My final project for the Harvard Educational Innovation and Social Entrepreneurship course - a non-profit business plan for the Early Math Initiative, 

"The mission of the Early Math Initiative is to promote mathematical understanding and problem solving among young children with a special emphasis on low-income children ages 2-5 in the United States. The Early Math Initiative provides high-quality, one-on-one interactions with trained volunteer 'buddies' in early ed settings such as preschools or daycares, plus family support and in-home materials, to develop the critical early math skills, confidence, and joy, which young children need to be successful in school and in life."

Short Prezi I made for my Harvard Social Entrepreneurship in Education course, describing more about the Early Math Initiative, a non-profit effort to promote mathematical problem solving and confidence in young children.

My first paper for EDUC E150, Educational Innovation & Social Entrepreneurship In Comparative Perspective, 
Spring 2014 - Harvard Extension School - a brief problem statement on School Readiness: Early Math Learning.

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.

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 Quora answer to "What foundational aspects of programming could be taught in early childhood education?" - http://www.quora.com/What-foundational-aspects-of-programming-could-be-taught-in-early-childhood-education/answer/Teresa-Gonczy

Programming as many programmers think about it (typing various commands in Java or C or whatever language of the day, long algorithmic procedures, waiting for it to compile, etc) is obviously not something that preschoolers can do, but there are aspects of programming and computer science that can be learned in early childhood - sometimes using computers, but often not using any 'technology'.
 
To start off, why programming in early childhood?  Because we want our kids to be creators, not just consumers.  “When human beings acquired language, we learned not just how to listen but how to speak. When we gained literacy, we learned not just how to read but how to write. And as we move into an increasingly digital reality, we must learn not just how to use programs but how to make them.”Program or be Programmed  Our kids (and thus our future adults) should understand how computers work - that it's not magic, but rather that a real person (or more likely a large group of people) designed the hardware and the software, and that anyone can hack at it or change it.
 
From a more academic standpoint, programming principles are wonderful for teaching sequencing, following a set of rules or procedures, and breaking a larger problem down into smaller 'bite-size' pieces - all of which are essential skills to learn in early childhood.  Algorithms don't have to be done on a computer - following a cooking recipe, remembering how to navigate around the school, even knowing the order of how to put your clothing layers on are all algorithms, albeit very simple ones.
 
Programming is also about abstract thinking, which is something that young children are not very good at yet - but I would argue that just because they're not good at it (and probably won't be for a while) doesn't mean that they can't practice basic abstractions at an age-appropriate level.  Asking generalized questions - not just "What do you need to put on before going outside?", but "What would a person need to put on before going outside?"  Helping children to use symbols to represent something else - possibly making up their own 'language'.  Using Legos or other basic building toys to create 'something' out of 'nothing' - a house from blocks, a necklace from pasta.
 
Many programming concepts are actually being taught to preschoolers already, without being thought of as programming or having anything to do with computers.  But learning how to use technology is also important - there are many programs coming out to help young children get even more into programming.  Scratch JR (Page on Mit) uses graphics, rather than typing.  And a project out of Tufts (http://ase.tufts.edu/devtech/pub...) uses physical/tangible objects that the kids can manipulate to lay out their computer programs, and has been shown to develop children's sequencing abilities (Page on Tufts) 
 
Estonia starts teaching coding in first grade (Why Estonia Has Started Teaching Its First-Graders To Code) - maybe we should one up them and start even earlier?  :-)
 
Also - Page on Pbskids

UPDATE 9/9/13 - you can also use board games to teach programming concepts to 3-8 year olds - check out Robot Turtles!  http://www.kickstarter.com/proje...

We can create the next generation of entrepreneurs by letting kids (and adults) create, fail, explore and collaborate in family-friendly makerspaces across the United States.

Originally published on Women2.0 at  http://women2.com/why-the-maker-movement-needs-to-be-kid-and-family-friendly/

It all started with a tweet. I don’t usually check Twitter, but for some reason, on May 4, 2012, I was paging through my feed, when I saw it – @BoingBoing “To do in LA this Sunday: Organize a kid-friendly hackerspace” And so that weekend, I met up with Tara Tiger Brown and a bunch of other teachers, hackers, entrepreneurs and makers to talk about creating a makerspace for families.

Well, we didn’t get it all done on that one Sunday, but now 7 months later after lots of meetings and tons of planning, the all-ages Los Angeles Makerspace is really happening!

We have a location in Downtown Los Angeles at the LA Mart, we’re fundraising to buy equipment, and best of all, we have real live children and families who are excited about our space and coming to our events and classes. 

WHAT’S A MAKERSPACE, YOU MIGHT ASK, AND WHY IS IT SO EXCITING, AND ALSO SO IMPORTANT FOR BOTH KIDS AND ADULTS.  A makerspace, sometimes also called a hackerspace, is a place where people can come together and create, invent, tinker, build, learn and play with all sorts of different equipment and materials. Some makerspaces focus more on electronics or robotics, others on arts and crafts, and a few even on biotechnology.

Makerspaces are popping up in schools, libraries and private locations all across the US and the world. At a makerspace, you learn by doing, by failing, by exploring, and by collaborating – and this is why makerspaces are wonderful for kids (and adults!)

There’s the saying that we learn 10% of what we read, 30% of what we see, and 90% of what we do. In a makerspace, you’re mostly learning by doing – you might read the manual, or watch someone else demonstrate first, but then you dig right in and get your hands dirty.  Whether it’s programming or soldering or 3D-printing, all of our makerspace classes and workshops are hands-on, where kids and adults are actually doing the activity. They’re not just sitting at a desk listening to a teacher or reading a textbook – they’re actively engaged in using their hands and their brains to figure out how to create something new. And that active engagement really cements the learning – much better than a traditional classroom setting.

And while they are actively exploring and creating, they’re also failing, sometimes over and over again – and that’s a good thing!   The world isn’t perfect, and we’re not going to be able to get everything right the first time we try – but how we really learn and keep improving is by continuing to try even after we fail. In many schools, getting an F on a test is a horrible thing and something to avoid – but failure is really just feedback, a way of telling you what you still need to work on, what else you still need to learn.

‘Grit’ matters – can you persevere even when you can’t seem to get it to work? When a baby is learning how to walk, they fall down so many times, but each time, they get back up and try again. By working on maker projects, kids and adults have the opportunity to try out different options, see which ways work and which ways don’t, and to realize that ‘failing’ is all a part of the process. As Edison once said, “I have not failed. I've just found 10,000 ways that won’t work.”

And with kids and adults more comfortable with failure, they’re likely to continue exploring, to keep that sense of wonder, to stay curious, and to feel capable!  “TEACHING’S PRIMARY PURPOSE SHOULD BE THAT EVERY STUDENT GRADUATES READY TO TINKER, CREATE AND TAKE INITIATIVE” – JENNIFER MEDBERY.  There’s so much, both big and small, that we could all be doing to help make the world and our local communities a better place, but all too often, people don’t think that they have the skills or abilities to do anything about it. And to some extent, that’s true – they might not know how to do it now, but that doesn't mean that they can’t learn and figure it out.

When we first met to organize a kid-friendly hackerspace, we didn't know how to do it – each of us had some related skills or experiences, but none of us had ever done this exact task before. But that didn't stop us – we kept exploring different options, and eventually things fell into place. And we hope to give our LA Makerspace makers, young and old, that same sense of exploration and curiosity and capability – that even if you don’t know how now, you can figure it out and make it happen!

“THE MOST IMPORTANT THING ABOUT MAKERS IS THAT THEY BELIEVE THEY CAN CHANGE THE WORLD.” – DALE DOUGHERTY, MAKE MAGAZINE.  And they’re not changing the world all by themselves – although we often call the Maker Movement DIY or Do-It-Yourself, it’s really DIT or Do-It-Together.  Having a makerspace brings the community together for collaborative learning. And it’s not just the kids learning from the adults – often times the young and old(er) are learning side-by-side, and sometimes the kids are even teaching the adults, such as with our Arduino class taught by 11-year-old Quin (also known as Qtechknow). In a makerspace, everyone shares not only tools and equipment, but also ideas and knowledge. And this makes learning and working on projects go a lot smoother and also a lot more fun! Together we can do much more than we could ever do alone.

“FIXING EDUCATION AND FIXING THE WORLD IS THE SAME THING.” – NOLAN BUSHNELL, FOUNDER OF ATARI.  Through changing the way kids (and adults) learn, we can build a new world and create the next generation of entrepreneurs. Education isn’t just about what happens in schools – education is happening all around you, every day – and you always have a choice as to how and what you’re going to educate yourself about.

And with the all-ages Los Angeles Makerspace and all of the other family-friendly makerspaces across the world, now you can educate yourself about creating everything from robots to holiday ornaments within a fun community of other makers! 


Read more at http://women2.com/why-the-maker-movement-needs-to-be-kid-and-family-friendly/

A long time ago, in a galaxy far far away, I wrote a paper for my Math History course at UCSD on Ancient Chinese Mathematics - Right Triangles and Their Applications.