My Final Policy Analysis Research Paper for SSCI E101, Education Policy Analysis and Research Utilization In Comparative Perspective, Fall 2013 - Harvard Extension School on the importance of numeracy in UK early learning policy.
My Quora response to "What are the best ways to foster math skills in very early childhood?" http://www.quora.com/Education/What-are-the-best-ways-to-foster-math-skills-in-very-early-childhood
There are definitely a lot more resources for early literacy than early math (about three times as many hits on Amazon), but early math is as important, if not more important. Research has found that early math skills are of course predictive of later math achievement, but are also more predictive of later reading achievement than early reading skills are. (Page on Ncpat)
Early math is so much more than just counting, but we can start there. Just as early language strategies tell you to "read, read, and then read some more", you should "count, count, and then count some more!" :-) Don't just recite the numbers, but count actual objects. Count your baby's toes, count the steps as you go up stairs, count out crackers as you're eating. "One wheel, two wheels, three wheels, four wheels, the car has four wheels!"
Besides counting, early math involves measuring. First measuring just means labeling with words, such as "bigger", "smaller", "longer", "shorter". And later, measuring involves using measuring tools like rulers and measuring cups. Just as with trying to use counting in everyday language, try to use measurement words when talking with your little ones.
Early math is also about recognizing patterns. Patterns are all over - there are patterns in time (our bedtime routine is snack, bath, song, and then lights out) and patterns in space (making a line of two short blocks, one long block, two short blocks, one long block). Ask your child, "What do you will come next?" or "What's missing?" You can use music and movement to create patterns, such as jump, clap, tap your head.
Early math involves sorting and organizing data. At the beginning, that just means matching socks by color or sorting food by whether it goes in the fridge, freezer, or cupboard. Later, analyzing data means making simple charts or graphs of the weather, or what color cars passed by the house that morning.
Interaction is the key - talking with your child about mathematical concepts, which doesn't mean explaining calculus to them - it just means saying "over" and "under".
The NAEYC (National Association for the Education of Young Children) has some good resources... Math Talk with Infants and Toddlers
The Twitter feed @EarlyMath also posts lots of interesting research and ways to develop early math skills. Early Math (earlymath) on Twitter
My Quora response to "What's the best way to promote early childhood development through technology?" http://www.quora.com/What-is-the-best-way-to-promote-early-childhood-development-through-technology
Although I don't agree with the absoluteness of the recommendation, there's a big reason why the AAP says no screen time before two years old. The best way to promote early childhood development is through high-quality interactions. These interactions are currently best provided by responsive caregivers, not technology.
But as some of the other responders have mentioned, technology can be beneficial to early childhood development if it is used to promote and enhance those high-quality interactions.
A post on Slate (When Baby Apps Actually Lead to Learning) talks about how 'baby apps' can be a positive influence on children - if parents use them as an interaction point! The apps and videos don't make a difference (and may even have a negative impact) if the parent just sets their child down in front of the screen. But if the parent engages with the child and the technology, asking questions about what's happening on the TV, helping the child to use the app and talking about what's happening, then this screen time can contribute to learning. Also another study (Skype Me! Socially Contingent Interactions Help Toddlers Learn Language -Children learn best during real-time interaction, new study finds) finds that young children can learn new vocabulary through screen time, if the people or characters on the screen are responding to children in timely and meaningful ways - aka grandparents interacting through Skype. Also there are other technologies, such as the LENA Recorder (Advanced technology to accelerate language development of children 0-5 and for research and treatment of language delays and disorders), which helps parents to see how much they're speaking with their children and how often they're engaging in back-and-forth interactions.
So in practical terms, use technology as a jumping off point for your interactions with your child and as a way to expose them to concepts they may not otherwise see in the real world.
* Does your toddler have a fascination with cars? Do a Google image search for 'cars' and instantly you have a treasure trove of pictures to talk about different types of cars, different colors, how many doors, etc.
* Is your preschooler asking "why?" too often? If you don't know the answer, admit that you don't know, and say let's figure it out together. Then use the internet to see if you can find out why.
* Did your kindergartener come home talking about a friend who just got back from a trip to Alaska? Watch videos of snow falling, and talk about what it might be like to live someplace so cold.
My thoughts on education, cognitive science, early childhood, organization management, non-profits, and whatever else I happen to be thinking about! :-)