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?
Presented as a natural science, mathematics mediates the three classical virtues: Truth, Beauty and Goodness.
By saying “No, that is not four, that is two twos!” when shown four fingers held together two by two, a four-year old child sees what exists, bundles of twos, and two of them. Likewise, preschool children have no difficulties counting in other units even if they only learn to count in tens. This observation motivates the following question: What kind of mathematical learning takes place when children count in bundles less than ten?
The MATHeCADEMY.net appoints an initiator and brings funding for hiring the initiator as a two-year professor, and for two postdoc scholars, plus an overhead for the university.
Replacing Numbers with Blocks allows for IconCounting and NextTo Addition – which allows preschool children to learn the Core of Mathematics, proportionality and integration, before being forced to count in tens only.
To deal with Many we count and add. The school counts in tens, but preschool allows counting in icons also. Once counted, totals can be added. To add on-top the units are made the same through recounting, also called proportionality. Adding next-to means adding areas, also called integration.
To master Many we ask ‘how many?’ To answer, we count by bundling and stacking to get a total T. Once counted, first a total can be recounted in the same unit to create overload or underload, or to create a different unit; next totals can be added NextTo, or OnTop if the units are the same. We separate the inside bundles from the outside unbundled singles by a cup becoming a bracket when reporting the result with cup-writing
Counting a total T of 7 ones in Bundles of 3s we get the result T = 7 = III III I = 2B1 3s