Reading is a noun, so the sentence is correct. Reading is technically a gerund, which is a noun formed from a verb by adding -ing. You can also say "reading skills", but you don't need "skills" for it to be correct. Her reading has improved greatly since she changed schools. Her reading skills have improved greatly since she changed schools. His golfing has improved. His dancing has improved.

The original sentence is correct. The word "reading" is a gerund. Also, non-specific plurals do not require the article "the".