I'd like to improve my English.

This is very nice. You are already writing in complete sentences, so you are already beginning to fulfill your dream. A few comments:

* "I like children and English." This sentence is a little awkward. When you list things that are not in the same category, it can cause confusion. (Example: "I like pizza and children" is awkward because "pizza" is a food and "children" are people. It would be even stranger if you said "I like eating pizza and children" （笑）but it would be natural to say "I like eating pizza and working with children.")

So, the sentence "I like working with children and studying English" is much more clear. However, it's longer, and not as succinct (手短に言う) as "I like children and English." So as a writer, you have to balance style and clarity.

** "I dream that I . . ." - Adding one or two words would help this sound more natural. "I often dream that . . ." is one way. "I have often dreamed that . . ." is another way. Just as 夢見る, 夢見ている, and 夢見てきます each have different uses and nuances, there are many choices in English.  

I'd like to improve my English.