I found a math book aimed at math grads going into official sub-college teaching positions, and was shocked about the historical context provided. Every idea had 2 or 3 variants that differed in origin. To me it would have made math 2x more fun for a lot of pupils. But none of it made it into our classrooms (lack of time ? a dusty pedagogical approach maybe ..). It's probably vital for most people that don't have their neurons naturally properly aligned to a subject to have various informations and point of views about the problems and goals.

Which book?

It's a french book. "mathematiques au concours de professeur des ecoles" (Hachette editions 2006)

For instance the numbering system chapter mentions non roman numeral symbols, babylonian, egyptian up to indian of course. Then various ways to multiply numbers. As a kid everything was pruned and we only saw one thing.

If you're interested in ring theory, for example, Kummer's 1844 manuscript on "ideal complex numbers" clarified a bunch of undergraduate algebra for me. Overviews:

https://projecteuclid.org/journalArticle/Download?urlid=bams...

https://arxiv.org/pdf/1108.6066.pdf

IME, you will get that information if you get a math degree. You are less likely to get it, unless you read the textbook (that is, not from the teacher) from any K-12 or non-major math classes because that's not their focus (for better or worse). But often the motivational cases for the math are present in high school and non-major math course textbooks. Just not part of the class because that's not what you're going to be evaluated on.