I do hate to display my ignorance, but is it possible we have a bit of a number prombem in the statement 'For a teacher who has to design or choose a formal achievement test for their learners...'?

Just curious. 

Hi Garza

Both examples you give are correct.

According to Practical English Usage by Michael Swan:

They/them/their is often used to refer to a singular indefinate person. This is common after a person, anybody/one, nobody/one, whoever, each, every, either, neither and no.

This singular use of they/them/their is convenient when the person referred to could be either male or female. He or She, him or her and his or her are clumsy, especially when repeated...

I've always preferred the usage of they/them/their when referring to an unkown person rather than repeating he or she etc as it's simpler to use.

I think in the past using they/them/their in this way to refer to a singular indefinate person may have been contentious. I have a vague memory of a news item about 10 years ago saying the use of they/them/their in this way had been officially accepted by the Oxford dictionary... maybe other readers have a better memory and will know if this is the case.

Well, I have the Fowler edited by Gowers (1965 edition, so perhaps even older than yours), and this is what it says: 

In a perfect language there would exist pronouns and possessives that were of as doubtful gender as they and yet were, like them, singular; i.e., it would have words meaning him-or- her, himself-or-herself, his-or-her. But, just as French lacks our power (without additional words) of distinguishing between his, her, and its, so we lack the French power of saying in one word his-or-her. There are three makeshifts: first, as anybody can see for himself or herself; second, as anybody can see for themselves; and third, as anybody can see for himself. No one who can help it chooses the first; it is correct, and is sometimes necessary, but it is so clumsy as to be ridiculous except when explicitness is urgent, and it usually sounds like a bit of pedantic humour. The second is the popular solution; it sets the literary man's teeth on edge, and he exerts himself to give the same meaning in some entirely different way if he is not prepared to risk the third, which is here recommended. It involves the convention (statutory in the interpretation of documents) that where the matter of sex is not conspicuous or important the masculine form shall be allowed to represent a person instead of a man, or say a man (homo) instead of a man (vir). Whether that convention, with himself or herself in the background for especial exactitudes, and paraphrase always possible in dubious cases, is an arrogant demand on the part of male England, everyone must decide for himself (or for himself or herself, or for themselves).

And that is how I have always known it. To complete the picture, perhaps I should say I am 62.