by Robert Rosenfeld The first book on arithmetic to draw on children's natural ability and experience of the world, influenced by ideas from Rousseau, appeared in the US in 1808
Very interesting (both parts 1 and 2). It was actually amazing to me to read that hundreds of years ago, people really did think of examples to try to show when or why you might want to do this calculation. The second is the use of real models (beans, etc). One generally thinks that math was taught solely by "show, then do" methods until fairly recently.
I read an interesting article once about how children can understand fractions starting at home, if they divide up real things (a. whole cake or some cookies for instance, as well as groups of items, which is quite different). I learned simple arithmetic learning to "play store" as a child (real groceries in our basement "store.") I don't remember what we used for money, but I do remember learning to give change by counting back, as well as learning to account for a person giving you coins to make the change simpler. I also played card games which involved being aware of total scores, such as Cribbage. I still enjoy number games.