An interesting article in ScienceDaily about reiterating the advantage of engaging, prosodic, and interactive reading with a child over simply reading a book. This is what I think teaching babies/young children to read and EL in general embodies, and is that 'difference' between working with flashcards and programs in most great EL programs vs. the idea many people have of what EL is about.

http://www.sciencedaily.com/releases/2013/09/130912112736.htm?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+sciencedaily+%28ScienceDaily%3A+Latest+Science+News%29

Very cute Kiwimum

I have a few thought and Ideas, most of which we either did or still do with Alex. We started really trying to work on her narration skills, story-telling, and teaching-back skills at about 2.5, with a big boost in effort just before her 3rd bday.
1) the first thing we started was just getting her to attempt to give a few sentence narration of what had JUST happened in a short picture book we read. Of course, with lots of prompts and questions in the beginning. It sounds as though you are doing something similar with story-telling (which we also did some of then), but I did want to make sure she was also modeling from great books with lovely vocabulary and proper sentence structure.

2) storyboards/puppets- Give her a venue! I bought one of the large felt storyboards, and several sets of felt 'characters' to go with it. I bought a few popular story sets like a farm set, a family set, etc, until there was a pretty good mix. Then I showed her how to use them to enact increasingly elaborate scenes and stories. I read somewhere that having them do this concretely helps them to develop more vivid mental imagery, in greater detail, that translates into their ability to do it without the aids. This made a lot of sense to me, and I have seen it work with Alex.
We also built a larger puppet theater for her for this reason!

3) Rory's Story Cubes- these I HIGHLY recommend! If you haven't seen them, it is a game of sorts. It is basically a set of 10 6-sided dice that have only pictures on them. We have two different sets, the original and an 'actions' set. You roll the dice, look at the pictures you garnered, and have to tell a story around them. It really is hilarious, and it has made me appreciate the sheer genius of the concept--as well as the ability of kiddos to do it!
At your daughters age I would actually suggest making your own: take 4-6 blocks, paste or draw a picture (more effective here than a word because you want them to think in terms of the images. I also find it is useful for memory practice.) these pictures should be things that interest her in the beginning, but make sure to vary the categories. You want a lot of pics that seemingly do NOT go together to get their creative juices flowing:)
Alternatively, there is a Rory's Story Cube app available that is nice.

4) definitely journaling. Let her watch you writing her stories and thoughts on paper. This made a big difference to Alex as she not only loved to read and reread the things she had made up, she wanted to make them bigger and better. I also think it is important that they I know you value their stories enough to record and share them

5) vocabulary building- this is something we do a lot of still, with lots of games and apps, but we use specific games for the story-telling/writing aspect of it. For example, if she uses a bland word, we might discuss 4-5 synonyms that might create a more powerful image or convey the meaning she wants. At your kiddos age you might just separately play a simple synonym/antonym game.

6) practice visualization, making 'pictures' in her head. Ask her to take a picture with her mind of something I. Front of her, close her eyes, and practice describing it in detail...eventually you can get her to visualize things for her stories, using more imagination that something tangible she can look at.

7) tell her stories of young children that have written and or published stories at young ages! There is something powerful about a child seeing that another child has done something. I can't think of names of the child authors off the top of my head, but I did look at one point.

Anyway, maybe a couple of ideas will appeal...

I just want to say we really like the DinoLingo sets!
Alex now has a few of the sets in different languages, and they are by far one of her favorite language programs.

One thing, if you are considering purchase of more than one language, or are a returning customer, DEFINITELY contact them directly as they are great about giving additional discounts in these situations!
For example, I phoned to purchase two sets this morning and was given a discount code for 20% off the total. ( not good in conjunction with other offers)

If anyone is interested, she gave me permission to post it here:
DINOFFS20

(She gave it to me via phone and I didn't clarify caps or no caps so you may have to play with it a bit!)

Welcome to the forum Brad44!

Before anybody can give you much in the way of specific advice, can you provide a bit of background? If this is your initial starting point into teaching your child to read, for example, then you will definitely want to start at the beginning. I hesitate to say your first foray into early learning (EL) as many parents in this forum worked with their tiny tots long before they stumbled upon BrillKids, Doman, or official EL and just called it good, involved parenting

If you perhaps did a DVD program such as Your Baby Can Read or Monkisee, then you may well be able to either skip the first few lessons or go through them fairly quickly so as to keep your child interested. I think that the first 20 lessons in LR are pretty much review of YBCR....the beauty of LR being the incredible volume after that, as well as the ability to customize.

And again, a bit of background regarding your LO's previous exposure to a baby math program will tell us more. If you did Doman dots, then this will make a lot of difference.
And for what it is worth, LM for a 3 year old seems to be hit or miss. What research there is here is a bit more controversial as the ability to subitize as babies is still questioned. However, I am absolutely certain that doing LM with my baby gave her a great basis for quantity and number sense that we built upon! I recently read a paper that hypothesized the ability to estimate quantity in the preschool years strongly correlates to long-term mathematical ability...of course, one can argue that there are stronger factors involved, but I do think this was a great stepping stone.
I also highly recommend picking up a copy of Marshmallow Math for fantastic ideas on building math skills with your 3 year old, with a caveat: I found the book to be much more useful and efficient if it is read in its entirety and the ideas/activities implemented concurrently...this made a huge difference in my math-loving child's understanding!

As far as music- definitely start LMus at the very beginning! It is so much fun and there is so much information included.

Hopefully a bit of feedback on your LO's previous exposure will give us all a bit more to go on as far as guidance for you! And don't forget to let us know how it is going

Krista-
Sorry for the late reply, I haven't been able to be around!

I LOVE the Andrew Campbell Living Memory book! I cannot say enough great things about it. Yes, everything in it can be found on other sites, books, library, etc. for free. But the book has SO much included in it, all in one handy, wonderfully organized and collated package.

Alex actually has delighted in memorizing poems and general memory work. I am convinced that it is because of EL and more RB visualization practice, but she tends to read them through a couple of times, read them aloud, and then spends a day or two fine tuning. We learn at least a new piece per week now, an the Living Memory book is my go to source as I have it in PDF format. She has memorized things ranging from the Preamble to the Constitution, Pledge of Allegience, Poems by Robert Lewis Stevenson, Jack Prelutsky, the National Anthem, Linnaeus's classification system, any number of things. So Much FUN!
And we only spend a few minutes per day. I made a binder as recommended in the book, with a simple review system for weekly and monthly, but she will start reciting for fun at random times during the day
One morning she wasn't even awake and was mumbling prime numbers!

I bought my copy in PDF format via Lulu.com, but I see that Amazon has it in HB as well. Honestly, I usually like to have physical copies of books but in this case the PDF works much better as I can print out the page I need and add it to her binder.
http://www.lulu.com/shop/andrew-a-campbell/living-memory/ebook/product-17520206.html

Oh! And it is designed for a Classical-style education, so there is a great deal of say Latin and Greek materials as well. Lots of history, although we are learning those more in a timeline fashion as I do not believe having her memorize lots of dates at this point, out of context, is effective or efficient.

Here is a video we made a few month ago of her reciting The Preamble to the Constitution and the Pledge of Allegiance when President Obama came to our city:

http://youtu.be/Ttp9OwFQoek

Absolutely teach grammar as soon as possible! As well as literary terms and devices, and anything else you might find in a lit class. Honestly, I have found it far easier to teach Alex with examples from children's picture books than anything else even college-level lit books might use as examples. The next time you open a picture book, take notice of the huge range of everything from sentence structure, punctuation, and literary devices. I think Alex was not even two when we introduced parts of speech, punctuation, and things like onomantopeia, alliteration, hyperbole, personification, etc.... So many more vivid examples in children's books. I will list some of our favorite resources below, but I also made little 10-inch long cards of all the parts of speech and lit devices and put them up on a wall near where we do our bedtime reading so that she has them in view. As we do our night time reading she likes to point out examples for me:)

So, as Lelask recommended, we started with the Scholastic Parts of Speech Tales, Grammar Tales, and Punctuation Tales, which have a separate little book for each individual topic.

Very soon I stumbled upon a series of fabulous and fun to read books by Brian P. Cleary. I can't say enough great things about them as each book concentrates on say, a part of speech. (Or similes, metaphors, whatever). With titles such as 'To Root, To Toot, To Parachute: a book about Nouns' or 'Hairy, Scary, Ordinary: a Book about Adjectives' they are just too cute. Most libraries carry these, so have a look.
Here is a list of some from Amazon:

http://www.amazon.com/s/ref=nb_sb_ss_c_0_15?url=search-alias%3Dstripbooks&field-keywords=brian+p.+cleary&sprefix=Brian+P.+Cleary%2Caps%2C995&rh=n%3A283155%2Ck%3Abrian+p.+cleary

Oh! There is a great vintage book called Grammar Land by M.L.Nesbitt that she enjoyed tremendously, it is very silly and fun. Listening to it really helped her solidify the ideas as well. Here are the links to download the free PDF and the audio recording if you like:

http://archive.org/details/grammarlandorgr00nesbgoog

http://www.booksshouldbefree.com/book/Grammar-Land

We did some of First Language Lessons as well, but I honestly find much of it very, very redundant and Alex gets very frustrated and uncooperative it I try to make her rehash something she already gets. Exactly how many lessons does one need on nouns?

I just bought her two levels of Michael Clay Thompson LA and I think this will be much more appropriate given all the EL she has already done in this area.

Tamsyn-
It's funny, that is one of the very first poems that I gave Alex for memory work after buying the Living Memory book by Andrew Campbell! We love it as well:)

MandaB-
As far as memorizing the periodic table in order, whilst this can be fun and a challenge, as well as good memory practice, I think it is far more important to learn the element names, symbols, and spellings. Then group according to metals, non metals, noble gases, etc.
For every class, major exam, etc., there will always be a periodic table available...and you wouldn't believe how many Uni kids come to class having memorized the symbols in order, but can't tell you what Ag actually is:)

For your kids age take a look at the Ellen McHenry Elements...and she has a FREE element game to download. The CD that comes with it (or download) has lovely songs to learn, and I am almost positive they are in order.
http://store.ellenjmchenry.com/?product_cat=elements

That being said: what REALLY might appeal to you kids is the more RB approach. There are whole books written on suggestions, but instead of a silly story method (which I think would be a blast-there are existing element cartoons that might help) they focus on visualization. Much like teaching to visualize the Soroban in a lot of ways . The best one I have seen is one that chunked the visualization by group of the periodic table so that they could 'zoom in', and then put it all together. I must say that this tends to be what happens after using it so often!

BTW- Dr. Jones has a system for this, a game using his bits for memorization that I remember him telling me about that sounded like a lot of fun. I know he does it in order and includes all sorts of extra information. Hhmmm.

Oh, oh, oh, I can help with the chemistry:)
...and maybe the Japanese, 
We just returned home and I have been thinking of trying to get Alex on video singing the song The Elements. We are chemists, so we have ideas all over the house. I will share so e of our favorites:)
Theodore Gray made a gorgeous version of the original The Elements song that is available on YouTube:

http://youtu.be/sm1uxjGm_N0

And if you get VERY industrious, here it is sung in Japanese!

http://youtu.be/ljsUVDOcYB0

Okay, so other fun ways to teach the periodic table to two-year-olds....
We started with a couple of things. We bought these periodic table building blocks for Alex I think when she was an infant because they were just too cute, and so they have always just sort of been around. Of course, a bit of creativity will give you myriad games to play with them. I know shipping might be a bit difficult to your area, but they would be incredibly easy to make your own version:)

http://www.amazon.com/Uncle-Goose-PT-20-Periodic-Building/dp/B005JAE052/ref=sr_1_1?ie=UTF8&qid=1375324609&sr=8-1&keywords=periodic+table+blocks

I actually think the single most useful item that helped was just the periodic table placemat! We have this one...actually I think we have 3-4 of them, the laminated kind that are great for teaching the kiddos just about anything! I remember playing games on it whilst eating or whatever. If you like the look of it and think it will help, please send me a PM. I will happily drop one in the post to you free of charge:) all in the name of great chemistry and The Great Baby Challenge!

http://www.amazon.com/Painless-Learning-PRD-1-Periodic-Placemat/dp/B000H6F4W6/ref=sr_1_3?ie=UTF8&qid=1375325760&sr=8-3&keywords=periodic+table+blocks

Oh! And ShenLi already did a wonderful job creating LR files for teaching the elements as well...

There is also a great jump-rope style chant that teaches the elements (in order) that would be fun to do with little ones whilst jumping on a trampoline, bouncer, bed, etc...I actually think it is available as a download. I want to say it is from Ellen McHenry's basement? I will have a look and see if I can find it...

Izp11-
Let's see if I can help with some of the more unusual, non- 'game', non-worksheet things we did to memorize addition/subtractions facts. I think your oldest is more active like mine, so maybe some of the physical methods will work better:)

1) mandabplus3 shared a truly great album of math facts songs that Alex enjoyed, especially whilst jumping on the trampoline. https://itunes.apple.com/au/album/addition-songs/id316086214

2) if she is up for a bit of artistic work, one of our favorite ways to do math is in the windows! Crayola makes some amazing window markers that have some amazing effects. Our favorite are called Crystal Effects, and are great for combining vertical writing work, math, and art:)
http://www.amazon.com/Crayola-Window-Markers-Crystal-Effects/dp/B006E5TAFQ/ref=lh_ni_t?ie=UTF8&psc=1&smid=ATVPDKIKX0DER

3) if she likes the idea of community service/feeding the poor, there is an amazing website called Freerice.com. They donate food to the hungry fro each correct answer, and the kids can keep track of how many grains of rice they have donated. This has made a big impression on Alex.

4) reading living math books! We make sure to include AT LEAST one living math book into our bedtime reading, as well as non-fiction, fiction, and primary science. I really believe this makes a huge difference and helps introduce topics and extra practice that simply would not fit into our schedule anywhere else.
You can find living math books by topic. Here are a couple of our favorite lists.
www.livingmath.net
www.the-best-children's-books.org/math

5) Ellen McHenry's Basement Workshop has a free download called 'Mr. Pig's Magic Math' and 'Storm the Castle' that she might like.

6) try allowing her to design art of her own with neat math facts ( I had to put those in nearly for Alex) and hanging them on the ceiling above Alex's bed. She would stare at them as she was going to sleep, saying some to herself. There is something amazing about putting them into your brain just prior to falling asleep, then allowing them to process whilst she is sleeping.

7) car-schooling...all I can say here is that a captive audience is great! Math facts music, mom reciting, whatever!

math facts hopscotch- give a problem and let her hop to the answer. We worked on listening skills at the same time, as in asking her to hop or proceed in a specific way. A funny story: Alex decided that hopping backwards was negative numbers, and thus learned to add and subtract combinations of positive and negative numbers in this manner with no fuss and lots of giggles.

9) Kakuru puzzles- these I had never heard of but found online. You can print them for free. They are similar to crossword puzzles but use numbers instead of letters. Some double as logic puzzles!

10) ball toss- get a light ball or balloon, and toss from one person to the next. Say a math fact, toss the ball, and the person catching it has to say the answer before tossing it to the next person. We actually started this game with Alex as a tiny tot with counting and geography (we used a blow-up earth ball and did continents, oceans, capitals, etc.) now I know that you can purchase inflatable balls with math facts printed on them, such as these:
http://www.amazon.com/American-Educational-Products-HUB1410-Addition/dp/B000CBWVQS/ref=sr_1_7?s=toys-and-games&ie=UTF8&qid=1373950835&sr=1-7&keywords=inflatable+math+ball

I actually think it simpler and more fun to inflate a balloon and tey to keep it off the ground. You can use a marker to write whatever facts you are working on directly onto the balloon.

And of course, all apps and computer programs are not created equal! There are SO many free math fact sites that might catch her interest whilst gaining some simple computer skills. If Alex gets to use a mouse, she suddenly becomes willing to try all sorts of new things:)

Ah! And I have a ton of ideas and things we accumulated to practice her multiplication tables, but I guessthat should be another post altogether

There are definitely lots of fun ways to teach math facts, and games are definitely some of my favorites. As others have mentioned, the GiggleFacts are a lot of fun, and we used programs, RightStart games, apps, and board games, among other things.

I think it depends on where you are in your math program. It sounds as though you already have a math program but just need to solidify those facts for fast recall.
I actually don't think that flashcards are the way to go for young kids memorizing facts. Don't get me wrong, it does work, but I think that the amount of time it takes (especially as they will get bored FAST!) isn't worth it. It is an opportunity cost for me, primarily because I think that it takes longer for them to get to the point where they can translate that to paper with understanding and the fact that I want them to enjoy what they are doing!

We did Jones Geniuses math in the beginning to familiarize her, and eventually did RS A and B, working on facts with the RS games. Most of the games you will need to work on addition/subtraction facts can be done with a deck of cards! One of Alexs favorites was a card game called 'Go to the Dump', a RS variation of Go Fish. Instead of making pairs of identical cards, the idea is to pair up card combinations where the sum is 10. I find this works really well with the idea of Singapore number bonds, and it really helped Alex now that we are using Singapore math. RightStart has a demonstration video of Go to the dump on their YouTube Channel. They also have card games like addition memory, and another favorite of ours, addition and subtraction war. Addition war is simply dividing a stack of playing cards into two piles, one for each player. Then each player further divides their stack into two piles. Then both players flip over two cards and find the sum/difference. Whichever player has the greater sum/difference takes all the cards in the hand. The game is over when one player has all the cards...or when mom says that's enough, in which case the winner is determined by the tallest stack:)

http://youtu.be/7d8ZvoES5U8

Here is another thread where I (and others) listed some more of our math fact games:

http://forum.brillkids.com/teaching-your-older-child/basic-math-facts-saxon-afterschooling-a-second-grader/

And one thing, if you like the GiggleFacts math, it is very inclusive.and while I know that it says a year for the program? Not for an EL Kid! I would be it could be mastered in A couple of months with daily play.

If you want to purchase a math games set for ALL operations and had to choose one set, I would choose the RS set. It is designed to cover a lot more and will grow with your child. The games aren't as cute and flashy, but are mostly fun and do work.

I have been meaning to post about a fantastic set of math games called GiggleFacts from http://www.gigglelearn.com/ that I stumbled upon as I REALLY believe this set is tailor-made for EL. Actually I would classify it more as a truly unique curriculum designed to master addition/subtraction. I actually found this when looking for a fun way to help my struggling nephew master his facts, and tried it with Alex. She LOVES the games! and, whilst she had already learned most of her math facts with other programs, this program has greatly enhanced not only her recall speed but has given her some new skills and strategies for solving them. And the absolute best part is that no writing is required, the games are fun, and we have a blast playing them

Here is why I think it is so unique. It is actually a set of 26 incremental steps that are based on strategies, for a total of 50 colorful and exciting games. The games are all different and involve things ranging from cards to dominoes to polyhedral dice to board games.  The program begins VERY gently, so you really need not already have worked seriously on the facts, but only really need a working idea of what addition and subtraction are. The first game is adding +0 and +1!

After I purchased the set, I was actually suprised by the fact that the kids start learning their doubles almost immediately...but not for long! It really is exciting, cohesive, and impressive the way the strategies flow together. You can almost immediately see how it starts to come together, as the kids then go to doubles+1... And then something I had actually never seen that quickly broadened Alex's repertoire of techniques, as well as her number sense over all.
Alex calls this 'Monkey in the Middle', named for one of the games that reinforces the technique, and it is by far her favorite. This strategy is designed for addition problems withh addends that 'sandwich' a number...say a problem such as 7+ 5. The idea is to recognize that there exists a 'monkey' (number) between the two addends whose double will be equivalent to the sum of 7+5. In this example, it is of course a 6, so 6+6= 12. Since they have already learned their doubles in the previous step, they can now add several more combinations to their knowledge base, which turns into fast recall through the use of the two separate games for this level. So you teach the strategy, which for Alex meant showing WHY, and play the fun games to reinforce. I cannot stress how much fun she has with these, and it carries over exceptionally well. Especially when she is working through her Singapore books for multi-digit numbers with carrying. it has made her SO much faster, and her enjoyment of what can be laborious and repetitive for her (especially as she quickly tires of the writing!), into giggle sessions as she calls out relationships. "look mom, its a double plus one, or look mom, a monkey in the middle!"
Even if she knows the math fact cold, she loves to identify the problems that she can utilize different strategies learned through the games to solve, which impresses me almost as much as solving the problem because I can literally SEE that she understands!

Regardless, I have already recommended this set to several good EL friends as it really is a fantastic EL tool, but I wanted to share it here as well. It is probably the most fun and effective way I have found yet to learn, reinforce, and master math facts for kids, but is especially ideal for EL kids. All games (it does come with some worksheets if you want to use them, but is absolutely not necessary!), lots of hands-on-fun, AND it uses many strategies that are compatible with major math programs like Righstart and Singapore.

I convinced Alex to let me videotape her playing a couple of the games to show you guys, so here goes.

http://youtu.be/bOXFB15tK0Y

Oh, wow!

I was just placing an order at Lakeshore and came across this Deluxe Doctor's Office Kit! It is mostly done for you, everything from a stethoscope to an eye chart:)

http://www.lakeshorelearning.com/product/productDet.jsp?productItemID=1%2C689%2C949%2C371%2C912%2C797&ASSORTMENT%3C%3East_id=1408474395181113&bmUID=137366753980

If nothing else, you could use the set for ideas....

Alex is really focusing much more on languages these days, and I have been looking for larger collections of children's literature, especially in Spanish and French.
I came across the Scholastic Storybook Collection DVD sets, and they are fantastic! There are two sets that have ONE HUNDRED classic children's stories included in each. They all come subtitled in English, and are a great way to let the kids read and engage in great children's books for those times parents are occupied.
If you are not in the US and are looking for ways to give your child access to all of these books, definitely check out this series. Many use just the illustrations from the books and would be a great way for your kids to hear books, see written language, and experience proper pronunciation.

Anyway, I was thrilled when I realized that many of the stories have a Spanish play option, and a few have a French option as well! It is working Amazingly well, as these are stories Alex  is well-familiar with. I purchased one of the sets of 100, and can't wait to get the second. There are also smaller sets done by theme, such as a set of 25 Fairy Tale-style books.
Just wanted to share:)

http://www.amazon.com/gp/product/B002PTBSE6/ref=ox_sc_act_image_1?ie=UTF8&psc=1&smid=ATVPDKIKX0DER

http://www.amazon.com/Scholastic-Storybook-Treasures-Treasury-Classics/dp/B003X2P9BM/ref=pd_bxgy_mov_img_y

http://www.amazon.com/Treasury-Storybook-Classics-Fairytales-Scholastic/dp/B001NKWLC6/ref=pd_bxgy_mov_img_z

Aah, but the catch is that the rules are written with this in mind:)
MENSA has put the list together loosely by grade level, but states that a reader should go by reading LEVEL, not by age. Each list (totally agree it isn't an all-encompassing list of literature like some of the curricula reading lists) has a few books really below the 'grade level', some in the middle, and then a few more challenging. For example, the K-3 list has a few books like Mrs. Frisby and the Rats of NIMH that Scholastic rates at grade level 5.8.
I also think it depends on how you approach it as well:) You CAN include books you are reading to the child, audio books, or you can choose to only include books the child read themselves to make it more of a challenge. This is what we are doing, with the exception that we will be buddy-reading some of the longer ones. I also may omit or substitute a book from the next list to replace Mrs. Frisby and the Rats of NIMH as I do NOT think emotionally she could do that one. She is way too sensitive and sheltered

Hi Ariana,
Welcome to the forum! So glad you are here.
As Manda said, it is NEVER too soon, (nor too late!!) to begin. There are members here who started Early Learning with their child literally in utero, and others who began when their child was preschool age or beyond. It is simply never too late to offer early education to a child.

One thing you might enjoy seeing is the results that one o our moderators, KMum, has achieved with her little one. Her daughter is a beautiful, amazing little reader, who just happens to have 47 chromosomes. KMum has a blog where she has chronicled some of their story, so I thought you might be interested in it.

http://downsyndromeupupupandaway.blogspot.com/?m=1

I can't wait to hear your updates. There are some amazing people in this forum, each with ideas, enthusiasm, and a willingness to help.