  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.
