The same school, the same teacher, the same learning environment, the same homework and the same learning materials are all brushing questions and even making up lessons outside the school, but the learning effect is completely different. Some students have excellent grades, while others have poor grades. Some people can't help but sigh, how can the gap be so big under the same conditions? Some people begin to doubt their IQ and even talk about whether they are a piece of learning material.
In fact, all children are equally clever. The same conditions, the same efforts, but different results, really frustrating. In fact, the real gap between good students and poor students is "the use of strategies." Good students make good use of strategies to call knowledge points, and they are like a duck to water in solving problems. Poor students only learn knowledge points and don't know how to call knowledge points!
So, what is a strategy? The so-called strategy is to arrange troops, and the "soldiers" here refer to knowledge points. To put it bluntly, strategy is actually an idea, that is, the idea of calling knowledge points.
Starting today, we will systematically talk about "strategies in mathematics", that is, "mathematical thoughts". Don't underestimate "mathematical thought". If you get the essence of "mathematical thought", you will be like a duck to water in your study, and you will get twice the result with half the effort, so that you can bid farewell to "ineffective efforts" and "fake efforts" forever!
From primary school, junior high school to senior high school, it is not difficult for students to find that no matter what kind of questions, as long as the relationship between various conditions in the questions is straightened out, the unknown conditions are found out from the known conditions, and then the formula is applied, the problem will be solved.
Yes, the first lesson we are going to talk about today is the core and soul of mathematical thinking, that is, relationship. As long as the relationship is straightened out, the problem will be solved!
In fact, it is not difficult to find that the conditions given in the title are not independent conditions, but interrelated. As long as we find the relationship between them and straighten out the relationship between various conditions, the thinking of solving problems will be clear.
No matter what kind of math problem, it is actually a test of students' ability to straighten out various relationships!
As we know, there are operation symbols such as addition, subtraction, multiplication, division and multiplication. In fact, these operation symbols serve the relationship between various conditions in mathematics.
We know that there are many relational symbols in mathematics, such as ">"< "=" and so on. In fact, it is not difficult for careful students to find that the symbol "=" is often used in various problem solving. If the relationship between the conditions on both sides of "=" is straightened out, the equation will be listed and the problem will be solved.
The process of solving problems is actually the process of finding and rationalizing conditional relations! Simply put, the process of solving problems is actually the process of "finding relationships and rationalizing relationships"!
Some students solved the same problem, while others didn't. The difference between the two is that the students who worked out straightened out the relationship between the conditions in the question, while the students who didn't work out didn't find the relationship between the conditions at all, let alone straighten out the relationship. To put it bluntly, when the problem is solved, the system between conditions is straightened out.
"Relationship" is the foundation and core of mathematical thought. If you stand on the idea of "finding relationships and straightening out relationships" to solve problems, you will find that you have the direction to solve problems and your ideas will come out, so that you will get twice the result with half the effort when you start the problem!
In fact, the process of all students doing problems is the process of finding relationships, but everyone doesn't realize this, but they don't realize the "mathematical thought" of "relationships"
Well, that's enough about the basic knowledge of "mathematical thought". We will talk about the "modeling thought" in mathematical thought in the next class.