+0
"I don't want them teaching it."

I saw the sentence and is it a short version of "I don't want them to be teaching it."? Of course, we must figure it out in context but I would like to know if to be here can be omitted? What do you think? Thank you so much as always and have a good day

I
+2
Yes, "I don't want them teaching it" is natural English. Similarly "I don't want him going there", "I don't want her seeing it", etc. etc. I would not use this style in very formal writing. Although they are connected in meaning, it is not obvious to me that these are specifically abbreviated versions of sentences with "to be".
+0
Hans51is it a short version of "I don't want them to be teaching it[no period]"?
I would say no, even though their meanings are very similar. The catenative verb want is one that licenses either a to-infinitival or a gerund-participial as complement, the latter being rather informal in style.
Hans51them, him and her are subjects …, right?
No. Them is behaving like an object of the matrix clause in that it can’t be separated from want by an adjunct (*I don’t want at all them teaching it is ungrammatical). This admissibility is like that of *I don’t want at all them.
Teachers: We supply a list of EFL job vacancies
Comments  
Thank you so much, so here whatever the grammar is, them, him and her are subjects and teaching, going and seeing are verbs in meaning, right?
 RandomGuy's reply was promoted to an answer.
Students: We have free audio pronunciation exercises.