Memory method of mathematical knowledge 1. Formula memory method
In middle school mathematics, some methods can help memory if they can be composed into rhymes or songs. For example, according to the unary quadratic inequality AX2+BX+C >; 0(a & gt； 0，△& gt； 0) and ax2+bx+c
Memorizing methods of mathematical knowledge II. Image memory method
Some knowledge, if you can use graphics, can strengthen your memory. For example, the transformation function y = asinx+bcosx (a >; 0, b>0) is a trigonometric function of an angle. Using A and B as right angles, images of number and logarithm functions can be made, which is helpful to remember its properties, definition range and value range. Using the image of trigonometric function is helpful to remember the nature, symbol, definition, scope, increase and decrease, periodicity and evaluation of trigonometric function. Using the image of quadratic function is helpful to remember the opening, vertex, symmetry axis and extreme value of parabola.
Memorizing methods of mathematical knowledge III. Tabular memory method
Some knowledge can also be remembered with the help of tables. Like 0? 、30? 、45? 、60? 、90? Trigonometric function value of equal special angle; The definition, general form, general term formula an, sum sn properties of the first n terms and matters needing attention of arithmetic and geometric series; Definition, image, domain, range and properties of exponential function and logarithmic function; Definition, image, domain, principal value interval, increase and decrease of inverse trigonometric function and related formulas; The general formula of the simplest trigonometric equation, etc. , you can use the table to remember. Some methods to solve mathematical problems can also be simplified by tables. For example, it is a good method to solve product or fractional inequality, equation or inequality with absolute value sign, polynomial multiplication, rational root of integral coefficient equation, etc. This memory method should be especially advocated in review.
Memory method of mathematical knowledge 4. Associative memory method
New knowledge can be linked with old knowledge that has been firmly memorized, and analogy can be used to help memory. For example, the relationship between roots and coefficients of higher-order equations can be compared with Vieta's theorem of quadratic equations to help memory; The factorization theorem of univariate polynomial of degree n can be compared with the factorization theorem of quadratic trinomial to help memory. Solutions to some math problems can also be remembered by association. For example, considering the order of real numbers, we can easily write the product inequality (2x+1) (x-3) (x-1) (2x+5).
A series of solutions of the equation. When writing the solution of this interval, the solutions of other intervals can be written smoothly forward every other interval. It can be seen that it is very convenient to solve the product or fractional inequality by using the order of real numbers after changing the coefficient of x in each linear factor into a positive number.
Memory method of mathematical knowledge. Classified memory method
When there are many mathematical formulas that are difficult to remember for a while, these formulas can be grouped appropriately. For example, the derivative formula of 18 can be divided into four groups: (1) constant and derivative of power function (2); (2) Derivatives of exponential and logarithmic functions (4); (3) Derivative of trigonometric function (6); (4) The derivative of the inverse trigonometric function (6). There are seven derivative rules, which are divided into two groups: (1) and derivative of the composite function of difference, product and quotient (4); (2) Derivatives of inverse function, implicit function and power exponential function (3).
Memory method of mathematical knowledge. Dos? mnemonics
Generally speaking, it needs repeated perception many times to make the memory object unforgettable for a long time. ? Dos? Reading, listening, reading and writing. Especially when reading and writing silently, the memory effect is better. For example, A simply copied a set of formulas four times, and B copied the same set of formulas twice and then wrote it by heart (you can read a book if you can't write it by heart). Experiments show that the memory effect of B is better than that of A.
Memory method of mathematical knowledge. Meditation memory method
Memory should start with calmness, and according to certain memory goals, find out the memory methods suitable for your own learning characteristics. For example, the choice of memory environment varies from person to person. Some people think they have a good memory in the morning; Some people think they have a good memory at night; Some people are used to reading and remembering while walking; Some people have to remember in a quiet environment and so on. No matter which way you choose to remember, you should keep it. Quiet? . A calm mind can concentrate on memory, and a calm mind can form the explicit excitement center of memory. Memory needs to start from silence!
Memory method of mathematical knowledge. First memory method
There are four ways to remember first:
1) Reciting mnemonics. Reciting and memorizing the operation process and results on the basis of understanding is called memorizing. For example, the laws of addition and multiplication, the sum of two numbers, the square of difference, and the expansion of cube are all memories.
2) Model memory method. There is a lot of mathematical knowledge with its concrete model, which we can remember. Some mathematical knowledge can be listed in charts regularly and memorized by charts. These memories are called model memories.
For example, remember the special angle of 30? ,45? ,60? The trigonometric function value of can be memorized by two models.
3) Differential memory method. Some mathematical knowledge has a great relationship with several opposite sex. To remember them, you only need to remember one basic and different feature, and you can remember everything else. This kind of memory is called differential memory.
For example, the definition of parallelogram, rhombus, rectangle and square, we just need to remember the definition of parallelogram and the distinguishing features between them.
4) Reasoning memory method. The logical relationship between many mathematical knowledge is obvious. To remember this knowledge, we only need to remember one, and the rest can be obtained by reasoning. This kind of memory is called inferential memory.
For example, we only need to remember the definition of parallelogram, and we can deduce that any diagonal of parallelogram is divided into two congruent triangles, and then we can deduce that its opposite sides are equal, its diagonal lines are equal, its adjacent angles are complementary, and its two diagonals are equally divided.
Memory method of mathematical knowledge. Repeated memory
There are three ways to repeat memory.
1) notation. When learning a chapter, read it first. For important parts, draw wavy lines with colored pens below. When repeating memories, you don't need to read the whole chapter word by word from beginning to end As long as you see the wavy line, you can retell the main contents of this chapter under its inspiration. This kind of memory is called symbolic memory.
2) Memory method. When memorizing a chapter repeatedly, we don't look at the specific content, but achieve the purpose of memory through brain memory. This kind of memory is called recall memory. In actual memory, recall memory method and mark memory method are used together.
3) Use the mnemonic method. When solving math problems, you must use the knowledge you have memorized. Once you use the relevant knowledge, you will be memorized again. This kind of memory is called using memory. Using mnemonic method is a kind of positive memory with good effect.
Memory method of mathematical knowledge 10. understand membery
Understanding knowledge is the basic condition of memory, especially for mathematical knowledge, we should remember it by understanding and mastering its logical structure system. Because mathematics is a subject based on logic, its concepts, laws, theorems and formulas are all in a certain logical system. Therefore, the understanding and memory of mathematical knowledge mainly lies in sorting out the logical connection of mathematical knowledge and grasping its context. Only what is understood can be firmly remembered. Therefore, the theorems, formulas and laws in mathematics must be understood in their context and their proof process, so as to be firmly remembered.