Blackcat, your original question poses quite a challenge.
One possible solution is converting spoken language into written mathematics, which is actually quite difficult. The most successful technical solution for this I know of is available at
https://mathtalk.com/, but it's a bit expensive for a single user.
If one wanted to build a similar system at home, the highest rated answer posted to the stackexchange question would be the most reasonable way to go. That is, use a speech-to-text program such as Dragon NaturallySpeaking (
https://www.nuance.com/dragon.html) to convert the spoken word into text. One can train the Dragon system to recognize specific word/text pairs, which can be used to generate LaTeX commands in the text output. NatLatex (
http://www.ataword.com/latex/natlatex.html) is one way to do this.
At it's core, LaTeX is a markup language. Similar to how HTML is used to format web pages, LaTeX is used to format mathematics. Unfortunately, the learning curve for LaTeX can be quite long (although, not necessarily steep). Most LaTeX users are also computer programmers, and so prefer to edit their documents in a code editor and then 'compile' the documents in a manner similar to compiling computer programs---not much help for kids that struggle with typing, I'm afraid.
But, LaTeX is also an open standard, so there are many programs available to generate documents from a LaTeX commands.
One program that I think bridges the gap between plugins like EquatIO and code editor and might fit your needs is LyX (available here:
https://www.lyx.org/, write-up here:
https://www.ibm.com/developerworks/library/os-lyx/). LyX is free, available on most operating systems, and offers a graphical interface similar to most word processors with output to PDF. A large library of LaTeX commands are available via pull-down menus, which can aid in learning them. It may also be possible to connect the Dragon NS system into navigating the menus, although I can't confirm that.
I hope this helps some in finding a workable solution for your DS.
