How to Improve the Ability to Solve Mathematical Comprehensive Problems [New Theory of Evaluation] The mathematical comprehensive problems of Li Yan 1864 words are generally understood as problems involving many mathematical knowledge points, many problem-solving methods and strategies, complex background and high ability requirements. According to the different degree of synthesis, it can be divided into two types: one with higher comprehensive difficulty and the other with lower comprehensive difficulty. In the usual exam or college entrance examination, many candidates doubt that they are incapable of doing it even if they have enough time to solve it, so it is easy to give up, which often leads to unsatisfactory math scores. To improve the ability to solve mathematical comprehensive problems, we should mainly start from the following aspects: (1) Firmly consolidate the "three basics", grasp the "three natures" and fully tap the "three basics" contained in mathematical comprehensive problems. The three basics refer to basic knowledge, basic skills and basic mathematical thinking methods. The investigation of "three basics" in college entrance examination requires a deep understanding of concepts, accurate and skilled operation, and correct and flexible methods. The basic thinking method of mathematics is as important and basic as basic knowledge and skills. It plays a very important role in mathematical decision. It enables students to make a basic judgment on the problem, prompt the possible direction to solve the problem, and enable students to quickly formulate strategies to turn uncertain decisions into risky ones. Therefore, we should pay attention to consolidating the "three basics" when studying at ordinary times. Comprehensive questions from the topic to the conclusion, from the question type to the content, the conditions are hidden and varied. Therefore, it determines the diversity of test questions design, and we should grasp the "three characteristics" when examining the questions, that is, (1) purpose: make clear the ultimate goal of solving the problem and the sub-goals of each step; (2) Accuracy: improve the accuracy of mastering mathematical concepts, formulas, axioms and theorems and the accuracy of operations; ⑶ Implicitness: Pay attention to the implication of conditions. This step of reviewing questions seems to be quite time-consuming, but it is not. When dealing with it, we should calmly and seriously grasp the direction of solving problems and rationally use the means of solving problems, which is the necessary premise and guarantee to improve the speed and accuracy of solving problems. (2) Attention should be paid to the novelty and flexibility of mathematics test questions in recent years. Many students focus on the more difficult comprehensive problems, thinking that only by solving difficult problems can they cultivate their abilities, thus ignoring the mastery of basic knowledge, basic skills and basic methods. This is a very wrong approach. Comprehensive questions are based on basic questions. Only by returning to textbooks at ordinary times and integrating exercise resources for variant learning. When reviewing, return to textbooks and fully tap the typical functions of textbooks and exercises. Through proper grafting, expansion, extension, variation and synthesis, the understanding and mastery of core concepts and core mathematical ideas are strengthened, so as to enhance knowledge understanding and cultivate mathematical thinking ability. At the same time, we should also strengthen the training of general calculation questions and proof questions. Every time we finish a problem, we can have a deeper reflection and association on such problems, such as the content it examines, the mathematical thinking methods used, the laws and skills of solving problems, etc. (3) We should pay attention to summing up and accumulating some general calculation problems and proof problems, especially the derivation process of some mathematical formulas and theorems, which itself contains important problem-solving methods and laws. When answering, students should pay attention to the thinking strategy of solving problems and often think about what angle to choose and what principles to follow. After doing the problem, you should learn to summarize and classify from multiple angles and levels: for example, (1) classifies from mathematical ideas; (2) Classification from problem-solving methods; (3) Classification of knowledge application, etc. To make the learned knowledge systematic, organized, thematic and networked. Usually, if students accumulate more methods and laws and apply them to solving comprehensive problems, they will certainly broaden their thinking and improve their ability to solve problems, thus laying a solid foundation for solving comprehensive problems of mathematics in college entrance examination. (4) Consciously improving one's various abilities, namely, calculating ability, logical thinking ability, abstract thinking ability, spatial imagination ability and problem solving ability, are the five abilities of senior high school mathematics. Spatial imagination, in particular, is the ability to purify thinking through examples, abstract entities in space in the brain, and analyze and reason in the brain. Especially for those liberal arts students whose foundation is not very solid, it is not easy to improve their spatial imagination. In fact, the solution is simple: (1) observe more; (2) Try to reproduce what you see in your mind; (3) Imagine a cube or other basic three-dimensional object, make it rotate, add shadows, etc. The improvement of these abilities needs a process from easy to difficult, from simple to complex. In order to help students cultivate these abilities, teachers will always carefully design some good class types, such as multi-solution to one question, changeable questions or multimedia teaching such as applying models and computers. In these courses, students must devote themselves to all aspects of intelligence. Learning is good at moving problems from one background to another, so as to achieve the effect of drawing inferences from others, which not only deepens the understanding and mastery of basic knowledge, but also plays a unique role in developing intelligence and cultivating and improving problem-solving ability. In addition, we should gradually improve our own requirements in our usual study, step by step, and gradually improve our abilities in all aspects. In a word, comprehensive questions are the essence of mathematics test questions in college entrance examination, which have the characteristics of large amount of knowledge, many problem-solving methods, high ability requirements, highlighting the application of mathematical thinking methods, and requiring candidates to have certain innovative consciousness and ability. Therefore, when students solve comprehensive mathematics problems, they should first adjust their psychology, be calm and calm, and face it with a normal heart; Secondly, we must have the determination and confidence not to give up easily to explore; Finally, we must grasp the law and find a breakthrough to solve the problem. Only in this way can we change constantly and make a breakthrough in solving comprehensive problems.