English Grammar: Singular Object Pronouns When Gender is Unknown

I am confused by the appropriate use of gender-specific object pronouns in English.  

I am writing an article and and am having trouble with this line:
Has your child done something that you appropriate? Let _______ know!

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What should go in the blank?  

I cannot use "him" because the child might be a girl.  I cannot use "her" because the child might be a boy.  I cannot use "them" because the line is referring to a single person.    

English a confusing language, at least for me.
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Saqib Husain, SyedEngineerCommented:
Let him/her know
In normal conversational English the phrase would be "Let them know". Native English speakers frequently use this plural when gender is not specific even though the object is an individual because the (grammatically correct) 'it' is considered too impersonal.

For more formal documents the him/her (meaning him or her) is frequently used; if its important for you to match the object then for a more friendly form you could also use 'your child'
The proscriptive rule in the past said to use "him".

Modern sensibilities would have us not follow the old rule. The use of "him or her" is now common.

Your example sentence has another flaw. Did you mean "appreciate"? Or "see as inappropriate"?
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
Them.  It's quite normal to say 'them' when unsure.
 eg 'Someone knocked on the door, but I couldn't see their face.
'Please ask your child to hang their own coat up so we don't have to do it for them.'
I perhaps should have used the word "prescriptive" rather than "proscriptive".

We are well into the territory between "prescriptive" and "descriptive" linguistics. The original prescriptive rule was to use the male pronoun in cases where the gender was unknown.

The form least objectionable to prescriptivists is "him or her". When written as "him/her", however, it still raises objections.

Another common way to handle the situation is to use the third person plural pronouns: they, them, their. This usage is in error, according to some prescriptivists, but has a fairly long history.

In a long passage, some speakers and writers resort to alternating between male and female pronouns; this sounds a bit jarring at first, but does not violate any rules.

Using "it" has generally not been seen as a possible solution.

A wide variety of gender-neutral pronouns have been proposed both to resolve the generic gender uncertain case as well as the case of persons whose gender is in transitional or intermediate state. None of these proposals has received widespread acceptance.

The Wikipedia article on Gender-specific and gender-neutral pronouns goes into a great deal of detail about this issue.

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I tend to agree with most of the above. Using them is more palatible even if plural and would have been my answer if first. I'd refer to him/her but that gives two pronouns, more overhead and potential conflict (battle of sexes) not to mention confusion of lgbtixyz etc along with preference preferred identified identity.

So goes my prejudice such as opposing forms requiring sex where only two options m/f. Lieing permitted and no need to know. Sex? How about answer yes or ok.

That said my 2nd comment likely to extend as others done did.

I'd not be texting were it not for author spelling it gender rather than <ugh> sex. Thanx.

I'd suggest best answer:

>> child

Remove the 'your', simplify/KISS. Is child biological, is person a sitter or teacher or tutor or adopter or physician etc. Also regretably 'it'  can be authorized as child up to age 30 yet remains among children for life (check obits).

Just sayin'
Btw use of.'her' remains increasing, given sins of past with desire for balance (retribution).
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