Teaching inquiry
Based on the fact that our school is an ordinary high school merged from the original schools of several factories and mines, the students in high schools are different from those in factories and mines, the students in rural schools are increasing, and the foundation of junior high schools is uneven. The new leadership of the school attaches great importance to the management of education, teaching and scientific research. According to the concept of new curriculum reform, we should comprehensively promote quality education, pay attention to strengthening the research and management of education and teaching, build an evaluation system of multiple evaluation of teaching quality, and advocate independent cooperation, inquiry and innovative learning. In the face of students with uneven foundations, it is proposed to implement "layered" teaching and manage teaching according to the principle of "teaching students in accordance with their aptitude". It is fundamental for the survival and development of Baiyun No.6 Middle School to let every student develop his potential, strengthen effective teaching, make AG outstanding and strive to improve the teaching taste of Baiyun No.6 Middle School.
Exploration of "Guidance of Mathematics Learning Plan"
According to the constructivist learning theory and the new curriculum concept, starting from this year, we tried to reform the traditional "teaching plan" into "learning plan" to guide students' autonomous learning step by step, and made a preliminary teaching practice and exploration on "high school mathematics learning plan guidance". At present, both at home and abroad attach great importance to the cultivation of students' autonomous learning consciousness, and some provinces and cities in China have also carried out the teaching research of "learning plan guidance", which has aroused great attention from colleagues in the education field. The implementation of the new curriculum has also accelerated the transformation from the traditional emphasis on imparting knowledge to a new teaching model that focuses on students' autonomous learning and active participation in learning.
Connecting teaching of subject knowledge in junior high school and senior high school
For the new students this year, the school proposed to strengthen the research and implementation of knowledge connection teaching in junior and senior high schools. It is clearly stipulated that all subjects are not allowed to attend high school courses in the first month of school, and the teaching of knowledge connection between junior and senior high schools must be implemented. As early as during the summer vacation, the school arranged the lesson preparation team leaders of various disciplines to organize the teachers of all disciplines in the first grade of the school to concentrate on studying junior high school textbooks, seriously discuss and formulate cohesive lesson plans, and prepare lesson plans according to the division of labor. During the summer military training for freshmen, the school conducted a diagnostic test for all freshmen. According to the test results, the preparation groups of all disciplines adjust the bridging teaching plan in time, and make it clear that the bridging teaching content is only linked to the relevant content of the last semester of senior three.
(A) junior high school mathematics knowledge convergence content and requirements
Commonly used multiplication formulas and factorization methods
Cubic sum formula, cubic difference formula, two-digit sum cubic formula, two-digit difference cubic formula, three-digit sum square formula, derivation and application (positive and negative use),
Familiar with cross multiplication and simple grouping decomposition.
Keywords classified discussion, quadratic root,
Algebraic operation and deformation
Absolute value with letters, piecewise problem solving and parameter discussion, unary linear inequality with letters
Concept and application of quadratic radical, simplest quadratic radical, similar radical, simplification and operation of radical.
Molecule (parent) is physical and chemical, and it is divided into fractions.
Equation and equation
Simple and unreasonable equation, fractional equation that can be reduced to quadratic equation of one variable, equation with absolute value, equation with letters, biquadratic equation, multivariate linear equation, biquadratic equation, discriminant of roots of quadratic equation of one variable and Vieta theorem.
Linear fractional function, three "quadratic"
On the basis of inverse proportional function, combined with the knowledge learned in junior high school (such as translation and central symmetry), the image and properties of linear fractional function are qualitatively studied to consolidate and deepen the ability of combining numbers with shapes.
Master the matching method, memorize and deduce the formulas of image vertex and symmetry axis, master the analytical formula of quadratic function with undetermined coefficient method, study the image and properties of function with the discriminant of root, and solve simple quadratic inequality with the combination of numbers and shapes.
Parallelism and similarity
This paper introduces the transitivity of parallelism, bisection theorem of parallel lines, trapezoid midline, ratio theorem and equal ratio theorem, introduces the concept of preparatory theorem, the proof of simple similar proposition, and the judgment theorem that the straight line or extension line of two sides of a truncated triangle is parallel to the third side.
Calculation and proof in right triangle, figure
Completes the concept and theorem of projection, consolidates the calculation of trigonometric function value with the trilateral ratio of special right triangle, remembers the trigonometric function value of special angle, supplements the simple proof of trigonometric identity, and the basic relationship of trigonometric function with the same angle in trigonometric function.
Supplementary triangle area formula (angle between two sides and three sides) and parallelogram area formula, calculation formula of side length in regular polygon, simple equal product transformation, related concepts and properties of triangle four centers, midpoint formula, bisector theorem of internal angle, and relationship between diagonal and side length of parallelogram.
circle
Relevant theorems of circles: vertical longitude theorem and inverse theorem, tangent angle theorem, tangent theorem, property theorem of connecting line between two circles, property theorem of common tangent of two circles; Tangent drawing, a simple proof of the proposition of circle, introduces the concept of four-point * * * circle and the properties of inscribed quadrilateral, consolidates the properties of circle, and introduces the concepts of tangent angle, inner angle and outer angle of circle, bisecting circle, inscribed circle of triangle and trajectory definition.
(B) Problems that should be paid attention to in teaching convergence
1。 Computing power and specification requirements
In addition to the above knowledge, we should also pay attention to students' computing ability, especially mental arithmetic, oral arithmetic and written arithmetic, which are the "worst" among students, because the senior high school entrance examination can bring calculators. In order to strengthen students' computing ability, we should limit the use of calculators. In addition, students are "random" and there are no strict writing requirements in the process of writing format and proof. As long as the truth in the answer to the senior high school entrance examination is correct, you can give them extra points.
2。 Instruct students how to study.
Junior high school mathematics knowledge is less, shallow, easy and comprehensive. High school mathematics knowledge is extensive, which will promote and extend junior high school mathematics knowledge, and also improve and sublimate junior high school mathematics knowledge. There are higher requirements for senior high school students in learning methods, self-study ability and thinking habits. Therefore, it is necessary to guide students to form good study habits and learn mathematical thinking methods in mathematics textbooks.
Pay attention to the guidance of learning methods
_ _ _ requires students to preview in advance, so that students can form a sense of excitement about the content to be taught in their minds in advance, and really attend classes with questions, which can obviously improve teaching efficiency and adapt to the intensive study of high school textbooks.
In teaching, we should cultivate students' ability to think and solve problems independently, and then cultivate students' strong interest and enthusiasm in learning.
______
Pay attention to cultivating students' thinking ability
The methods of training thinking are:
Design more meaningful exercises, encourage students to think and keep active thinking; To improve the depth and breadth of thinking, training can take many forms, such as problem group training, variant training, multi-solution training, multi-solution training and error correction training, so that students can taste the bright spots in solving problems.
Set the situation and introduce new lessons.
For the introduction of the new curriculum, it is designed in the form of questions in teaching, so that students can find the connection between old and new knowledge and transfer it. The problem of design should fully expose the connection between old and new knowledge, that is, the problem should be based on old knowledge, so that students are not unfamiliar and have room for thinking, and on this basis, it naturally extends to the new curriculum, so that students can make new discoveries in their thinking, which will naturally make students enter the new curriculum state and situation.
Let students master the formation process of knowledge.
_ For the study of new knowledge, the formation process of knowledge is revealed in the form of questions, so that students can try, explore and discover by themselves, and the effect is far better than the teacher's simple explanation. Any knowledge point in mathematics has its forming process, or it is a mathematical abstraction of practical problems, or a conclusion drawn by induction and analogy of old knowledge. This process of mathematical abstraction or reasoning is the process of knowledge formation. If students can master the formation process of this knowledge, they can grasp the knowledge structure as a whole, communicate with knowledge, find out the ins and outs of knowledge and "live" it.
Teaching Exploration of "Mathematics Learning Plan Guidance"
Theme definition
"Teaching plan" is a case of teaching content, teaching material organization and teaching method compiled by teachers according to the teaching syllabus (curriculum standard) and teaching materials after analysis and processing. It focuses on what the teacher says and how to say it.
"Learning plan" is a kind of aid scheme aimed at guiding students to study on the basis of teaching plans, so as to open up students' wisdom and develop their abilities. Its focus is "what to learn" and "how to learn".
Teaching mode of "learning plan guiding learning"
The essence of learning plan is a bridge used by teachers to help students master the teaching content, communicate learning and teaching, and also an important medium to cultivate students' autonomous learning and knowledge construction ability. It is a written expression that teachers think, process and sort out the teaching content according to students' knowledge level and life experience, and attach importance to the cultivation of students' autonomous learning ability. "Learning by plan" teaching is a teaching mode with learning plan as the carrier, learning by plan as the method, teacher's guidance as the leading factor, students' autonomous learning as the main body, and teachers and students completing teaching tasks together.
The general idea of "learning plan guiding learning" teaching
Highlight the implementation of students' dominant position, reflect the teaching goal of subjective participation and independent development, cultivate students to learn to learn, give full play to their initiative in the learning process, and strengthen the cultivation of learning ability.
"Learning by learning plans" breaks the conventional practice of teaching only with lesson plans. With lesson plans as the carrier, it guides students' autonomous learning, inquiry learning and active learning, combines after-class with classroom, combines learning plans with lesson plans, combines students' autonomous learning with teachers' explanation and guidance, and combines knowledge, skills and ability training to form an all-round, multi-channel and multi-angle "overpass", allowing students to explore independently and learn actively.
The general idea of "learning plan guiding learning" teaching
Students read the textbook carefully according to the study plan designed by the teacher, and then complete the relevant content according to the requirements of the study plan. Students can put forward their own opinions, and teachers and students can study together. With the help of "learning plan", students can learn independently, master basic knowledge and concepts, sort out knowledge clues, try to answer questions in "learning plan" with their mastered knowledge, conduct self-ability training or discussion and exchange, and make relevant learning records on "learning plan". Students can learn and master what they can do; The rest is solved in classroom teaching discussion, so as to improve classroom teaching efficiency.
Learning plan design requirements
1。 Composition of learning plan
The basic elements of learning plan include five aspects: clear learning objectives; Clear knowledge structure; Systematic cognitive method; Effective skills training; Conducive to ability expansion.
New teaching plan
General new teaching plans should include learning objectives, learning priorities, difficulties, learning activity design, standard exercises, homework, etc. When designing a study plan, the emphasis should be placed on the "design of learning activities", including the guidance of learning content and learning methods (such as observation, recording, association, comparison, reasoning, induction, thinking, discussion, etc.). ), but also need to develop what kind of thinking methods to cultivate students, what kind of subject ability to cultivate, what kind of problem-solving methods to guide, so that the static learning content is dynamic.
Review the course plan
The compilation of the review lesson plan should reflect the characteristics of the topic, and its content should include the following four elements: learning objectives, knowledge structure, cognitive methods and skill training.
Basic requirements of learning plan design
1。 Pay attention to the guiding role of learning plan
When designing the study plan, we should fully consider each student's personality and cognitive level. When designing and compiling a study plan, we should adopt various ways and methods in a timely and appropriate manner according to the teaching content, and treat the difficult and chaotic content into an orderly and step-by-step study plan that conforms to the students' cognitive laws. Through the scientific, inspiring and interesting problem design and scenario design of the learning plan, a strong situational atmosphere is created to let students enter the role.
2。 Pay attention to the problem string design
According to students' cognitive rules, the knowledge points are divided and combined, and different levels of questions are designed to make the learning content problematic and show the process of knowledge occurrence. Under the guidance of questions, students teach themselves textbooks, answer questions and explore by themselves, so that students can form clear learning ideas, turn knowledge points into exploratory questions and ability points, and cultivate students' ability and innovative quality through questioning, questioning, dispelling doubts and inspiring thinking about knowledge points.
3。 Pay attention to the collation and induction of knowledge
The knowledge system of middle school mathematics is complete and logical, but many students really feel that their knowledge is fragmentary and difficult to master. Teachers should rearrange, summarize and sort out their ideas in the design of learning plans, and find a breakthrough in knowledge, so that knowledge can be systematized more easily and accepted by students more easily.
4。 Strengthen the guidance of learning methods and ability training.
While guiding students to form basic learning methods, we should attach importance to students' developmental learning and let students use the learned methods to solve new situations and problems. The study plan should pay attention to the deepening and migration of textbook knowledge, and should not be a copy of book content.
5。 Design of exercises and homework
According to the formation process of knowledge, some topics such as choosing, filling in the blanks and judging are set up, so that students can practice on the basis of trying, so as to better grasp the connotation of the concept and form a clear and complete concept. The design of exercises should be closely related to the teaching content, ability training objectives and students' cognitive level. When practicing problem design, we should pay more attention to dispelling doubts. In the process of no doubt-doubt-doubt, students can learn from the unknown, from the shallow to the deep, from the outside to the inside, so as to master knowledge and improve their learning ability. Homework is the extension and supplement of textbook exercises, which strengthens the exploration of textbook examples and exercises, and fully excavates the value function of textbook examples and exercises.
Unity and cooperation, give full play to the role of groups.
This teaching mode has high requirements for teachers and high labor intensity, which can be better completed by relying on collective strength, collective preparation and mutual cooperation. In the process of compiling the study plan, we give full play to the spirit of group cooperation. At the beginning of the semester, the project research leader decomposed the task of compiling this semester's learning plan into the design of situation introduction in the mathematics learning plan of senior one and senior two and the exploration of examples and exercises in the mathematics learning plan of senior one and senior two; The design of exercises and homework in the math study plan of senior one and senior two: the design of knowledge structure and cognitive method in the math review plan of senior three: the design of skill training and the compilation of overall design in the math review plan of senior three.
The compilation of learning plan is the key to the success of "learning plan guidance", and an excellent learning plan should play the following roles: (1) stimulate motivation and imagination; (2) Close to the teaching materials and broaden our horizons; (3) Pay attention to learning methods and cultivate abilities; (4) Omni-directional and multi-level; (5) The structure is reasonable and the operation is convenient. This is also what we need to study and work hard in the design and compilation of the study plan in the future.