Under the purpose of consolidating the knowledge in this section, they should change the questions and carry out variant training. As mentioned above, although the topics in the basic layer are all based on the tangent judgment theorem, the types and contents are slightly different, so that students will not be bored, and at the same time, they will strengthen their understanding of the theorem in the process of repeatedly using the tangent judgment theorem.
3. Self-study links arrange for gifted students to make self-summary, self-reflection and ask questions at the basic level during the learning process, and teachers can provide guidance. You can also use group learning as appropriate, so that eugenics can help basic students answer questions.
4. Summary: The eugenics summarize and the teacher supplements, which not only achieves the purpose of summary, but also checks the induction of the eugenics.
5. Assign homework in the same way as classroom exercises.
Fourth, hierarchical counseling.
Consultation is a process of dispelling doubts. In classroom teaching, students with a lower level will have more content they don't understand and ask more questions. Therefore, the tutoring in the classroom should be mainly aimed at such students. Because hierarchical teaching is carried out in the same class, in addition to considering the teaching objectives, reasonable self-study time should be designed in teaching design, so that gifted students can use this time to reflect, summarize and improve, and teachers can also use this time to coach other students in need.
Outside the classroom, counseling is not only for students with low level. In order to keep outstanding students' interest in learning mathematics, we should also know the research situation of outstanding students after class, and give guidance in time if they need guidance, instead of letting them develop on their own.
It can be said that the focus of in-class counseling is on middle-level students, taking into account basic-level students, so the counseling efficiency will be higher; Extra-curricular counseling focuses on gifted students and students at the basic level, especially those at the basic level. Because of the poor foundation, more counseling time should be arranged, and after-school counseling is relatively appropriate.
After all, a teacher has limited energy and time. While doing a good job of tutoring, he will also set up a study group of six people, with gifted students leading the basic students to study together.
Five, hierarchical evaluation
Hierarchical evaluation is an effective measure to promote students' personality development. Through diversified evaluation, students can taste the joy of success in evaluation and lay the foundation for their sustainable development. Take different evaluation standards for students at different levels, pay attention to process evaluation, affirm students' efforts and progress in the learning process, and make every student feel satisfied in their studies. The evaluation of students can be divided into daily evaluation and evaluative evaluation.
1. Process evaluation
The process evaluation is evaluated from four aspects, such as classroom records. In the class record, the basic students' classroom workbook requires students to write down all the exercises they have done in class. Because the causes of many basic students are related to their own consciousness and study habits, teachers must do a good job of supervision and guidance in daily life. This is the purpose of setting up classroom exercise books. See the following table for specific evaluation methods:
2. Assessment and evaluation
Assessments are usually tests, unit tests, term tests and other test assessments. Examination evaluation is a double-edged sword. If used properly, students' expectations of good grades can be used to guide them and help them diagnose problems in their studies. At the same time, affirmation of grades can stimulate students' desire and enthusiasm for further study. Therefore, the key to make good use of this kind of evaluation lies in stratification, so that students can succeed and be affirmed in their own proficiency tests and promote their further desire. Quizzes can be used as a means of hierarchical assessment. Teachers can use hierarchical quizzes before each class, which will help teachers understand students' mastery, help students diagnose learning problems and motivate students to study hard.
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