What does number and algebra include?

Question 1: What does the number and algebra course include? The content of number and algebra plays an important role in the mathematics curriculum in compulsory education and has important educational value. Compared with the relevant parts of traditional mathematics in primary and secondary schools, the standard has greatly changed the learning field of number and algebra in terms of objectives, contents, structure and teaching activities. It is very important to understand the educational value, design ideas, content arrangement and teaching methods of the number and algebra part in the nine-year compulsory education mathematics curriculum for effectively implementing and implementing the standard.

The content of number and algebra occupies a large proportion in traditional primary and secondary mathematics, and has accumulated a lot of teaching experience for a long time. However, compared with the requirements of the times, there are still many problems in accordance with the new educational concept. For example, excessive pursuit of scientific and systematic, complicated and even cumbersome content; Too much pursuit of formalization, ignoring the connection with real life, the course is full of tedious calculation and deduction, but students do not understand the essence of the problem, see the usefulness of mathematics, realize the value of mathematics, and will not use what they have learned to solve the problem; As a result, many students feel that mathematics is boring and lose interest and confidence in mathematics learning.

In the process of formulating the standard, the reform of logarithm and algebra was carefully studied and thought, and the direction of reform was further clarified, especially in the following aspects: paying attention to the understanding of logarithmic meaning, cultivating students' sense of number and symbol; Desalinate the requirements of over-formalization and memory, and attach importance to experiencing and understanding relevant knowledge in specific situations; Pay attention to the process, advocate students' independent activities in the learning process, and improve their ability to discover and explore laws; Pay attention to application, strengthen the cultivation of students' mathematical application consciousness and ability to solve practical problems; Advocate the use of calculators, reduce the requirements for computational complexity and speed, and pay attention to estimation.

The Educational Value of 1. Numbers and Algebra

The content of' number and algebra' mainly includes number and formula, equation and inequality, and function. They are all mathematical models for studying quantitative relations and changing laws, which can help people understand, describe and grasp the real world more accurately and clearly from the perspective of quantitative relations. (standard page 1 1)

The educational value of this part is mainly reflected in the following aspects:

(1) can make students realize the close relationship between mathematics and real life, that numbers and symbols are important languages to describe the quantitative relationship in the real world, that equations, inequalities and functions are mathematical models in the real world, and that mathematics is an important tool to solve practical problems and communicate, from which they can feel the value of mathematics, and initially learn to observe and analyze the real society by using mathematical thinking mode, so as to solve problems in daily life and other subjects' study and enhance their application awareness.

(2) In the learning process of number and algebra, the exploration of the quantitative relationship and its changing law in the real world, the establishment and expansion of the concept of number, the operation of number, the establishment and derivation of formula, the establishment and solution of equation, and the exploration of functional relationship are helpful to promote students' interest in mathematics learning, improve their ability to solve problems and self-confidence, and cultivate their initial innovation consciousness and discovery ability.

(3) In number and algebra, there are not only the unity of opposites in knowledge, such as positive and negative numbers, addition and subtraction, power and roots, constants and variables, precision and approximation, but also the unity of opposites in the research process, such as known and unknown, special and general, concrete and abstract, practice and theory. At the same time, the study of variables and functions is full of ideas of movement and change, and in the study of numbers and other parts of algebra, from the perspective of movement and change, we can also make our understanding more profound. Therefore, this part of the study will certainly help to cultivate students' dialectical materialism and help students understand the real world from a scientific perspective.

The number and algebra under the guidance of the "standard" concept will present a lot of rich realistic backgrounds for students, and based on students' existing experience, paying attention to the formation process of knowledge, students' interest in learning and self-confidence, and cultivating students' ability to explore and use mathematics will change the tedious content of number and algebra ...

Question 2: What is number and algebra? It mainly includes numbers and formulas, equations and inequalities and functions.

Question 3: What are the aspects of mathematics number and algebra in primary schools? Classification of numbers+representation of letters+scientific counting method.

Question 4: What are numbers and algebra, and what are their differences and connections? Algebra is a branch of mathematics, which studies the algebraic operation theory and method of numbers and words, more accurately, the algebraic operation theory and method of real numbers and complex numbers, as well as polynomials and their coefficients. Elementary algebra is the extension and development of old arithmetic. In ancient times, when a large number of solutions to various quantitative problems were accumulated in arithmetic to seek systematic and more universal methods.

There is no doubt that algebra is developed from arithmetic. As for when algebra came into being, it's hard to say clearly. For example, if you think that "algebra" refers to the skill of solving symbolic equations such as bx+k=0, then this kind of "algebra" was developed in the 6th century.

If we don't want to be so concise now, algebra can be traced back to an earlier era. Westerners regard Diophantine, an ancient Greek mathematician in the third century BC, as the originator of algebra. In China, algebraic problems expressed in words appeared earlier.

Algebra, as a proprietary mathematical term and a branch of mathematics, was formally used in China as early as 1859. That year, Li, a mathematician in the Qing Dynasty, and Valeria Li, an Englishman, translated a book written by Di Yaogan, which was called Algebra. Of course, the contents and methods of algebra were produced in ancient China, such as

The central content of elementary algebra is to solve equations, so algebra has long been understood as the science of equations, and mathematicians have also focused on equations. Its research method is highly computational.

When discussing equations, the first problem is how to combine the actual quantitative relations into algebraic expressions, and then list the equations according to the equivalence relations. So an important content of elementary algebra is algebraic expression. Because of the different quantitative relations in things, elementary algebra generally forms three algebraic expressions: algebraic expression, fractional expression and radical expression. Algebra is the embodiment of numbers, so in algebra, you can perform four operations, follow the basic operation rules, and you can also perform multiplication operations.

In the process of the emergence and development of elementary algebra, the study of solving equations has also promoted the further development of the concept of numbers, extending the concepts of integers and fractions discussed in arithmetic to the scope of rational numbers, so that numbers include positive and negative integers, positive and negative fractions and zero. This is another important content of elementary algebra, that is, the expansion of the concept of number.

With rational numbers, the problems that elementary algebra can solve are greatly expanded. However, some equations still have no solution within the scope of rational numbers. Therefore, the concept of number was once extended to real numbers, and then further extended to complex numbers.

Then, in the range of complex numbers, is there still an equation that has no solution and must be extended again? The mathematician said: No need. This is a famous theorem in algebra-the basic theorem of algebra. This theorem only means that an equation of degree n has n roots. 1742, 15438 February 5, Swiss mathematician Euler clearly stated in a letter. Later, another mathematician, Gauss of Germany, gave a strict statement in 1799.

Combined with the above analysis, the basic content of elementary algebra is:

Three Numbers-Rational Number, Irrational Number and Complex Number

Three types ―― Algebra, Fraction and Root.

The central content is equation-integral equation, fractional equation, radical equation and equation.

The content of elementary algebra is roughly equivalent to the content of algebra courses offered in modern middle schools, but it is not exactly the same. For example, strictly speaking, the concept, arrangement and combination of numbers should be classified as the content of arithmetic; Function is the content of analytical mathematics; The solution of inequality is a bit like the method of solving equations, but inequality, as a method of estimating values, essentially belongs to the category of analytical mathematics; Coordinate method is the study of analytic geometry ..... These are just an arrangement formed in history.

Elementary algebra is the continuation and expansion of arithmetic. The research object of elementary algebra is algebraic operation and equation solving. Algebraic operations are characterized by a limited number of operations. There are ten rules in all elementary algebra. This is the key point to understand and master when learning elementary algebra.

These ten rules are:

Five basic algorithms: additive commutative law, additive associative law, multiplicative commutative law and multiplicative associative law. & gt

Question 5: What are the core concepts of number and algebra? What is the core idea of the new mathematics curriculum standard? Talk about your own understanding in combination with teaching practice.

The core concepts of the new mathematics curriculum standard include number sense, symbol consciousness, space concept, geometric intuition, data analysis concept, computing ability, reasoning ability, model thinking, application consciousness and innovation consciousness. They are closely related, and these ten concepts are all in the new mathematics curriculum.