word choice - Is there a correct gender-neutral singular pronoun ("his" vs. "her" vs. "their")?

Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?

Each student should save his questions until the end.
Each student should save her questions until the end.

Added 10/27/2019
We could use an answer from the transgender community. There are none amongst the first 23 answers. I know there's a term (in America), but i can't remember what it is.

Answer

Singular they enjoys a long history of usage in English and can be used here: "Each student should save their questions until the end."

However, “singular they” also enjoys a long history of criticism. If you are anxious about being criticized (for what is in fact a perfectly grammatical construction) I would advise rewording to avoid having to use a gender-neutral singular third-person pronoun.

Some rewording strategies that can be employed:

• Use a plural noun: Students should save their questions until the end.


• Use the formal one: One should save one's questions until the end.


• Use his or her: Each student should save his or her questions until the end

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OED References for “singular” they

Here for the benefit of those who lack access to its paywalled source are the full and complete operative senses from the Oxford English Dictionary. Per the OED the pronoun they has these specific subsenses for the various scenarios under discussion here:

2. In anaphoric reference to a singular noun or pronoun. 🗨

   
   
   

   ^{Use of they to refer to a singular antecedent has sometimes been considered erroneous.}

_{🗨 Dennis Baron • A brief history of singular ‘they’}

_{…But that’s nothing new. The Oxford English Dictionary traces singular they back to 1375, where it appears in the medieval romance William and the Werewolf. Except for the old-style language of that poem, its use of singular they to refer to an unnamed person seems very modern. Here’s the Middle English version: ‘Hastely hiȝed eche … þei neyȝþed so neiȝh… þere william & his worþi lef were liand i-fere.’ In modern English, that’s: ‘Each man hurried… till they drew near… where William and his darling were lying together.’…}

^{[4 September 2018]}

• 2a. With an antecedent that is grammatically singular, but refers collectively to the members of a group, or has universal reference (e.g. each person, everyone, nobody).

  
  
  

  ^{Sometimes, but not always, used to avoid having to specify the gender(s) of the individual(s) being referred to; cf. sense A. 2b.}

  
  
  

  [[citations ranging from 1350–2014 omitted]]

• 2b. With an antecedent referring to an individual generically or indefinitely (e.g. someone, a person, the student), used esp. so as to make a general reference to such an individual without specifying gender. Cf. ʜᴇ pron. 2b.

  
  
  

  ^{In the 21st century, other th– pronouns (and the possessive adjective their) are sometimes used to refer to a named individual, so as to avoid revealing or making an assumption about that person’s gender; cf. sense A. 2c, and quots. 2008 at ᴛʜᴇɪʀ adj. 2b, 2009 at ᴛʜᴇᴍ pron. 4b, 2009 at ᴛʜᴇᴍꜱᴇʟꜰ pron. 2b.}

  
  
  
  

  [[citations ranging from 1450–2010 omitted]]

• 2c. Used with reference to a person whose sense of personal identity does not correspond to conventional sex and gender distinctions, and who has typically asked to be referred to as they (rather than as he or she).

  
  
  
  

  [[citations ranging from 2009–2019 omitted]]

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