Asked ‘How old next time?’, a 3-year-old says ‘Four’ showing four fingers; but objects when seeing them held together two by two: ‘That is not four, that is two twos!’ A child thus sees what exists in the world, bundles of 2s, and 2 of them. So, adapting to Many, children develop bundle-numbers with units as 2 2s having 1 1s as the unit, i.e. a tile, also occurring as bundle-of-bundles, e.g. 3 3s, 5 5s or ten tens.
Recounting 8 in 2s as 8 = (8/2)x2 gives a recount-formula T = (T/B)xB saying ‘From the total T, T/B times, B can be pushed away’ occurring all over mathematics and science. It solves equations: ux2 = 8 = (8/2)x2, so u = 8/2. And it changes units when adding on-top, or when adding next-to as areas as in calculus, also occurring when adding per-numbers or fractions coming from double-counting in two units. Finally, double-counting sides in a tile halved by its diagonal leads to trigonometry.
The following papers present close to 50 micro-curricula in Mastering Many inspired by the bundle-numbers children bring to school.
Learn Core Mathematics Through Your Kid’s Tile-Math:
Recounting Bundle-Numbers and Early Trigonometry
This first paper is written for the conference ‘The Research on Outdoor STEM Education in the digiTal Age (ROSETA) Conference’ planned to take place between 16th and 19th June 2020 at Instituto Superior de Engenharia do Porto in Portugal.
The Power of Bundle- & Per-Numbers Unleashed in Primary School:
Calculus in Grade One – What Else?
This second paper is written for the International Congress for Mathematical Education, ICME 14, planned to be held in Shanghai from July 12th to 19th, 2020, but postponed one year.