Education is about supporting humans in their growth, with a special focus on exploring their intellectual potential. Learning to act following a given (even complex) pattern is losing its educational value very fast, because all well described activities can be automized. Education therefore should focus on developing those cognitive process dimensions of pupils where technology cannot compete with humans. This means teaching how to describe and discover the world, how to verify own imaginations and models, how to think and how to design, analyze and evaluate new products of science and technology instead of learning the products of science and technology, and their applications. In this article we claim that teaching numbers and fundamental arithmetic operations in schools starts on a too high abstract level resulting in learning algorithms of symbol manipulations without understanding the nature of the fundamental calculations. In this paper we show that starting with the historical development of number representations (not with the decimal positional system) offers a natural, more understandable way for teaching mathematics in primary schools. We show, that going consequently from concrete to abstract empowers pupils to be able to design own representations of numbers and rediscover the execution of arithmetic operations on their own. We take the operation of division of integers to exemplary illustrate how a successful process of rediscovery of arithmetic algorithms can be designed.