Vedic math has been active for over several hundred years in the Indian subcontinent. This kind of math, a kind of alternative algebra, is nearly unheard-of in the Western world, and is almost never taught in school. One of the reasons it had been nearly unknown is that the first book on its techniques was not published until 1965.
Vedic math a system of reckoning with solving equations which seeks to do the same thing as arithmetic and algebra. It is really a system of techniques and sutras which provide fast and easy ways of reckoning with arithmetic operations which would otherwise be burdensome. A student I know was able to, mentally, without a pen, pencil or calculator, perform multiplications consisting entirely of 3-digit numbers. The same student of Vedic math was also able to mentally find answers to calculus questions that would take over a page of work.
My student had an impressive skill, and certaily taught me quite a bit. But did he “understand” math this way? It turns out that Vedic math reduces math operations to a series of tricks which coax an answer from a problem. It doesn’t require any deep understanding of what is going on. It doesn’t even require you to have even a conceptual understanding of basic arithmetic.
We have tricks too in the Western world. Ever heard of cross-multiplication? Or the FOIL method? Mistakes students make in executing these tricks arise from a misapplication of the trick, not from a misunderstanding of math. Teaching tricks makes a better obstacle to a math education than a passageway. And this is the main objection to Vedic math, and a reason as to why it hadn’t caught on with the western world.
For better or worse, us westerners demand reason, evidence and analysis as a keystone to the understanding of anything, let alone math. Accepting an idea without evidence makes it too easy to reject the idea without evidence. Accepting an idea without analysis makes it easy to reject the idea without analysis. And in this age of “post truth”, it makes it too easy for governments to rule at one’s whim if evidence, analysis and reason are not offered for a decision or policy.