本文分析了高等数学教育领域中在能力培养方面存在的若干问题，探讨了能力和数学能力培养的必要性，客观借鉴了心理学原理，对能力和数学能力进行了较全面的阐述，提出了某些新颖的见解，并着重结合数学分析内容就数学能力的表现与培养进行了全面和系统的论述。

In this paper, the writer analyses a certain number of issues existing in the development of abilities in the field of advanced mathematics education. He probes into the necessity of the development of abilities and mathematics abili-ties, which he elaborates rather all-sidedly. He raises certain original views objectively using psychological principles for reference.He expouds all-sidedly and systematically the manifestation and development. of mathematics abilities, integrating mainly with mathematics analysis.