Eight methods to improve mathematical thinking
? 1
Conversion method
Transformation is both a method and a thinking. Transformational thinking refers to changing the direction of the problem from one form to another from different angles when encountering obstacles in the process of solving problems, and seeking the best way to make the problem simpler and clearer.
2
logical method
Logic is the foundation of all thinking. Logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, generalize, judge and reason things with the help of concepts, judgments and reasoning in the process of cognition. Logical thinking is widely used to solve logical reasoning problems.
three
Reverse method
Reverse thinking, also known as divergent thinking, is a way of thinking about common things or opinions that seem to have become conclusive. Dare to "do the opposite", let thinking develop in the opposite direction, conduct in-depth exploration from the opposite side of the problem, establish new concepts and shape new images.
four
Corresponding method
Corresponding thinking is a way of thinking that establishes a direct connection between quantitative relations (including quantity difference, quantity times and quantity rate). General correspondence (such as the sum and difference times of two or more quantities) and ratio correspondence are more common.
five
Innovative way
Innovative thinking refers to the thinking process of solving problems with novel and original methods. Through this kind of thinking, we can break through the boundaries of conventional thinking, think about problems with unconventional or even unconventional methods and perspectives, and come up with unique solutions. It can be divided into four types: difference type, exploration type, optimization type and negative type.
six
Systematic research method
Systematic thinking is also called holistic thinking. Systematic thinking refers to having a systematic understanding of the knowledge points involved in a specific topic when solving a problem, that is, analyzing and judging what the knowledge points belong to when getting the topic, and then recalling what types of such questions are divided into and the corresponding solutions.
seven
analogy procedure
Analogical thinking refers to the thinking method of comparing unfamiliar and unfamiliar problems with familiar problems or other things according to some similar properties between things, discovering the essence of knowledge, finding its essence, and thus solving problems.
eight
method of images
Thinking in images mainly refers to people's choice of images in the process of understanding the world, and refers to the thinking method of solving problems with intuitive images. Imagination is the advanced form and basic method of thinking in images.
Error-prone knowledge points of numbers and formulas
Error-prone point 1: The concepts of rational number, irrational number and real number are misunderstood, and the meanings of reciprocal, reciprocal and absolute value are confused. And the classification of absolute value and quantity. Choose a compulsory exam every year.
Error-prone point 2: The key to real number operation is to master the concepts and properties related to real numbers and flexibly use various algorithms. In more complex operations, the order of operations is not paid attention to or the algorithm is used unreasonably, which leads to errors in operations.
Error-prone point 3: the difference between square root, arithmetic square root and cubic root. Fill in the blanks must be tested.
Error-prone point 4: When the score value is zero, students tend to ignore that the denominator cannot be zero.
Error-prone point 5: Pay attention to the change of algorithm and symbol when calculating the score. When the denominator of a fraction is a polynomial, factorization should be carried out first, and then factorization should be carried out until it can no longer be decomposed. Pay attention to the calculation method, you can't remove the denominator and turn the fraction into the simplest fraction. Fill in the blanks must be tested.
Error-prone point 6: the nature of non-negative numbers: the sum of several non-negative numbers is 0, and each formula is 0; Integral replacement method; A completely smooth road.
Error-prone point 7: The first calculation problem must be tested. Calculation of five basic numbers: 0 exponent, trigonometric function, absolute value, negative exponent and simplification of quadratic root.
Error-prone point 8: scientific notation. Precision, significant number. I haven't taken the exam in Shanghai yet. It's good to know!
Error-prone point 9: Substitution evaluation should make the formula meaningful. To master the calculation methods of various numbers, we must pay attention to the calculation order.