After a lot of searching, I found a few good academic resources on this subject. Jo Boaler’s book, What’s Math Got To Do With It, and the Sidwell Friends School Math website for lower schoolers, provide lots of good tips for parents. Neuroscientist Lise Eliot makes an interesting case for the early and deliberate development of visual-spatial skills in her book "Pink Brain, Blue Brain" and Stanislas Dehaene explores the way our brains process and understand numbers in his book Number Sense.
Don’t just think books. Think blocks. Lots of blocks and building sets. Since a strong spatial ability is tightly linked to higher level Math proficiency, most researchers believe that block play will help kids in Math. In fact, there are studies that show a correlation between the sophistication of early block play and later Math achievement.
Play-doh, art, sand play, and general outdoor play are obviously really important at this stage as well. From the research that I've done, general manipulation of objects/play with objects helps children create a strong foundation for Math. Similarly, activities that involve sorting, classifying, and stacking/nesting of objects are great as well.
Count with kids A LOT.
If you live in a big city with lots of skyscrapers, get them into elevator math. Going up and down on an elevator is kind of like riding a number-line. Kids get to press a button and then see the elevator move up each floor. Talk to kids about the numbers on the elevator. Read the numbers. Calculate how many more floors you need to travel to get to the desired one.
Count when you grocery shop (I need five apples) and when you clean up (Let’s put five blocks back in the bin). Get them to help you cook (we need five eggs). Count whenever you can.
Use Math talk when you can; for example, can you find me two blue blocks. Great, now find two green ones. How many blocks do you have altogether? Let’s count. See two plus two equals four. Use words such as add, subtract, half, one third, taller, shorter etc.
Don’t just think numbers. Think shapes and patterns. Get kids to draw and color shapes. Get them to identify shapes around them. Get them to look at and identify patterns with shapes.
And finally, let them measure stuff. For some reason, my kids love playing with measuring tapes. So get them to measure all the furniture.
This is when Asian moms start getting very serious about Math. They figure that kids are now old enough to start learning the real thing. So they introduce concepts, and then they do what Asians love to do: they practice A LOT.
Most Asian kids I know start a Math enrichment program like Kumon, Abacus, or Math Monkeys around age 4 or 5. The idea here is to get kids really familiar with numbers and mental math. I researched these programs and found that they are very, very drill based. Now, I’m all for some daily drilling, but to me Kumon seems mind-numbingly boring. As a result, I chose not to enroll my son in Kumon. However, I know several moms who swear by it, and it definitely makes kids very, very familiar with numbers and basic computations (add, subtract etc.) If, like me, you’re not willing to go the Kumon route, you can still buy the Kumon books and use them a few times a week so that kids get some amount of drilling/practice.
Other great ways to get kids to become very familiar with Math include board games. Play lots of Snakes and ladders and any other game that involves adding and subtracting. Play card games. Make up games with dice and cards. Games like Yahtzee and Ludo work well too. Play mental math games when you're in a car or bus.
Use lots of blocks, legos, jigsaw puzzles, and games that involve numbers and strategies (Connect Four, for example). All of these will help kids develop spatial skills, which are tightly linked to higher level Math proficiency.
Introduce the Tangram game – great for getting kids to disembed shapes, and thus develop spatial skills.
Singapore Math workbooks are great for this level. They introduce kids to interesting and complex word problems that require good verbal comprehension and significant logical and analytic thought. These books are not for the faint-hearted. They are about two or three years ahead of your average American text book, but then Americans don’t seem to care about Math the way Asians do.
According to Conrad Wolfram, director of Wolfram Research and author of an article on connecting Math to the modern world, "programming is the way you write down Math in the modern world." It makes sense to begin programming activities (lego-programming/elementary robotics, Scratch, Logo etc.) with kids in elementary/middle school.
I think that creating a Math rich home and investing significant time and energy in Math from the get-go is a good idea. Just as early reading and talking help prime kids for success in school, I’m fairly convinced that early exposure to Math games and Math concepts help prime kids for success in Math. One more thing: in Asian families, succeeding in Math is not an optional thing. Just as kids have to learn to read fluently, they have to do well in Math, and that’s that.