The two major difficulties in the second year of junior high school, geometry and function, are difficult because they are no longer competing for the meticulousness of calculation, but competing for logical thinking ability, which seems to increase suddenly, but it is a concentrated phenomenon of the thinking ability gap in the long-term learning process from primary school to the first year of junior high school, and the first year of junior high school is the key stage of improving thinking ability before the watershed of the second year of junior high school.
Although from the perspective of grades, it is still a competition for computing ability, which is the embodiment of the ability that can be recognized on the bright side, but the gap in thinking ability on the dark side has changed in Xiao Ran, and the dark side has become obvious in the second stage of junior high school, and there is a two-level differentiation in grades.
The first year of junior high school has begun to compete for thinking ability, but the previous learning mode can still replace thinking ability to get high scores, and the difficulty of the second year of junior high school has been improved, directly examining thinking ability, so that some students who still follow the thinking mode of primary school have begun to be uncomfortable.
Mathematics in the first semester of junior high school, although it is still embodied in algebraic calculations, but there is a corresponding way of thinking behind the calculation, such as the algebraic formula of the letter representing the number, if you don't understand its essence, you can still calculate the answer step by step, and the same is true for the inequality in the next semester, but if you just calculate, and don't understand the relationship between numbers, you will feel that it is difficult to understand when you enter the function part, and you don't have the ability to analyze the specific problems of the relationship between numbers and numbers, and you can't do anything if you simply want to calculate and do problems.
Although the concept of function only appeared in the second semester of junior high school, functional thinking has appeared in the first semester of junior high school, including the thinking of moving points and classification discussion, the essence of the moving point of the number axis is the classic pursuit problem of functions, and the classification discussion thinking is also the most basic way of analyzing the problem of functions, junior high school mathematics is very different from primary school mathematics, in that junior high school mathematics is no longer a simple solution straight line, but requires continuous trial and error and reasoning, and this ability is not established in the second year of junior high school, the first year of junior high school is a very important improvement node.
Another difficult point in junior high school mathematics geometry, in the transformation of thinking is more obvious than functions, if to the Pythagorean theorem, congruent triangles begin to recognize the difficulty, it seems a little later, the first semester of the inner angle sum, the sum of the outer angles, the theorem and proof of the intersection of parallel lines, has entered the world of geometry.
From the perspective of the exam, the questions at this stage are very simple and introductory, but if you start from the perspective of adapting to the geometric difficulty of the second year of junior high school, you need to improve your own difficulty. The difficulty of geometric proof is not reflected in the theorem itself, but in the superposition of logical chains.