  Nowadays interactive digital scientific environments have become an integral
part of scientific computing in solving various scientific tasks in research,
but also STEM education. We introduce SageMath or shortly Sage -- a free open
Python-based alternative to the well-known commercial software -- in the frame
of our course Methods of Physical Problems Solving for future scientists and
science teachers. Particularly, in the 1st illustrative example from the
Physics Olympiad, we present Sage as a scientific open data source, symbolic,
numerical, and visualization tool. The 2nd example from the Young Physicists'
Tournament shows Sage as a multimedia, modeling, and programming tool. By
employing SageMath as an open digital environment for scientific computing in
the education of all STEM disciplines, teachers and students are empowered not
only with a universal educational tool, but a real research tool, enabling them
to engage in interactive visualization, modeling, programming, and solving of
authentic, complex interdisciplinary problems, thus naturally enhancing their
motivation to pursue science in alignment with the core mission of STEM
education.
