数学可以分为三个层面,即知识、能力、意识.代数、几何、微积分学均为数学知识.过去我国提出的数学能力是:基本运算能力、逻辑思维能力和空间想像能力.后来数学教学大纲又提出了分析和解决问题的能力.2000年美国数学教师协会发布的《数学课程标准》中,提出了六种能力:(1)数的运算能力;(2)问题解决能力;(3)逻辑推理能力;(4)数学联结能力;(5)数学交流能力;(6)数学表达能力.数学联结能力是指,把问 Mathematics can be divided into three levels, namely, knowledge, ability, consciousness.Algebra, geometry, calculus are mathematical knowledge.Many mathematics ability proposed in the past are: basic computing ability, logical thinking ability and spatial imagination ability.Many mathematics teaching Outline also put forward the ability to analyze and solve the problem.American Mathematical Teachers Association in 2000 published “mathematics curriculum standards”, put forward six kinds of ability: (1) number of computing power; (2) problem solving ability; (3) Logical reasoning ability; (4) mathematical connection ability; (5) mathematical communication ability; (6) mathematical expression ability.