Alexander knew that even tutors of nobles used the ground as a cheap and easy blackboard because using things like papyrus, valium, or parchment for little children to doddle and practice on was too wasteful.
And though this type of teaching was very similar to a blackboard, where the writing was also periodically rubbed off, the most easily identifiable problem with that was that writing on the ground limited the number of people who could see it.
Basically, only the very first rows could clearly see it.
This might have worked when there were only two or three kids, but would not work for a class of twenty five.
Hence Alexander decided to splurge on the blackboard and consumable chalk.
Though it was not really splurging given the blackboards were just a cheap, slab of wood and the chalks were made from gypsum which was already being mined in huge quantities to be used in cement products.