Preschool allows rethinking mathematics outside the tradition of ordinary school. Seeing schooling as adapting the child to the outside world containing many examples of the natural fact Many, we can ask: How will mathematics look like if built as a natural science about Many? To deal with Many we count and add. The school counts in tens, but preschool also allows counting in icons. Once counted, totals can be added. To add on-top the units are made the same through recounting, also called proportionality. To add next-to means adding areas also called integration. So accepting icon-counting and adding next-to offers golden learning opportunities in preschool that are lost when ordinary school begins.