The difference between junior high school mathematics and primary school mathematics
1, from "natural numbers and fractions" to "real numbers"
In primary school mathematics, only natural numbers and fractions are involved, that is, positive rational numbers. After entering junior high school, the first problem of algebra is "negative number". Negative number is a new abstract concept, which depends entirely on understandable knowledge. The calculation of negative numbers and the change of symbols will certainly make students suffer a lot, such as: (-2)+(-4) =-6, and some problems such as absolute value, reciprocal and number axis will follow, and it will be even harder to start when encountering slightly difficult problems.
For example, from the "natural number and fraction" in primary school to the "rational number and irrational number" in junior high school, it is tantamount to a deep gap for students who have just entered the middle school campus. Therefore, students need to understand the concept carefully, do more exercises, and gradually fill this gap, because it can be said to be the foundation of junior high school algebra. If the foundation is not good, the later study will be completely confused, and it will be too late to come back to study.
2. From "quantity" to "type"
In the six years of primary school, I mainly studied specific numbers and the operation between specific numbers, but when I was in the first grade, I came into contact with letters to represent numbers, so I needed to establish its algebraic concept. For example, -a stands for the opposite of A, in our opinion. "Algebra" means using letters to represent a number, but it is by no means like this. Mathematics in Senior One begins with "expressing numbers with letters", then goes deep into "equation", then expands the concept of "formula containing letters", and then begins to learn "function".
In fact, careful classmates will find that the content of junior high school learning is mostly the expansion of primary school content. There are actually many connections between elementary school mathematics and junior high school mathematics. In the process of transition from grade six to grade one, as long as teachers find out the internal relations and differences between "number" and "type" under the guidance and build a bridge between knowledge, they can lay a solid foundation for learning more knowledge in the future, so that they will not be confused and comfortable in the face of numerous exams.
3. From "arithmetic method" to "equation"
Most application problems in primary schools can be solved by arithmetic. The so-called "arithmetic" refers to a formula composed entirely of numbers and symbols. Because of its simple calculation, it has become the "main course" for primary school students to solve problems in the past six years. Even if they learn equations in primary school, they can only be regarded as "side dishes" But after entering junior high school, it is different. Since the first semester of junior high school, we have studied the unary equation in detail. Gradually, our first reaction to any application problem is to establish an unknown equation, but we have no impression of the original "arithmetic method". This is because solving application problems with arithmetic mostly requires reverse thinking, while equations mostly require forward thinking, which is difficult and easy to see. The following question is a good example:
1500 years ago, in the Art of War, there was this question: "Chickens and rabbits live in the same cage, with 35 heads on the top and 94 feet on the bottom. What are the geometric figures of chickens and rabbits? "
This problem is more troublesome by arithmetic calculation. Let's think of rabbits as having two feet, so 35 chickens and rabbits have 70 feet (35× 2 = 70) and the remaining 24 feet (94-70 = 24). These 24 feet belong to rabbits, because "rabbits are first considered to have two feet", so every rabbit should have two feet. Then there are 23 chickens (35- 12 = 23).
If this problem is solved by an equation, it will be much simpler. If there are χ chickens and (35-χ) rabbits, the equation is as follows: χ 2+4 (35-χ) = 94. To solve this equation, χ = 23 rabbits, 12 rabbits.
From the above three points, the main differences between junior high school mathematics and primary school mathematics are as follows:
To learn junior high school mathematics well, we must make our thinking more logical and learn to find, analyze and solve problems with mathematical eyes.