I’ll do my best to give an overview. It is very complicated for the mom; expect to read this multiple times (I read the book over and over). If you can get your hands on the book “How to teach your baby math,” it would help a lot, but I realize shipping costs or buying new is not always feasible (I’ve only read it from the library myself).
The pre-step is to make cards with dots on them, starting with a card with 100 dots and working down to 1 dot. Doman suggests a 14 in square of posterboard and red pre-gummed stickers; I used a pack of regular A4 cardstock (bought on sale at a local craft store) and a bottle of red tempura paint with a sponge applicator top that was round. Other people in this forum have suggested a cork dipped in red ink and a few other things. Making the cards took a couple of hours and was annoying, but worth it. Write the number of dots in each of the four corners of the card, so no matter in which orientation you hold it, you know what the number is.
The theory is that babies are born with the ability to instantly perceive quantity; they know how many dots are on the card without counting. They lose this ability between age 3 and 5 usually. What you are doing is first labelling quantities (this many dots is called 4) and then helping the baby intuit the rules of arithmetic (what adding, subtracting, multiplying, dividing means you are doing to the quantity) in the same way a baby of this age intuits the rules of grammar from listening to you speak.
Step one is showing the dots to your baby. Take the numbers 1-5, sit facing your child (or hold a smaller child in your lap), and show them as quickly as possible, no more than 1 second per card, saying the number as you show it. Act happy and only do it as long as your child is having fun. Once you’ve done 5 cards, put them away for a while (how long is up to you; do something different with your child before doing more cards). Doman suggests using two sets of five cards every day (eg 1-5 and 6-10); I found that to be too much and only did one set a day. Each set should be shown 3 times a day, and you shuffle the cards between each showing…
Do this with 1-5 (and 6-10 if you’re doing two sets a day) for one week. From then on, every day take the lowest-numbered card out of each set and retire it, then add the next higher card (retire 1, add 11).
Once you’ve retired 1-20, continue showing number sets three times a day, and add showing equations using retired cards three times a day. (Make sure the sessions are still a little bit apart, even though you’re now doing 6 or 9 sessions a day. Each one should still only take a few seconds.) Start with addition. Take the 1 card, the 3 card, and the 4 card, and show the number as you say it when you tell the baby “1 plus 3 equals 4.” Do three equations like that in a set (I only did 2) and do three different sets every day (don’t repeat equations).
The theory here is that the baby will learn what “plus” means just like they learn that adding an -s to a word makes it plural. You don’t explain it; you just give lots of examples.
For two weeks you show one or two sets of numbers three times a day each and three sets of addition equations a day, for a total of six or nine sessions of math daily. After two weeks, stop showing addition and start showing subraction. Two weeks after that, stop showing subtraction and replace it with multiplication. Two weeks after that, stop multiplication and show division.
Somewhere in there you will finish all 100 dot cards. Show a blank card and tell your baby it is named “zero.” Then stop doing number cards entirely; only do three sets of three different equations every day.
It’s now been about three months and you’ve done all the dot cards and the four basic operations. Now you can go different directions, like only showing the answer card, or showing two possible answers and letting the baby pick the correct one. (5+7= what? 13 or 25. Let the baby grab the correct card.) Try 3 and then 4 step equations (1+3+7=11). More ideas are in the book; if you do it and get to this point, I’d ask on the forums for more ideas.
That’s a basic overview. I hope it’s not too confusing. I thought it sounded crazy when I read the book, but I really wanted to find out if it worked. I guess I don’t know for sure yet, but it seems to be doing something. It’s fun, too!