The tokens used on such a counting-board are called jettons. I’ll second your recommendation, and add my own next step: moving on to using a slide rule. Seriously, seeing how real numbers move on a slide rule really helped give me a feeling for how they ‘dance’ in calculations.

I think http://www.mernick.org.uk/lnc/jetton/jetton.htm was a good reference I found when I first used jettons, but it’s been so many years now that I can’t say for sure. http://www.chicagocoinclub.org/projects/PiN/juh.html has some information too.