Mathematics is a very important basic subject, especially in understanding physical concepts, physical laws and solving physical problems, mathematical knowledge plays an important role as a tool. Some junior high school students learn mathematics well, but they may not learn physics well, because these students often use pure mathematical thinking to understand physical concepts, laws or solve physical problems, which leads to mistakes in applying mathematical knowledge to solve physical problems. The effective way to solve the above problems is to transform physical problems into mathematical problems and effectively use mathematical knowledge to solve physical problems. 1. Use mathematical expressions to express physical concepts and laws, and use letters to express physical quantities, known quantities and unknown quantities. When junior high school students begin to learn physics, they are often not used to using symbols to express the relationship between physical quantities. They will not use the symbols of these physical quantities to express the corresponding digital information. It is unclear which symbols in the formula are known and which are unknown, which leads to formula deformation errors, formula confusion and physical results errors. Solution: (1) First, guide students to learn the method of "examining questions → scalar → choosing formulas". That is, while reading the topic, students mark the symbols of the corresponding physical quantities under the corresponding numbers. The purpose of this is to make clear the known quantity and the unknown quantity, and then choose the appropriate formula to solve the physical problem according to the situation. (2) Stress the "three-step method" when solving problems, that is, "formula → data (number+unit) → result (number+unit)". In order to let students know that physical formulas are the important basis for solving physical problems, we should write out the formulas first, then bring in the corresponding numbers and units, and then calculate the results with mathematical knowledge. (3) Physical quantities are represented by prescribed symbols, and students often cannot associate letters with the physical quantities they represent. For example, the unknowns in mathematics can all be represented by X and Y. Sometimes when students solve physical problems, no matter which physical quantity they seek, they all use X and Y. The physical meaning is difficult to understand. When analyzing the problem, ask them to write the symbol representing the physical quantity beside it, and then see which quantity is found, and use the letter marked by him beside it. Through continuous strengthening and practice, students can learn to use mathematical ability to solve physical problems, and their understanding of symbols can be changed from unfamiliar to flexible. Second, use equations to express physical relations and solve physical problems. Students often do equations to solve equations in mathematics, but they can't solve physical relations. Solution: Teachers should teach students to organically combine the concepts of physical relations and mathematical equations, so that students can understand that physical relations actually give concrete and practical contents to the concepts of equations. On the basis of establishing physical situation, we use mathematical methods to solve physical problems. For example, an iron block with a volume of 10cm3 is carried by a spring dynamometer and does not touch the bottom when immersed in water. What is the reading of the spring dynamometer at this time? Guide the students to analyze: to find the instructions of the spring dynamometer is actually to find out how much the iron block has been pulled up in the water. (1) force analysis, and draw the force diagram, as shown in the figure: gravity, buoyancy, tension. (2) Guide students to analyze what quantities can be obtained: for example, F-float = ρ water gV iron, G=ρ iron gV iron (3) Establish a force balance formula F-pull+F-float =G (4) Substitute it for solving F-pull =G+F-float, and we can see that the force balance formula in physics is actually an equation in mathematics. Through example analysis and training, students gradually strengthen the consciousness of combining mathematics with physics, and can consciously and flexibly transform physical problems into mathematical problems that are restricted by physical laws and express physical laws and physical situations. Thirdly, the unit conversion is carried out by using the idea of equivalent replacement of fractional properties. Beginners in physics become obstacles to learning physics knowledge in unit conversion. Solution: Let students understand the unit conversion in physics first, which is actually the embodiment of the idea of equivalent substitution in mathematics, and then let students understand the basic conversion relationship of memory. For example, the unit conversion of speed, guide students to use mathematical methods: (1) numerator and denominator are changed separately, for example, 20m/s = 20 = 72km/h(2) use rate method:1m/s = 3.6km/h20m/s = 203.6km/h = 72km. Fourth, distinguish between physical average and mathematical average. Students' understanding of the concept of average in physics often stays in the idea of average in mathematics, without paying attention to the conditions and scope of application, which leads to wrong results. Solution: Teachers should guide students to understand the difference between the concepts of average in physics and average in mathematics, and pay special attention to the applicable conditions and scope of the formula. For example, to solve the problem of average speed, in principle, S stands for the total distance and T stands for the total time (1) when an object moves in a straight line, the speed in the first half is 1 and the speed in the second half is 2. Find the overall average speed. The implicit condition is S 1 = S2 = S, but some students don't understand the meaning of average speed in physics, so they directly use the idea of average in mathematics to solve problems and draw wrong conclusions. (2) When an object moves in a straight line, the speed in the first half is 1, and the speed in the second half is 2. Find the average speed of the whole process. The implicit condition is t 1=t2 = t Another example is to measure resistance by voltammetry. It is of practical significance to calculate the average resistance value by using the mathematical weighting method of multiple measurements. The average value of electric power has no practical significance. It can be seen that when applying mathematical knowledge to analyze physical problems, we should pay special attention to the particularity of physics, the physical meaning of concepts and the conditions for the establishment of laws. Therefore, in physics teaching, we should strengthen the guidance of physical meaning, physical connotation, formula formation process and the conditions for the establishment of physical laws, so that students can properly and flexibly apply mathematical knowledge to solve physical problems on a solid physical basis. 5. Use function images to understand physical meaning. The relationship between physical laws and physical quantities can be represented by images. However, some students can't connect function images with physical knowledge, which makes it difficult to solve physical problems. Solution: First, let students know what physical quantities the abscissa and ordinate represent respectively, and then analyze the physical meaning represented by this image. For example, in an image of a proportional function, the slope indicates that the density ρ=m/v, that is, m is directly proportional to v, which means that the volume of the same substance has increased many times, and the ratio is inconvenient. This ratio is density. This helps students understand that density is a property of matter. In a word, the effective way to solve physical problems with mathematical knowledge is to transfer mathematical knowledge and mathematical thinking methods to learning physics. Therefore, teachers should strengthen the combination of mathematical knowledge in teaching, promote the transfer of mathematical knowledge by using multi-channel effective ways, and enable students to better use mathematical knowledge to solve physical problems.