The article describes the essence of pedagogical strategy the Inquiry-based learning (IBL). It considers the features of the pedagogical strategy IBL application in the educational process of higher education institutions during teaching of mathematical disciplines (Inquiry-based mathematics education, abbr. IBME). There are indicated some difficulties to implement the IBME paradigm in the context of blended learning, which limits direct "live" contact between the teacher and students, and students among themselves. Modern techniques are able to compensate "live" communication sufficiently, moreover it is not lost completely due to the blended learning. The most important task on which the article focuses is the search for the digital tools that would help implement the main idea of IBME. It is active and research-oriented teaching of mathematics on a constructivist basis, which optimally combines individual (autonomous) and group work of students. Possibilities are revealed, and the expediency of using the virtual platform GeoGebra Classroom in IBME classes is argued. In particular, this expediency is justified to ensure the research orientation of teaching higher mathematics on the basis of inquiry and own experience, effective pedagogical control of students individual work and team work developing their own knowledge. In the article there are stated examples of practical exercises in the disciplines "Mathematical analysis" and "Projective geometry and image methods", which illustrate the way how not to lose the opportunity to form ability of students to learn independently through implementing the principle of collaborative learning.