Of course, I am fan of methods of Doman.

I will explain my point. If you teach in Doman-style, with flashcard sessions, and do not do anything else, your child hears some 15 - 200 words per day.

Children definitely need more words 
http://forum.brillkids.com/general-discussion-b5/30-000-words-a-day/

In his books, Doman says that children of loving and interacting parents develop faster. But he does not go deep in it. It is possible that parent follows directly to described method, does flashcards sessions only, and nothing else, and than this child can be language-delayed.

Helping kids learn math and science: Why kids benefit when they teach others
© 2009 -2013 Gwen Dewar, Ph.D., all rights reserved

Want to help your kids learn math and science?

Ask them explain—or, better yet—teach what they are learning in their own words.

This simple tactic can help kids master new material.

You’ve probably experienced it yourself. People become better problem-solvers when they are asked to explain how or why a solution is correct.

Explaining is an especially effective learning aid when people try to teach another person. But it’s also helpful if they merely explain their reasoning to themselves.

For instance, a study of novice chess players found that individuals who were told to explain a computer’s moves became better players than people who simply observed the computer’s moves (de Bruin et al 2006).

And here’s another example: In a study of 9th graders, students were presented with a new geometry theorem. Some students were trained to “self-explain” as they studied. Other students were allowed to study in their usual ways.

When the teens were tested on their overall comprehension, the “self-explainers” had the advantage. They were better able to solve new problems that were superficially different, yet conceptually connected with the assigned theorem (Wong et al 2002).

Explaining appears to help younger kids, too. In one study, Bethany Rittle-Johnson and her colleagues (2008) gave 5-year olds some pattern-detection problems to solve.

Each problem consisted of a sequence of 6 plastic bugs—e.g.,

<picture>

And kids were asked what comes next (e.g., a red spider).

After each child gave his answer, the experimenter told him the correct answer. Then the experimenter asked the child to explain the correct answer.

Compared to kids who were asked merely to repeat the right answer out loud, the “explainers” went on to become better problem solvers. When they were asked to solve a new set of pattern-detection problems, they were more likely to get the right solutions.

.......

and more 
http://www.parentingscience.com/kids-learn-math-and-science.html

Thanks! I found free solfege program named Solfega!

I also found that it is called "fixed-Do solfege" but these keywords were too narrow    

I will add this

Sid the Science Kid-Inclined Plan and Simple 
<a href="http://www.youtube.com/v/tvLDkNdDrqY&rel=1" target="_blank">http://www.youtube.com/v/tvLDkNdDrqY&rel=1</a>

and all Sid the Science series. Teaching physics and mechanics.

I found that MyCoala and similar apps can be used also for early readers who do not learn foreign language.
If there are five commonly used words and you ask your toddler to point "which is the apple" than you can get some fun 

I found many very nice apps for android using keywords "music notes" and "teach perfect pitch". Very useful applications, indeed. However, they all use "A B C" system which is not used in our region; we use only "do re mi" system. I have learned in music school for 2 years and I even do not know which letter corresponds to each note. I was not able to find any app for "do re mi" system and currently I am not able to find how this system is called and which is the right keyword.

My educated friends, can you please help me? With keyword.

 

I have checked several language learning apps for android.
With lingling there is a strange thing that it randomly offers very rarely used words. Words which are used by adults and not by 3 year olds.

The only app we found useful is MyKoala. It does not have that advanced teaching part - but it starts with easy words like animals and fruits. And, the most important, with one download you get dictionaries of very many languages, and even rare languages (like my language) are included. So my 5 year old get answers in her native language; other apps do not offer this.

I was surprised that she checked right most of the answers; I do not teach her English directly and I did not know that she can read English

I have completely different approach to cartoons. We watch movies together, and I am telling and explaining what is happening on the screen. This is a good way to increase vocabulary and EK. For this reason I need very simple movies with no language. The best movie series of this type is "Little mole". Like this
<a href="http://www.youtube.com/v/lv0eU9DDt_A&rel=1" target="_blank">http://www.youtube.com/v/lv0eU9DDt_A&rel=1</a>

With little kid, I comment like "mole is running... looking for mouse". Later I comment more complex things, like "mole is upset because...".

This is for little kids. With my oldest we used to watch movies about Disney princesses. As they are in foreign language I explain the events. Each time I explain something new about the circumstances, about the history and about the relationships.

In result, my kids do not watch cartoons without me

Thank you!

My 3 year old has some limited access to computer. After setting strong time limits and website blockers he get this
http://boowakwala.uptoten.com/kids/boowakwala-games.html
where he gets games I find useful.
Labyrinths, form sorting, diference finding, route finding etc.

basic EFT material is this manual http://www.thrivingnow.com/gary-craig/

it looks easy but for me it was long way to go (6 months and I am still continuing) to find my emotional reasons of back pain. if you are in hurry and you want to try EFT -  you should find EFT therapist (not available in my area) or psychotherapist who will help to find reasons.

I believe to emotional freedom technique EFT. I cured my debilizing back pain with it. There is a lot of free information over the Internet, you should start with articles of Garry Craig. Best wishes.

I learned about Doman 5 years ago so I am used to the lack of scientific articles  

Currently I am thinking that Doman says that it is enough to work with his methods only - but he does not say anything about the development of speech and logical thinking. Early talking and logical thinking are considered as the signs of giftedness. Methods of Doman seems tabu in scientific research - but here are another interesting materials on brain development

When my daughter was born, I disliked pink color. I bought only clothing which was green, yellow, white and sand. Daughter had also some pink clothing, given by relatives. When she was 1.5 years old, I discovered that it is mush easier to dress her if the clothing is pink. With other colors, she had much more resistance You know, sometimes children do not allow to dress up them. This way, pink color came in our house. I did not resist to her desire to wear pink.

And I started to think - what I have against the pink? It is just a color, like other colors. Nowadays, pink is connected to femininity. Probably, my dislike towards pink color is connected to some denial of femininity inside myself. Something went wrong with me in this age. I know it. And I lack confidence. Well, and I wish that this will be better with my daughter.

Another aspect. I will translate the answer of psychologist Anita Plūme. I like this.

... discussion about the girl named Elisabeth and her interest on princesses and pink color.

====

Pink color is a good taste for little girl. If mother will allow for her girl to try things which are characteristic for this age, later her taste will be similar to taste of her mother. If mother will forbid and criticize, later (age 20 - 25) this girl will find hard to adopt the taste of her mother. It would be unnaturally if little girl would have taste of adult women. Little girl with reason wants to feel like princess because when she will grow up she often will be Cinderella which can transform only in ball. But she needs the ability to transform, to enjoy the life. Parents are responsible for the creation of this ability by allowing to live the role of princess - the especial, the marvelous. Othervice this girl later will feel unpriced, frightened and unsafe. Every little girl is a little princess which will grow up as warmhearted and hardworking Cinderella - but not in the opposite.

Lolobride

would you recomend the book

http://www.hsperson.com/
http://www.mandalachildrenshouse.com/DYK/Did_You_Know-Highly_Sensitive_Child_1-08.pdf
http://www.amazon.com/The-Highly-Sensitive-Child-Overwhelms/dp/0767908724
http://www.scribd.com/doc/60743155/The-Highly-Sensitive-Child

good luck, you have an exceptional and gifted child