In this paper, we show that it is possible to develop artificial neural networks building on school mathematical knowledge – initially avoiding AI terminology and comparisons with biological neurons since both are unnecessary to understand the underlying mathematical concepts. We present a didactical reduction of the mathematical foundations of artificial neural networks using the example of regression problems. It becomes clear that numerous connections to school mathematical content exist, not only from statistics but also from the area of analysis and linear algebra. As part of a design-based research project we developed digital teaching and learning material that builds on the presented didactical reduction. The material allows upper secondary students to develop the mathematical ideas of artificial neural networks in a problem-oriented way. The central building blocks of the material and first experiences with students are described.