Chapter one (that is, the chapter following chapter zero) of Here’s Looking at Euclid started off with an extensive analysis of the base 20, base 12, base 2 (binary) and other number systems. Aside from the brief realization that when converting between TBSP and cups or cups and gallons I can actually think in an essentially base 16 system, I find it hard to wrap my head around non-base 10 systems of numbers, so on that subject I simply refer you to Toby’s defense of the base 12 system: http://geekofmanytrades.blogspot.com/2014/03/math-and-sciences-monday-cheaper-by.html
The more intriguing (or at least less brain bendingly intriguing) part of the chapter was the discussion how becoming proficient with an abacus (specifically a Japenese style soroban, with five beads to a row) can improve the speed of mental calculations. I’m beginning to wish that I learned how to properly use my childhood abacus instead of arranging the beads into patterns and rolling my eyes at manipulating the beads to show answers to basic math problems I could already do faster in my head.
After reading about the intensive mental calculations achieved by school children who master the soroban it seems like a very good way to teach basic math skills. Manipulating physical objects as a way of doing math changes which parts of the brain are used, which means that not only could it make basic math concepts much easier to grasp for more creatively and less logically minded children, but even for logically minded children, the crossover of using multiple parts of the brain should improve their ability to recall what they’ve learned. Add to this the fact that soroban then becomes a basis for much more complex calculations later, and I’m a bit tempted to go back and learn to use a soroban in my spare time myself.
Maybe right after I finally tackle quantam physics.