The idea of writing on a portable flat surface goes back a very long time - thousands of years.
We know from archaeological records and from the writings of ancient authors such as Cicero (106 BC - 43 BC) Romans wrote on a wax tablet, called a tabula, with a stylus.
Here's an image from Wikipedia showing what some of these tablets look like. Basically, it consisted of a wooden frame with some wax on the surface. Note that there are two tablets joined together to form a unit.
The Romans did not have modern paper, but instead used papyrus which is similar. It's unclear how expensive papyrus was (see this SE question on the cost) but in any case its easy to see why a wax tablet might be useful because it relied on everyday materials and could be erased and reused.
Even earlier in this image from Wikipedia, a painter of vases named Douris around 500BC produced of an image of man using a wax tablet, stylus in hand. Although, humorously and anachronistically this does look like someone using a laptop :-)
Here, from Douris and the Painters of Greek Vases by Edmond Pottier, you can see the a schoolmaster depicted with a stylus and tax tablets.