When "To" is used as a preposition rather than an infinitive?

[albertino]

May I ask if the using of "to + gerund" is correct in the sentence?

"In parallel to this, teachers should be given enough room to establishing a collaborative mechanism under administrative arrangements, so that they can conduct teaching discussions at the same period of time and make plans for the school-based curriculum."

And is there any way to test whether the "to" is a preposition or an infinitive in a sentence?

[engee30]

May I ask if the using of "to + gerund" is correct in the sentence?

"In parallel to this, teachers should be given enough room to establishing a collaborative mechanism under administrative arrangements, so that they can conduct teaching discussions at the same period of time and make plans for the school-based curriculum."

Well, to my way of thinking, the sentence with the to used as a preposition is fine as well as it is with the to-infinitive.

In parallel to this, teachers should be given enough room to establish (= so that they can establish) a collaborative mechanism under administrative arrangements, so that they can conduct teaching discussions at the same period of time and make plans for the school-based curriculum.

In parallel to this, teachers should be given enough room to establishing (= enough room with the possibility of establishing) a collaborative mechanism under administrative arrangements, so that they can conduct teaching discussions at the same period of time and make plans for the school-based curriculum.

And is there any way to test whether the "to" is a preposition or an infinitive in a sentence?

You can tell that it's the preposition that is used, not the to-infinitive, because all prepositions take the gerund form of the verb.
___________________________
NOTE:
Bear in mind I'm not a teacher!

[engee30]

No, sorry, that isn't natural English.
Níall
Grammar grad and trainee teacher.

I do believe you - I'm not English, I'm afraid.

[engee30]

Argh! Why does everyone think it's only Sassenachs that speak the language?

Níall,
Proud Scot.

Let me correct myself then - I do believe you, for I am not British!

[Tdol]

Argh! Why does everyone think it's only Sassenachs that speak the language?

Níall,
Proud Scot.

Because they can understand us?

[Jason72]

Let me correct myself then - I do believe you, for I am not British!

Sassenach - English person, British person... It's all the same...

[sydneysider]

Sassenachs ? Do they have anything to do with Anglo-Saxons ?

[Jason72]

Sassenach is the Scots' term for an English person.

[Casiopea]

No, in that case it should be to establish. I can't explain why, but I'll think about it and get back to you if I can....

It's in the verb's subcategorization frame:

give + someone + something to do.

Active: The school should give teachers enough room to do something.

Passive: Teachers should be given enough room to do something.


____________________

albertino, there is a way to test whether to functions as a preposition or a particle.

If to is short for towards, it's a preposition:

preposition
10 steps to establishing a fund
10 steps towards establish a fund

If to is short for in order to, it's a particle:

particle

Teachers should be given enough room in order to establish a collaborative mechanism.

Teachers should be given enough room to establish a collaborative mechanism.

______________

engee30, to establishing does indeed work here--at least in my dialect.

... teachers should be given enough room towards establishing a collaborative mechanism ...

... teachers should be given enough room to establishing a collaborative mechanism ...

But given that to is ambiguous in that position; i.e., to(wards); (in order) to, a good writer would have spelt/spelled out the word towards.

In sum, the particle lead infinitive to establish has my vote.

[engee30]

engee30, to establishing does indeed work here--at least in my dialect.

... teachers should be given enough room towards establishing a collaborative mechanism ...

... teachers should be given enough room to establishing a collaborative mechanism ...

But given that to is ambiguous in that position; i.e., to(wards); (in order) to, a good writer would have spelt/spelled out the word towards.

That's true. Let me show another two sentences that are similar, yet different to each other, with a little change in meaning (the change that you provided, Casiopea, I guess):

Two-way trade with foreign nations is the only really practical way to (= in order to) achieve peace on this earth.
Nixon is well on the way to (= towards) achieving a historic reconstruction of the postal service.

In sum, the particle lead infinitive to establish has my vote.

I opt for the same.