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.

I just started a new Twitter feed @EarlyMath to support early math learning for ages 0-8 through high-quality interactions & research-based strategies.

In early childhood education and initiatives to promote parent interactions with their children, early literacy skills are emphasized, and early math skills are often neglected.  While learning to read is extremely important (as is building executive functioning and social emotional skills), mathematical thinking needs to be brought up to the same standard if we want our children to be able to function in our increasingly technological world. 

Early math skills are important of course for later math skills, but research finds that early math skills are also predictive of later success in literacy.  And yet, being 'bad at math' is still seen as socially acceptable, where as hardly anyone says that they're 'bad at reading'.  Part of this is because people don't understand what mathematical thinking really is - they think that it's calculus and linear algebra - when really, mathematical thinking is about being able to problem solve, follow a logical flow, see similarities and differences, and analyze data. Math is just a way to understand the world around us.

There are some outside initiatives (after school programs, etc) that are working on promoting early STEM skills, but the change also needs to come in daycares and schools and in homes.  Unfortunately getting parents and teachers to help their children develop math skills is not as easy as telling them to read more books to the kids*.  The adults need to be interacting mathematically, talking about numbers, noticing ways to group objects, helping their little ones to recognize patterns.  Learning early math doesn't happen in a vacuum - kids need to have high-quality interactions.

I'm hoping through the new @EarlyMath Twitter feed, I can start to build a community of early math supporters and disseminate information about some best practices.

*Of course, developing literacy isn't as easy as just reading more books, but it is an initial step in the process that's easy to market and promote.

My first paper for the Harvard Extension course I'm taking in comparative education policy - I focused on the socio-economic inequalities in early childhood experiences that lead to differences in school readiness.

My Quora response to "What are the best educational baby toys for 0-6 month old babies?" - http://www.quora.com/Babies/What-are-the-best-educational-baby-toys-for-0-6-month-old-babies/answer/Teresa-Gonczy

Quick answer - the best educational baby toy, especially for a 0-6 month old, is.... YOU!  :-)  
 
Babies at that young age don't really need 'toys' - they need interaction.  Someone to hold them, someone to talk with them, someone to take care of their needs in a comforting way.
 
Once they get closer to six months old, it's nice for them to have objects to reach for and to practice grabbing & holding, but an empty toilet paper roll or a kitchen serving spoon or that random mate-less sock from the dryer is just as good as any 'educational toy' you can buy.

My Quora answer to "What are the most high leverage activities I can do with my 1-2 year old to promote his mental and cognitive development?" - http://www.quora.com/Child-Development/What-are-the-most-high-leverage-activities-I-can-do-with-my-1-2-year-old-to-promote-his-mental-and-cognitive-development/answer/Teresa-Gonczy

Good diet, rich & varied environment, and having fun are all very, very important!  Overall, happy parents = happy baby, so if you're stressing out about promoting development, then it's not worth it.  But that being said, there are specific things that you can do to promote baby & toddler mental and cognitive development...

-Talk with your baby.  A lot!  Describe everything that's going on - focus on the here and now so that your baby can connect the words you saying with the world that he can see and interact with.

-Make sure that you are using specific words, not pronouns (he, she, it, etc).  For example, "Oh look, there's a dog.  See the dog running.   That's a pretty black dog.  Oh, the dog is coming over here.  Ha, the  dog licked your nose!" will teach the word 'dog' much faster as opposed  to "Oh look, there's a  dog.  It's running.  Isn't it pretty?  Oh, it's coming over here.  Ha,  it licked your nose!"

-Be sure to talk *with* your baby, not at your baby.  Interaction is just as important, if not more important, than amount.  Turn your speech into a conversation.  Watch and listen to your baby for their responses - little coos, widened  eyes, puckered lips, waving hands.  Also when you aren't interacting directly with your baby, try to stay aware enough to still respond to these little cues.  By giving attention to these 'language/conversation attempts' no matter how small, you're teaching your baby and your baby's brain that his noises and vocalizations are important - and then he will  practice them more, and the more he practices verbal interaction, the  better he will  get!

-Learn some basic sign language and do the signs with your baby.  Combining the physical movement with the lots of verbal language helps your baby to use multiple parts of his little brain.  You didn't need to learn a lot of signs - in fact, it's often better if you don't because then it often helps parents (and thus babies) to really focus in on the most relevant concept in a string of words.  Using the 'dog' example from above, if you combine it with doing the sign for 'dog', then the baby cues in more to that the word 'dog' refers to the fluffy thing running around, rather than any of the other words you said.

-Start practicing executive functioning games.  Self-control and the ability to inhibit behavior is strongly correlated with success later in life.  So start working on it now, but in a fun way.  Play Opposite Simon Says where your toddler has to do the opposite of whatever Simon Says.  For example, if you tap once, toddler should tap twice and vice versa.  Or if you say 'dog' they point to the 'cat' and vice versa.  (Obviously you do this after your baby has a very firm grasp on the correct or non-opposite way.)

-Make sure your baby gets enough sleep and downtime.  Your baby's brain needs time to consolidate all of the input it's receiving.  So baby needs sleep!  :-)  Also your baby needs some time to just take in the world, be able to self-regulate, etc - so you don't need to be interacting with your baby all of their waking hours either.

Hope that helps!  :-)  As another responder said, it's not worth hothousing your child, but there are some simple changes you can do in how you interact with your baby and what types of activities you do with your baby, which can have a huge effect on helping them to grow and develop mentally and emotionally.