There or their. Which one is correct?

Their

Their is correct. Have you considered examining your own comment for standard usage, including punctuation, spelling, and capitalization?

Comprehension of the chenwish language, rooted as it is in an opinion on student assessment rather than grammar, reaches its lowest ebb then flows.

Well dayum, I certainly hope so.

There: represents location or a point in a process.
Examples--Over there or there he is, There is a time and place for everything.

The word "their" is correct.

Lowest something certainly applies.

One possibility could be:

There, missing test . . .

The "there" could refer back to the school

THEIR missing high test scores could lose the school some federal aid and make the school look like it isn't giving children a good education."

Finally, the equal penultimate denominator, second to none, a rebel without.

In the sentence (there) is incorrect. If the word is used as a group of people, the correct word is (their)

As I child I was taught that "there" contained the word "here" so to remember "here and there"

"Their" contains the word "heir" to whom something belongs.

As far as too, to and two, well, "too" has too many o's in it.

I can't understand why people have such a hard time remembering to use their utensils from the outside in toward their plate. Seems simple enough.

Here is a link that I believe will help clarify the difference between (their, there, and they're). This link explains the proper use of each of these words. It also provides examples of the proper uses of these words. I hope this link will be useful.

http://www.grammar.cl/english/there-their-they-are.htm

This sentiment bears repeating. Not because it allegedly hits a mark of high academic standards but because of it's horrible monstrous abuse of the language.

Gawd! The horror and the mutilation!

tsar, I felt the same way when I once mixed up my crab and strawberry fork.

It was horrible the way that strawberry was mutilated.

It should be 'their' in both the first and last sentence.

Their refers to a person/ownership:
"Their cat", "Their score", "Their school," etc

There is a place/location/object/etc
"I went over there", "There was candy at the store", "We're going there after school", "She was there," etc

They're is used in place of 'they are', so if it can't be substituted with 'they are', it's the wrong usage

"They're going to the concert after school", "They're studying for their test tomorrow", "We're not going if they're going to be there," etc

There missing high test scores could lose the school some federal aid and make the school look like it isn't giving children a good education.

There is an adverb meaning primarily in that place: at that location. The personal pronoun their is possessive and is often considered to be an adjective because it tells Which one? Their test scores. A pronoun usually refers to a word in the sentence that it is in or a word in the previous sentence. It is obvious from the previous sentence that the "missing high test scores" is referring to the "honor students." They are the ones with the high scores that can benefit the school financially in the long run. So, the antecedent (the word the pronoun refers to) is students, which is modified by the noun "honor" being used as an adjective.

CORRECT:

Their missing high test scores could lose the school some federal aid and make the school look like it isn't giving children a good education.

As for the first sentence...

Maybe these parents should have let their honors students read and explain the paperwork about testing to them.

Here, the antecedent for the pronoun their is parents. Whose honor students are they? The parents. The antecedent for the pronoun them is parents. Who is them (who are they?)? The students should read and explain the paperwork about testing to the parents.