This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in Mathematics Education, and in the broader frame of STEAM Education. In particular, we discuss the transformation of Mathematics Education into exploration-discovery-conjecture-proof scheme, avoiding usage as a black box . This scheme fits well into the so-called 4 C's of 21st Century Education. Communication and Collaboration are emphasized not only between humans, but also between machines, and between man and machine. Specific characteristics of the outputs enhance the need of Critical Thinking. The usage of automated commands for exploration and discovery is discussed, with mention of limitations where they exist. We illustrate the topic with examples from parametric integrals (describing a "cognitive neighborhood" of a mathematical notion), plane geometry, and the study of plane curves (envelopes, isoptic curves). Some of the examples are fully worked out, others are explained and references are given.

翻译：本综述论文是2022年8月在以色列海法举行的ThEdu'22研讨会特邀主题报告的扩展版本。在简要介绍计算机代数系统（CAS）、动态几何系统（DGS）及其他实用技术的发展历程后，我们阐述了其在数学教育以及更广泛的STEAM教育框架中的启示。具体而言，我们探讨了数学教育如何向"探索-发现-猜想-证明"范式转型，避免将其作为"黑箱"使用。这一范式很好地契合了所谓"21世纪教育的4C"理念。交流与协作不仅强调人与人之间，也强调机器之间以及人机之间的互动。输出结果的特性强化了批判性思维的需求。我们讨论了自动化命令在探索与发现中的应用，并指出了存在的局限性。通过参数积分（描述数学概念的"认知邻域"）、平面几何以及平面曲线（包络线、等角曲线）研究中的实例加以说明。部分实例为完整推导，其余则予以阐释并给出参考文献。