Algebra knowledge is developed on the basis of arithmetic knowledge, which is characterized by using letters to represent numbers and making the concept and operation of numbers.
Abstraction and formulation of law. When the first grade of junior high school first came into contact with algebra, students had to go through the transition from arithmetic to algebra.
The main symbol is the transition from counting to letter number, which is a higher-level drawing method based on the concept of primary school number.
Elephant. Letters represent numbers, but not specific numbers. This general and special relationship is exactly what junior one students learn.
The difficulty is.
In order to overcome the learning obstacles caused by this change, we should pay special attention to "basic knowledge of algebra" in teaching.
Chapter teaching. It is important to understand the meaning from the beginning before inheriting the knowledge of primary school and after the enlightenment of junior high school, and to make a good connection between primary school and secondary school.
Link. In mathematics, we should grasp the depth of the main content of the whole chapter, start with the knowledge of using letters to represent numbers learned in primary school, and try our best to use it.
Some examples of letters representing numbers naturally lead to the concept of algebra. Let's talk about how to use column algebra to represent common numbers.
Quantitative relations, and some preliminary application knowledge of algebra. Always pay attention to the algebra knowledge that primary school has come into contact with (there is no primary school)
Based on the formulation of Algebra, this paper systematically summarizes and reviews it, and strengthens and perfects it appropriately. Cultivate students
I feel that entering the first grade is as natural as upgrading a primary school, which reduces the negative effects of the feeling of entering a higher school.
In the first algebra class of grade one, generally speaking, we will not give lectures on this knowledge, but give some descriptions and guidance to the students who are learning algebra for the first time. eye
The purpose is to give students a general understanding and let them know something about middle school mathematics. As introduced: (1) Mathematics
Features. (2) The characteristics of junior high school mathematics learning. (3) The prospect of junior high school mathematics learning. (4) Learning all aspects of middle school mathematics.
Methods, including preview, listening, review, homework and evaluation. (5) Pay attention to intelligence such as observation, memory, imagination and thinking.
The relationship between factors and mathematics learning. (6) Non-intelligence factors such as motivation, will, personality, interest and emotion are related to mathematics learning.
Contact.
two
The concept of students' number has been expanded twice in primary school mathematics, one is to introduce the number 0, and the other is to introduce the fraction (referring to
Positive score). However, why students need to expand the concept of logarithm has not been deeply understood. When it comes to the new number to be introduced on the first day-
Negative numbers are not closely related to students' daily life. They are used to saying "up" and "down"
Method, and now it is not used to saying "down 5 meters" as "up minus 5 meters". Why do you say that? There was a time when it was even worse.
Not easy to understand. Therefore, it is the first difficulty for students to understand the necessity of introducing negative numbers. We officially
Before introducing the concept of negative numbers, we should make a systematic arrangement of the knowledge about numbers in primary school mathematics, so that students can pay attention to the popularization of numbers.
Thought is gradually developed to solve practical problems, and it is also caused by the contradiction between the original number set and solving practical problems.
Extension of the new number set. That is, natural number set addend 0→ expanded natural number set (non-negative integer set) plus positive fraction → arithmetic number set.
(non-negative rational number set) plus negative integer, negative fraction → rational number set. In this way, the series will be expanded again.
Get ready. This can be done when the concept of negative numbers is formally introduced. For example, in primary schools, 60 tons are shipped in and 40 tons are shipped out, increasing production by 3.
00 kg and 100 kg are very clear. How to fully express their meaning with a simple number?
What about coming out, so as to stimulate students' thirst for knowledge. Then let the students give their own examples to illustrate that this opposite quantity is common in life.
In addition to the arithmetic numbers learned in primary school, this quantity also needs to be explained by sentences.
The opposite meaning. If we take a quantity as a benchmark, that is, "0", and stipulate that one of the quantities is a "positive" quantity, we will be in phase with it.
The quantity of antonym is the quantity of "negation". Use "+"for affirmation and "-"for negation. In this way, positive and negative numbers are gradually introduced.
The concept of new numbers will help students understand the necessity of introducing new numbers. So as to produce psychological identity, and then successfully put the quantity
The category extends from the arithmetic number in primary school to the rational number in senior one, so that students will not have a great sense of jumping.
three
The four operations in the first grade of junior high school are rational number operations developed from non-negative rational number operations in primary mathematics, not just calculating absolute values.
Value, but also to determine the operation symbol, which students are very unhappy at first. Calculation often occurs under "parameter calculation" of negative numbers.
The accuracy of the mixed operation of rational numbers is low, especially the practice needs to be strengthened. In addition, for transportation
In this way, the result of calculation is no longer unique like that of primary school. Such as | a |, the results will be discussed in three situations.
This change is hard to accept for the first grade students, and algebraic operation is a brand-new problem for them.
To solve this difficulty correctly, we must attach great importance to it and let students master rationality on the basis of correctly understanding the concept of rational numbers.
The arithmetic of numbers. The deeper you understand the algorithm, the better you master it. But the math foundation of junior one students is still not good.
We can't understand these algorithms, so we should pay attention to setting appropriate gradients and deepening them step by step. Four rational numbers
Then the operation will eventually come down to non-negative operation, so the concept of "absolute value" should be the key we must grasp in teaching.
Point. The concept of "reciprocal" is used to define absolute value, and "number axis" is the basis for teaching these two concepts.
We must pay attention to the combination of numbers and shapes, strengthen intuition, and do not rush for success. Students correctly master and skillfully use the concept of absolute value.
Reading is a process. After illustrating the concept of absolute value with examples of number axis, it should be deepened gradually in practice.
Understand and consolidate.
Students do exercises in primary schools and are content to do only calculations. And on the first day, in order to make it understand the algorithm correctly, try to
In order to avoid mistakes in calculation, students should not only be satisfied with getting a correct answer, but should ask them to think about every step.
According to what, flexible use of what you have learned can achieve good teaching results. In this way, we can not only cultivate students' luck.
Computational thinking ability can also help students gradually develop good study habits.
four
The age of students entering junior high school is mostly 1 1 to 12, and the thinking of students in this age group is changing from image thinking to abstract thinking.
Transition. The instability of thinking and the formation of thinking mode determine that the study of solving application problems with equations will be in the first grade.
The students face a very difficult obstacle. The teaching of solving application problems with equations is often laborious and ineffective. because of study
Students are only used to applying the formulas in primary school thinking when solving problems. They belong to the mindset and are not good at analysis, transformation and further in-depth thinking.
Exam, narrow-minded, boring, a little change in the topic will be helpless. There are three main ways for junior one students to solve application problems.
Difficulties: (1) can't grasp the equation relationship; (2) After finding the equation relationship, the equation will not be listed; (3) Used to solving by arithmetic.
The method is not suitable for algebraic analysis of application problems, and I don't know how to grasp the equality relationship. The first aspect is the main solution.
After it, the other two aspects will be solved. Therefore, in the teaching of solving application problems by equations in the eighth volume of primary school mathematics, we must learn.
Students master the similarities and differences between arithmetic methods and algebraic methods, and make clear the idea of solving application problems with equations; Second, students should make targeted supplements.
It would be good for primary school students to rewrite the actual quantitative relationship into algebraic training, which will make more complicated reactions.
It is difficult to turn a problem into a simple one. We should pay attention to the process of knowledge generation when teaching equation solving practical problems in junior one. Because mathematics itself is
A kind of thinking activity, students should participate in teaching as much as possible, so as to form and develop an intellectual structure with thinking characteristics.
Students should often participate in activities such as examining questions, analyzing the meaning of questions, arranging equations and solving equations. So as to understand the practical significance of solving application problems with formulas.
Righteousness and problem-solving methods and advantages, in which the examination of questions should be the most critical link. Try to find out the meaning of the question and find out what you can say.
The equivalence relation of the meanings of all application problems. If we can't find the equation relationship, the equation can't be listed, but we can find such an equivalent relationship.
After the system, some numbers involved are set as unknowns, and the rest are known or contain known and unknown numbers.
When the contemporary number expression is expressed, the equation is listed. Students should be taught to read the topic, understand the meaning of the topic, and then find out the equivalent level.
System, list the equations to solve the problem, make it form a good habit of "observation-analysis-induction", that's right.
It is very important for the whole mathematics study. In addition, students should be told in teaching that some problems are solved by arithmetic.
It's inconvenient, so we have to solve it by algebra. For some typical problems, after helping students solve them with algebraic methods, they can be calculated at the same time.
The comparison of technical schemes makes students have a clearer understanding, thus gradually abandoning the thinking habit of doing application problems with arithmetic solutions.
In short, students are exposed to relatively intuitive and simple basic knowledge in primary school mathematics. After entering the first grade, they must learn what they know.
Knowledge has made a leap in abstraction and rigor. As a senior one math teacher, it is very important to analyze and study related problems carefully.
It is of great practical significance to link up mathematics classroom teaching in primary and secondary schools and improve teaching quality.