The Doctor had a blackboard in his TARDIS. The Fourth Doctor used a blackboard to teach Leela how to write. (TV: The Invisible Enemy) In his new control room, the Twelfth Doctor wrote undecipherable calculations over his blackboard. (TV: Into the Dalek onwards) While talking alone in the TARDIS about the possibility of never truly being alone, the Twelfth Doctor wrote various points on his blackboard. After placing a piece of chalk on a book, he returned seconds later to find it missing and that someone or something had used it to write the word "LISTEN" in what looked like the Doctor's handwriting onto another board. When the Doctor told Clara he couldn't have just written it and forgotten, Clara asked him, "Have you met you?". (TV: Listen)
Other references
When Rubeish wrote equations on the TARDIS with a piece of chalk, the Third Doctor reproached him because the TARDIS was not a blackboard. (TV: The Time Warrior)
On April Fools' Day 1963, Ian Chesterton sent one of his Coal Hill School students, Little Titch Critchley, to the supplies cupboard for "a left-handed blackboard rubber". (PROSE: Time and Relative)