Computer Assisted Proofs and Automated Methods in Mathematics Education

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.