Education will be essential to the continued viability of any permanent settlement. Even if there is a constant influx of educated colonists from Earth, the long term health of the colony will depend on a continuously educated population. Skilled workers are needed for equipment maintenance and engineering. Health workers and specialists need to keep up with progress in their field of expertise. Continuous education will be an important part of the settler's life. Example of this are the continuous education of military personnel on ships during long postings, or the modern emphasis on continuous education in professions such as engineering and medicine.
Earth based lecture may be possible, but face an important limitation due to communication latency. The round trip delay of 8 to 30+ minutes will make interactions practically impossible. Pre recorded lectures will be available as with modern university services.
Children's education will require live teachers. Parents, scholars,
As the settlement(s) grow education will require schools and other educational facilities. To keep the martian population on Mars will require higher education, and eventually universities. In fact, universities may be some of the first educational facilities built on Mars, as Students from Earth and graduated colonists seek degrees and continuous education.