have poor knowledge of

[joham]

I have a poor knowledge of fractions and division.
I thought 'a' should be used because the Oxford Dictionary says 'He has a wide knowledge of painting and music' until I came across the sentence on the FRAZE.IT website:
Many health workers and educators have poor knowledge of HIV and hold their own biases and stigmas towards those at risk or infected with HIV. ( en.wikipedia.org)
I feel confused about whether to use a or not before the structure of 'adjective + knowledge of'. Could we say that 'a' can always be used and it can be omitted?

 

[Barque]

Could we say that 'a' can always be used and it can be omitted?

You'll hear both structures.

 

[jutfrank]

I'll give you a rule to take home: If the subject is a single person, use the indefinite article:

She has a good knowledge of the law.
He has a good understanding of the key issues.

It's okay to say these sentences without the articles, but it's a bit more natural to say them with the articles in place. Even though the words knowledge and understanding are normally used as uncountable nouns, they work well as countable nouns in cases where they apply to a particular area of knowledge/understanding of a particular person.

The issue with the example you quote is that health workers and educators is a plural phrase, which doesn't work well with the singular countable phrase created by the article. And since you can't use the plural/countable poor knowledges, then the singular/countable poor knowledge is the better choice.