Some understandings of mastering junior high school mathematics ability
[Keywords:] junior high school mathematics; Basic ability; Comprehensive ability; Mathematical thought; problem-solving ability
This paper puts forward some views on the understanding and requirements of junior middle school mathematics basic ability and comprehensive ability. It is pointed out that mathematical thought has a controlling effect on mathematical knowledge, mathematical methods and skills, and mathematical operations. Therefore, it is necessary to cultivate students' ability to use mathematical ideas to solve mathematical problems.
[Document ID] A [DocumentNo.]1002—5308 (2000) 04—0028—04 [China Library ClassificationNo.] G633.6
Nowadays, with the vigorous promotion of quality education, people pay more and more attention to the cultivation of students' ability. In junior high school mathematics teaching, the majority of teachers realize that the requirements of quality education should be strongly reflected in mathematics teaching, and this embodiment depends to a great extent on the cultivation of students' mathematical ability. According to the characteristics of compulsory education, junior high school mathematics ability can be divided into two levels: the first level is the basic mathematics ability, that is, the basic academic ability level; The second level is the comprehensive ability of mathematics, which is the level of developing academic ability. It is true that both basic mathematical ability and comprehensive mathematical ability need to be based on basic mathematical knowledge and skills; On the other hand, the acquisition of basic mathematical ability and comprehensive ability makes the mastery of basic mathematical knowledge and skills more solid, consolidated and applied more freely. The following is about the understanding and requirements of junior high school mathematics basic ability and comprehensive ability, and puts forward some understandings.
First, the understanding and requirements of basic mathematical ability
In junior high school, the basic ability of mathematics refers to the basic calculation ability, thinking ability, spatial imagination ability and basic application ability reflecting the relationship between mathematics and production, life and related disciplines. These abilities are necessary for qualified junior high school graduates who have completed nine-year compulsory education.
The so-called basic operation ability refers to not only correct operation according to laws and formulas, but also understanding operation theory according to subject conditions and finding reasonable and simple operation methods; Refers to the ability to control uncomplicated mathematical operations. The aspects of detecting basic operation ability are: ① real number operation; (2) Algebraic operations (including algebraic expressions, fractional and radical operations); ③ factorization; ④ Exponential operation; ⑤ Operations related to functions; ⑥ acute angle triangle ratio operation; ⑦ Solve equations and column equations to solve application problems; ⑧ Solve the unary linear inequality and the unary linear inequality group; Pet-name ruby the most basic geometric calculation. The requirements for basic computing ability are: correct, reasonable, fast and solid in basic skills.
However, there is no requirement for complicated operation, so we should properly control the difficulty of operation when reviewing, make more efforts to improve the accuracy of operation, and further require reasonable and rapid operation on this basis.
The so-called basic thinking ability refers to observation, comparison, analysis, synthesis, abstraction and generalization; Able to use induction, deduction and analogy for reasoning; I will explain my thoughts and opinions accurately and form a good thinking quality. In junior high school, basic logical reasoning ability is the main component of thinking ability. Basic logical reasoning ability mainly refers to the ability to seek the idea of proving basic geometric problems without adding auxiliary lines or only adding common auxiliary lines (this auxiliary line has appeared obviously in textbooks), and to write the process of proving problems by analytical method and comprehensive method. This kind of basic proof questions mainly prove the equality of line segments and angles, the vertical relationship and parallel relationship of straight lines, the congruence or similarity relationship of triangles, or that graphics are parallelograms (including rectangles, diamonds and squares) and trapeziums (including isosceles trapeziums and right-angled trapeziums), the proportional relationship of line segments, the tangent relationship of straight lines and circles, and so on. The requirements for basic logical reasoning ability are: clear and concise expression of logical relations, clear explanation of "joint points" and not skipping key steps. Reasoning should be based on definitions, axioms and theorems within the scope of mathematics textbooks for junior high schools in nine-year compulsory education.
The so-called basic spatial imagination ability refers to the concept of space, which can imagine geometric figures from simple objects and physical shapes from geometric figures; Separate a simple basic figure from a more complex plane figure, and find out the basic elements and their relationships in the basic figure; Be able to make or draw plane graphics and basic space graphics according to conditions. In junior high school, the concept of space specifically refers to expressing the solution set of inequality and inequality group with number axis; Find out the nature of the function from the known function relationship; Observe the figure, estimate the position and approximate quantitative relationship of geometric objects, draw geometric figures with tools such as rulers, compasses, protractors and triangular plates, and draw with rulers and compasses (including five basic drawing methods, three basic trajectories, simple ruler drawing questions in textbooks, etc.). ).
Basic application ability refers to the ability to solve practical mathematical problems and related subject problems, as well as the ability to solve practical problems in production and daily life. The junior middle school stage is mainly reflected in the application of solving equations, solving right triangles, applying statistical knowledge, applying functional knowledge, and applying the knowledge of similarity and circle in geometry to solve practical problems, especially using mathematics as a tool to solve some practical problems in life (such as business and economy). ) and production construction (such as growth rate and measurement, etc. At present, the examination of strengthening the ability of mathematics application has gradually attracted everyone's attention.
Second, the understanding and requirements of mathematical comprehensive ability
The so-called comprehensive application ability of mathematics mainly refers to the ability to solve problems by combining algebraic knowledge and geometric knowledge; The ability to apply mathematical knowledge and methods to solve practical problems in real life (usually called "problem solving"); The ability to use basic mathematical ideas to solve mathematical problems containing one or more mathematical ideas; The ability to solve some simple research-oriented, exploratory and open-ended problems, in the same problem, sometimes need to use more than one of the above abilities, often need to use the above abilities, and sometimes need to use other disciplines related to mathematics, which involves general abilities.