Sophisticated computation methods were developed 4000 years ago in Mesopotamia in the context of scribal schools. The basics of the computation can be detected in clay tablets written by young students educated in these scribal schools. At first glance, the mathematical exercises contained in school tablets seem to be very simple and quite familiar, and therefore, they have little attracted the attention of historians of mathematics. Yet if we look more closely at these modest writings, their simplicity proves deceptive. The feeling of familiarity primarily results from a projection on to the past of thought patterns ingrained from our own early learning. Careful observation of school tablets reveals subtle differences between ancient and modern notions of number, quantity, measurement unit, order, divisibility, algorithm, etc. In fact, we find a completely original mathematical world with rules of its own. This article explores the computation practices developed in scholarly milieus in the light of the mathematical basics that was taught in elementary education.