Mathematical geometry comes and goes suddenly, competing for thinking ability, but not completely competing for thinking ability.
In the first semester of the second year of junior high school, the style of mathematics painting changed abruptly, calculation is not the focus, reasoning and proof is the key, from walking the straight road to walking the maze, the rise of mathematical difficulty is not gradual, but a sudden change of track, and the thinking ability between students is particularly obvious.
Learning geometry well is not to memorize a few common theorems, but to be able to sort out a complete logical chain, it is not difficult to understand the problem-solving process, it is not easy to do it yourself, it is no longer to practice more but to think more, understanding is not the same as being able to do, thinking is the key.
As the first gentle slope of thinking ability improvement, although geometry is difficult, it is an opportunity to change the thinking track, gradually master the way of thinking in the learning process, from the perspective of the continuation of knowledge points, the difficulty and distinction of geometry are mainly reflected in junior high school, from the congruent triangle in the second year of junior high school, the Pythagorean theorem to the similar triangle and circle in the third year of junior high school, but it suddenly fades in high school, but the scientific thinking ability embodied in the learning process is difficult to compare with other disciplines and knowledge sections.
Some students rely on excellent logical thinking ability, starting from geometric proofs, and their grades begin to enter the fast lane, while other students whose grades are good rely on a lot of training, all kinds of brushing and memorizing questions, and know how to do it relies on conditioned reflexes, rather than independent thinking, which is to bypass the gentle slope of difficulty, and it seems that the grades are acceptable, but they do not have the ability to maintain the sustainability of the grades.
The second year of junior high school functions, you will really know, you don't understand really don't understand, it seems to be very important, but it is actually quite important.
The functions in the next semester do not have the complexity of geometry, but the concept of functions is very difficult for some students to understand.
The core of science in middle school can be regarded as the formation extension and application of functional thinking, functional thinking is formally formed in the second semester of junior high school, but it has begun to be implanted in the first year of junior high school, the most obvious number axis moving point problem, is a function travel problem, algebraic formulas, inequalities, equations can be regarded as the accumulation of concepts before function learning.
The quadratic functions of the third stage of the junior high stage, as well as the sets and intervals of the first stage, the monotonicity and parity of the functions, the exponential functions, the power functions, the trigonometric functions and the composite functions, etc., are all extensions of functions, and the physical forces and motions of the first stage of the higher stage, and the calculation of the quantity of chemical substances can be regarded as the scene application of functions.