As the mother of special needs kids, I know the value of manipulatives. They can be important ways to reach those who learn differently as well as literally make math more hands on. If you think manipulatives are something new in terms of helping children learn math, consider these pages from Study Arithmetics: Grade Three, published by Scott, Foresman & Company in 1930:
These pages (from the 1940 edition) show using "toy builders", wooden toys like Tinker Toys.
As I mentioned in my article on vintage primers and antique school books, there are still some things you can learn in those old pages.