Elementary math is about recursion. It can now be studied on that basis in the New Math Done Right series. This brings down university materials to below college level.
What holds students, teachers, and parents back from using these materials is apathy.
Learning the natural numbers in terms of recursion sets the pattern for rational numbers and real numbers. This is why Grassmann, Dedekind and Peano did it. This is what distinguishes them from Euler. Euler thrashes around to explain the natural numbers and can’t.
GDP figures out how to explain the natural numbers, and their operations and properties.
The modern K-12 system and college pre-service math ed decide they are smarter than Euler and can simply invent on the fly the meaning of natural numbers.
But they don’t want to read GDP and use their methods. Which is stupid, because GDP found what the concepts of natural numbers are. In Euler, we see he did not know them. Neither do you, gentle reader, unless you are among a very few.
It is apathy that holds you back, let me kindly say. You have to fight it. You can’t change your IQ but you can change your apathy.
When you learn natural numbers in terms of recursion, you understand the patterns of numbers. These hold good with easy changes for rationals and with somewhat more difficulty for reals.
This leads deep into mathematical analysis. You can learn calculus before you know it.
You can learn recursive algorithms for probability and for mathematical finance. All this comes from learning natural numbers in terms of recursion. A feast and an opportunity.
Business majors and MBAs who can’t get option pricing can learn recursion with the natural numbers with this material. Then they can learn dynamic programming, option pricing, and stochastic processes using this as a base.