"Application" is a dynamic concept and an indispensable link in the process from knowledge to ability to quality. At the same time, this is also a comprehensive process that does not divide the region into chapters.
Therefore, if you want to prepare for math class, you must pay attention to the following aspects:
First, understand the knowledge system and teach students in accordance with their aptitude
A systematic understanding of the knowledge system The "systematic understanding" mentioned here is not to let teachers know what a chapter or chapter is, but to ask teachers to carefully study the development history of mathematics, and repeatedly inspect the knowledge system of existing textbooks (mainly referring to the position and function of each knowledge point in the whole knowledge system and their internal relations), the latest research results of elementary and advanced mathematics at home and abroad, and the practical application and future development trend of mathematics in other marginal disciplines and social fields.
After careful discussion of the internal relations, it can be found that compared with other disciplines, mathematics textbooks are relatively stable, and it can be said that it is common to use one version for several years. This provides a very favorable condition for teachers to better explore the internal relations among textbooks, chapters, sections and knowledge points. Without connection, there is no mathematics. A detailed mathematical system has incomparable internal relations with any other discipline: the derivation of formulas and rules, the introduction of theorems and axioms, the combination of numbers and shapes, the establishment of three-dimensional sense, and so on.
Paying attention to the ability requirements of "sustainable development" is not a new topic. To realize the sustainable development of talents, the cultivation of ability is very important. Mathematical ability is usually divided into general ability and professional ability, among which general ability includes: observation, understanding, memory, application, etc. Professional abilities include: calculation ability, logical thinking ability, reasoning and proof ability, spatial imagination ability and so on. The cultivation of different abilities often requires different methods. Therefore, before imparting knowledge, teachers must be clear about the ability requirements, so as to be targeted and targeted.
To fully implement the strategy of teaching students in accordance with their aptitude, each student has his own characteristics, and it is obviously unrealistic to "unify all students" with a teaching plan. The lesson plan must be oriented to all students, which requires the content of the lesson plan to have a considerable "gradient". This kind of "gradient" should make students with good foundation "endless". Leave some thoughtful questions as a continuation of the class content; Let students with relatively poor foundation "eat well and be reluctant to leave"
Let students find self-confidence and sense of accomplishment in simple topics. Whether to teach students in accordance with their aptitude is an important aspect to test teachers' ability to control the classroom and teaching level, and it is also a prerequisite for preparing math lessons.
Second, the organic unity of content and method.
Reasonable arrangement, optimization and reorganization (content) There is a saying: "Books are dead, people are alive." Because the local cultural heritage is thick and thin, the teaching quality is high and low, and the large-scale unification of teaching materials means that their pertinence is weakened, so the content of teaching materials can only be used as the main reference, not the only standard. From the ultimate goal of education, students should learn some aspects of the knowledge system, not what version of the textbook. Therefore, it is very necessary to arrange, optimize and reorganize the relevant contents in the textbook according to the specific situation of students when preparing lessons.
People-oriented, according to the needs of distribution (object) Mencius said: "The mind of the official thinking, thinking is obtained. Not without thinking. " The process of learning is a process of integrating, updating and expanding the original knowledge system, and it is also a dynamic, arduous and irreplaceable psychological process. In order to achieve the expected teaching effect, we must follow the principle of "people-oriented, distribution according to needs" when preparing lessons, find the breakthrough point of "teaching" and "learning", and stimulate, cultivate and satisfy all students' interest in learning mathematics.
Happy education, moderate tension (psychology) Confucius once said: "Knowing is not as good as being kind, and being kind is not as good as being happy." (see the Analects of Confucius). It can be seen that the process of preparing lessons for teachers is essentially a process in which "directors" use various "props" to form various considerable and sensible information sources. Only when the course arrangement is clever and the classroom setting is reasonable can we give students a variety of benign sensory stimuli and induce them appropriately, so that they can improve their minds comprehensively and quickly under the joint action of happy education and moderate tension.
Take advantage of the situation, step by step (method) Mathematics is famous for its unique "rigor", which means that its logical system is "inseparable". This "inseparable" feature determines the integrity, connectivity and order of mathematics teaching process. Any idea of "once and for all" and "reaching heaven in one step" is unrealistic. Only teachers can guide students step by step according to the situation. This "potential" often includes students' age characteristics (physiological age, psychological age, social age), knowledge structure (different stages of the same subject, the same stage of different subjects, different stages of different subjects), cognitive level (intellectual factors, non-intellectual factors), etc. The methods of "guidance" are: inspiration, suggestion, interaction, praise, correction and so on.
3. "Scattered in form but scattered in spirit" is the highest realm of prose art and teaching art.
There is no loophole in the limited space. "Skynet" As the saying goes, "Skynet is long and slow, but it does not leak." Every lesson plan should be an endless "skynet". Although the teaching plan can't cover everything in content and form, it should be an omnipresent skynet in knowledge, ability, skill and even quality. Never let any opportunity conducive to students' development disappear in the "blind spot" of the teaching plan. In order to weave and make good use of this "net", teachers' "cultivation" is very important, which requires teachers to have a complete knowledge system, strong organizational ability, good foresight and emergency ability.
Mathematical beauty and "showmanship" and "boredom" are recognized mathematical characteristics, and there is a saying that "mathematics is boring, physics is difficult, and chemistry is fun". Maybe mathematics is a little annoying sometimes, but behind it, there are often "wonderful mathematics" hidden one after another. The reason why this wonderful is not often perceived by the vast majority of people is mainly because people lack the literacy of a certain aspect of mathematics. Mathematical beauty exists objectively, but sometimes there is a lack of eyes to find beauty. How can we show the beauty of mathematics to every student? "show" Exquisite packaging and moderate display can make students appreciate the beauty of mathematics and stimulate their interest in learning mathematics. Therefore, it is very important for students to "enter" and "lay out"-prepare lessons.
Mathematical model and its practical application "Mathematical model" is a formatted problem-solving model. In fact, the process of establishing the model is to combine the existing knowledge organically, so that students can have as much knowledge, skills and abilities as possible as soon as possible, and prepare for the contents, methods and means.
Because of the differences in teaching content, knowledge structure and difficulty, form dispersion and spirit dispersion are the same mathematical theme. When preparing lessons, the expression and techniques of lesson plans should also be changed: either highlighting nature, emphasizing graphics, marking symbols, or analyzing ideas, each with its own form, and so on. Sometimes a finishing touch, a superb number, an unusual formula and an unexpected idea may become an excellent teaching plan. This formulation may not be accepted by most people. In fact, the style of lesson plans often lies in her inner charm, not in the form. If the teacher only pays attention to "form", it is easy to make "metaphysical" mistakes and get "metaphysical" bitter fruit. There is every reason to think that "scattered in form but not scattered in spirit" is the highest realm of prose art and teaching art!