The above principles are interrelated and interdependent, and together form a harmonious whole. In the process of designing learning plan, these principles should be comprehensively applied to effectively improve the quality of learning plan design. 4. The content of learning plan design
4.2 Learning process The learning process includes five aspects: study preparation, reading inquiry, questioning, practice consolidation, reflection and expansion. Teachers' guidance on students' learning methods and students' questions in the learning process are not listed separately, but are organically integrated into the learning process in combination with the learning content. For example, the specific design of learning method guidance can be guided by guiding words such as "prompt", "suggestion", "attention" and "requirement", and teachers' learning requirements and suggestions and learning method guidance can be integrated into specific learning content to guide students to learn independently. 4.2. 1 The key to learning preparation lies in the understanding of knowledge, and the essence of understanding is to establish the internal connection between old and new knowledge and incorporate new knowledge into the original cognitive structure. In order to make the old and new knowledge interact and establish contact, the premise is to have the corresponding basic schema. The "study preparation" in the study plan is to establish a certain psychological foundation for students before learning new knowledge, and set up the corresponding basic schema to pave the way for learning new knowledge. Learning preparation includes knowledge preparation, tool preparation and emotional preparation. Knowledge preparation is mainly the knowledge reserve you should have when learning this section. In the study plan, students can be guided to introspect and review by asking questions, group exercises and suggestions, so as to clear the obstacles for learning new knowledge and play the role of "advance organizer". Emotional preparation is to create a learning situation, stimulate students' interest in learning, make students have the desire and heart to learn, and make emotional preparation for learning new knowledge. The desire and orientation of learning belong to the driving force of learning, and the role of emotional preparation is to stimulate students' internal driving force of learning, so that students have curiosity and desire for reading and self-study. For example, the "learning preparation" in the first section of the square formula can be designed as follows: "① You need to be familiar with the algorithms such as polynomial multiplication polynomial, power of power and power of product studied in this section, and you can check whether you are familiar with these rules before learning; ② Do students feel a little fussy when they use polynomial multiplication? Are you eager to have a formula that can get a quick result? After learning this section, your wish will come true! " The first is knowledge preparation, the main purpose of which is to clear away the knowledge obstacles in learning the square difference formula; The second is emotional preparation. When designing, we should put ourselves in the students' shoes and ask questions from their psychological needs of expecting a concise formula to stimulate their interest and desire in learning. 4.2.2 Reading inquiry teaching materials are divided into two parts: interpreting teaching materials and excavating teaching materials. First, interpret the textbook (read the textbook). This means that under the guidance of the study plan, students can read the teaching materials by themselves, including the understanding of the meanings of related nouns involved in concepts and formula theorems and the contents they express. As we know, what students learn is mainly book knowledge, that is, text knowledge in textbooks. The text knowledge expressed in the textbook is concise, abstract and logical, which is difficult for students to understand, so it is necessary to interpret the textbook. This kind of interpretation is manifested in the study plan, that is, the content that students are difficult to understand or are not sure about is decomposed into small questions that are easy for students to understand and accept after the teacher's interpretation, and then reflected in the study plan in the form of explanation, questioning or filling in the blanks, or pointing out the relevant reference materials that need to be consulted, so as to guide students to read the teaching materials and achieve an understanding of the meaning of the teaching materials. At this time, learning belongs to the category of meaningful acceptance of learning. In the concrete design of learning plan, we should design methods to guide students how to read textbooks, so as to guide students to read and understand textbooks effectively. Second, mining textbooks (read through textbooks). This means that under the guidance of the study plan, students explore, explore and summarize the mathematical ideas, methods and laws hidden behind the textbook knowledge content, so as to read the textbook through. Learning at this time belongs to the category of autonomous inquiry learning. Because the content of students' learning mainly comes from textbooks, we must dig deep into textbooks if we want to deeply understand and master what we have learned. The content of mining textbooks is: (1) the essential characteristics of knowledge. For example, the connotation and extension of concepts; Applicable conditions, characteristics and scope of formulas, theorems and laws; (2) The context of knowledge and its internal relations; (3) the potential value and function of knowledge; (4) The function and value of examples and exercises; (5) Mathematical thoughts, methods and laws hidden in knowledge. In the previous teaching, teachers generally excavated and processed the teaching materials, and then passed them on to students completely. Students' learning style is "listening to explanations-taking notes-doing homework", and students are completely passive. Although in this kind of teaching, students also have some thoughts, but the time for thinking is after the teacher explains, and some problems that can be solved independently are done by the teacher, which makes students' independent inquiry neither sufficient nor in-depth, thus affecting the cultivation of students' inquiry ability. When we talk about digging textbooks here, we mean that the teacher digs out the textbooks and then writes them in the study plan in the form of questions or blanks, so as to guide the students to dig by themselves, thus putting the students' thinking time before the teacher's explanation. According to the teacher's questions, students think independently and dig out the content of the textbook to answer, and then through the communication and discussion between teachers and students in class, they finally achieve a profound understanding and mastery of what they have learned. In this way, students can not only deeply understand the teaching materials, but also cultivate their reading comprehension ability and exploration and discovery ability. 4.2.3 Questioning students will have many problems that they still can't solve when they study according to the study plan; In the process of learning, there will be associations and conjectures about some problems; Questioning some questions and so on. , are effective teaching resources to cultivate students' problem awareness and innovation ability. Therefore, the study plan should require students to record the problems, doubts, associations and conjectures in self-study, so that students can walk into the classroom with questions. The advantages of doing this are: (1) it can make students focus on the unsolved problems in class and make the class more purposeful and targeted; (2) It can cultivate students' awareness of problems and innovation, and improve their ability to find, ask, analyze and solve problems; (3) It can enable students to gradually develop good self-study habits and master correct self-study methods. In the specific design, questions are not regarded as a separate column, but students are required to write down specific questions immediately for classroom discussion and communication. 4.2.4 After practicing and consolidating students' self-study textbooks, students can be guided to try to solve textbook exercises and consolidate their knowledge of digestion and learning; The second is to test the effect of self-study; Third, find the existing problems. At the same time, we should design some variant exercises at different levels to consolidate new knowledge, form skills and cultivate migration ability. 4.2.5 Reflection is an important part of learning. The main contents of reflection can be divided into three aspects: first, reflect on the gains and losses in your own learning and adjust your own learning strategies and methods; Second, reflect on the internal relationship between what you have learned and other knowledge, build a knowledge network and improve the cognitive structure; The third is to reflect on the process and methods of solving some mathematical problems and accumulate experience in mathematical activities. At the same time, on the basis of reflection, further extend and expand some knowledge, and extend the learning content and activities from in-class to after-class. 4.3 Standard Evaluation After learning the first section, a set of test questions is designed according to the content of this section, which is used for students' self-evaluation and finding problems, and it is also convenient for teachers to feedback students' learning effect in time, which is beneficial to teachers' teaching. 4.4 Resource links provide and introduce relevant learning materials in combination with learning content to guide students to consult and read after class. Through the evaluation of famous mathematical application cases, the introduction of mathematical technology, the link of network resources, the display of students' excellent mathematical application results, etc. Students can broaden their horizons, understand the applied value of mathematics and stimulate their interest and desire in applied mathematics. This can not only improve students' interest in reading, form the habit of reading mathematics, but also cultivate their awareness of applying mathematics. The above columns and contents are the general requirements of the mathematics learning plan, and some appropriate adjustments can be made when designing the specific content learning plan. For example, if the above columns are properly adjusted according to the characteristics and requirements of the problem-solving class, the columns of the learning plan of the problem-solving class can be obtained as follows: learning theme, learning goal, learning focus, learning process (learning preparation, typical example analysis, variant exercise, reflection and expansion), standard assessment, after-school homework and resource connection; According to the characteristics and teaching requirements of the review class, the columns of the general study plan can be adjusted appropriately, and the study plan columns of the review class can be obtained: learning theme, content analysis (current situation, interaction, examination requirements, etc. ), learning objectives, learning priorities, learning process (learning preparation, knowledge structure (frame structure, making necessary prompts), knowledge point arrangement, typical example analysis, variant exercises, reflection and expansion), and standard assessment. The main purpose of designing learning plans is to give full play to the functions of learning plans and improve the efficiency of teaching and learning. The main links of learning plan teaching are "guiding learning", "explaining" and "evaluating". This teaching mode is called "guided learning and comment teaching". Due to the limitation of space, the author will elaborate it in another article.