(1) Make plans, (2) preview before class, (3) listen carefully, (4) review in time, (5) work independently, (6) solve problems, (7) summarize systematically and (8) study after class.
This method is summed up through the investigation of 200 excellent middle school students, 40 junior college students of Huazhong University of Science and Technology and 60 college students admitted to Wuhan University with high scores. As long as a student can learn according to these eight links and implement them step by step, he will become the master of learning and an excellent student in the class.
2. If you want to finish a math learning task clearly, you need to finish it step by step in order to master the knowledge firmly. Because the process of mathematics learning is a complicated cognitive process, all the steps must be completed in order to complete a mathematics learning task and truly master knowledge. In psychology, the cognitive process is generally divided into four basic stages: perception, understanding, consolidation and application. In the four-round learning strategy, a class is also divided into four rounds. The first round: preview. The second round: class, breaking obstacles; The third round: review and remove obstacles; The fourth round: homework, apply what you have learned. In fact, these four rounds correspond to the perception, understanding, consolidation and application of the above cognitive processes. Although the angle is different, there are four stages, and the learning requirements of each step are very similar. Preview is for the initial perception of a lesson, lecture is for a better understanding of the text, review is for consolidation, and homework is for applying what you have learned. Four-round learning strategy is popular in recent years.
There are other ways to learn. According to different learning situations, the learning process is divided into four steps and five steps. Students can choose according to the characteristics of what they have learned, and even create their own learning steps, such as reading, listening, writing and practicing, and then browse, ask questions, read, repeat and review the five-step learning method.
3. Make clear how to learn in order to truly master knowledge. Considering mathematical knowledge as a system, the structure of mathematical knowledge has four elements, namely, facts, reasons, things and things. Specifically, according to the different levels of knowledge structure, these four elements can be listed as follows:
Four things, facts, reasons, applications, materials, problems, topics, topics, topic methods, topic paths, questions, what, why, how to use, what inspiration, concepts, names, definitions, judgments, relationships, theorems, conditional conclusion proofs, applications, methods, formulas, expressions, deduction, calculation and connection.
In our opinion, no matter what level of knowledge we learn, we should master the corresponding four elements. If you only know "what" and don't know "why", you can't understand the principle of the conclusion. If you only know theoretical knowledge and don't know how to use it, it will become useless knowledge. If there is no clear thinking, the knowledge points are not closely linked and scattered, then the knowledge is not solid and the foundation is not solid, so it is difficult to innovate when learning new knowledge.
4. Clear from what aspects to learn a mathematical concept, theorem and formula. In the process of learning mathematics, there are always a lot of concepts, theorems and formulas. How can we really master them? Teachers should clearly point out what kind of process is needed, what kind of requirements should be met, and what aspects should be understood and mastered in general.
Learning methods of mathematical concepts.
Mathematical concept is a form of thinking that reflects the essential attributes of mathematical objects. Its definition is descriptive, denotative and conceptual addition difference. A mathematical concept needs to remember its name, describe its essential attributes, realize the scope involved, and make accurate judgments by applying the concept. Without teachers' requirements and learning methods, it is difficult for students to study normally.
Let's summarize the learning methods of mathematical concepts.
Read the introduction and remember the name or symbol.
Recite the definition and master the characteristics.
Give two positive and negative examples to understand the scope of conceptual reflection.
(4) Practice and judge accurately.
⑤ Compare with other concepts and find out the relationship between them.
2. Learning methods of mathematical formulas.
The formula is abstract, and the letters in the formula represent infinite numbers in a certain range. Some students can master the formula in a short time, and some students have to experience it repeatedly to jump out of the ever-changing mud pile of numerical relations. Teachers should clearly tell students the steps needed in the process of learning formulas, so that students can master formulas quickly and smoothly.
The learning method of the mathematical formula we introduced is:
(1) Write the formula and remember the relationship between the letters in the formula.
⑵ Understand the cause and effect of the formula and master the derivation process.
⑶ Check the formula with numbers and experience the laws reflected by the formula in the process of concretization.
⑷ Transform the formula to understand its different forms.
⑤ Imagine the letters in the formula as an abstract framework to use the formula freely.
Learning methods of mathematical theorems.
A definite reason consists of two parts: conditions and conclusions. This theorem must be proved. Proving process is a bridge between conditions and conclusions, and learning theorem is to better apply it to solve various problems.
Let's summarize the learning methods of mathematical theorems:
(1) Recite Theorem.
⑵ Conditions and conclusions of the distinguishing theorem.
(3) the proof process of understanding theorem
(4) Applying theorems to prove related problems.
5. Understand the internal relations between theorems and related theorems and concepts.
Some theorems contain formulas, such as Vieta theorem, Pythagorean theorem and sine theorem, and their learning should be combined with formula learning methods.
5. Learn the method of self-study.
Self-study refers to a person's conscious activity of mastering knowledge, applying knowledge and acquiring skills independently without the help of others. Self-study is the best learning method in life, which mainly includes independent reading, independent thinking, self-organization, self-examination and self-supervision, and flexible use of knowledge to solve problems.
How can we effectively cultivate and develop students' mathematics self-study ability and form self-study ability? Wu Chuanhan put forward "self-study for ten times" in his "Learning Methods of Mathematics", that is, reading independently for a while and going in and out for a while; Three mistakes will win; Fourth, focus on energy; Five self-selected topics; Six will find their own materials; Seven will solve the problem; Eight will learn from others; Nine will make rational use of time; Ten will evaluate themselves.
There are several learning methods related to self-study, which are popular abroad. For example, fractional learning is an efficient and comprehensive learning method created by American scholars, which is popular all over the world. The specific steps are: browsing, copying titles, setting goals, reading and evaluating. Another learning method similar to this is also created by Americans, and it is called SQL2R learning method. Its specific steps are browsing, asking questions, reciting and reviewing.
In the process of self-learning mathematics textbooks, according to the characteristics of mathematics, we respectively put forward two methods: algebra self-learning and geometry self-learning:
Algebraic learning method.
(1) Copy the title, browse and set the target.
⑵ Read and record the key contents.
Try to do an example. Do exercises quickly and summarize the questions.
5] Memory summary.
Four steps of geometry learning.
(1).( 1) Write the topic and browse the teaching materials; (2) Teach yourself and write the contents;
⑵. ① Read the teaching materials according to the catalogue, ② Teach yourself geometric concepts and theorems;
(3).① Reading examples to form ideas, ② Writing out the process of solving problems;
(4).① Do the problem quickly, ② Summarize the method of solving the problem.