I believe that we should start mathematics education with programming, then go to generator systems for numbers and operators over them, then how to form lattices and operators on patterns in the lattice, and do approximately continuous math and physics only at the very end.
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agree & catchy phrase there! How would you practically upgrade/reform math education & notion? Programming goes a long way towards that - but i doubt it will take-over in school anytime soon.
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Even more catchy phrase as an answer: the revolution will be extracurricular! I don't think that I would start with a general, one-fits-all solution, but with specific children, motivations and styles of understanding, and then see what generalizes.
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