Dear Rommaya,
I have not met this phrase until now, but my little bit of research suggests the following.
PRODUCTIVE.
a) The creative capacity of language users to produce and understand an indefinitely large number of sentences.
b) The potential of a linguistic rule to produce many instances of the same type.
Examples.
1) The use of �s � to produce regular Plural Nouns. Dog; dogs; cat cats, book books; etc.
2) The use of �ing � to produce the Present Participle, (the -ing Form), of many verbs. Think thinking; speak speaking; see seeing; etc.
3) The use of �ed � to form the Past Simple Tense ending of regular lexical verbs. Believe believed; talk talked; look looked; etc.
4) The 9 modal verbs, (can; could; may; might; shall; should; will; would; must), are always followed by a �bare infinitive � verb, (a verb without �to �). I can walk to London; I could cycle to London; I may fly to London; etc.
This contrasts with non-modal verbs, (excepting the auxiliary verb �to do�), which use the �to infinitive �. I want to walk to London; I prefer to cycle to London; I intend to fly to London; etc.
NON-PRODUCTIVE.
Patterns of language which lack this potential.
Examples.
Several nouns, which are 1 in number, but are regarded as �a pair�, so, they CANNOT have an �s � added to make them plural. Binoculars; spectacles; scissors; forceps; tweezers; scales; trousers; underpants; tights; etc.
SEMI-PRODUCTIVE.
Patterns where there is a limited potential to produce a rule.
Example.
It is possible to use the prefix �un- �, so as to form opposites, in NUMEROUS cases. Happy unhappy; suitable unsuitable; intelligent unintelligent; etc.
But, it is NOT possible to do this in EVERY instance. For example, sad unsad; useful unuseful; stupid unstupid; etc.
I believe the following would be examples of productive questions.
"Can you give me a list of words beginning with a certain letter of the alphabet, the letter �a�, for example?" Apple; and; answer; etc.
"Can you give me a list of words ending with the letters of the alphabet, �tion�, for example?" Nation; function; addition; etc.
"Answer these questions with your approximate age! How old were you when you first started school?; ... learned to read?; ... learned to write?; etc." Five; six; eight; etc.
"Answer these questions with the name of your teacher!" Who was your first teacher of Maths?; ... History?; ... Geography?; etc." Miss White; Mr Main; Mrs. Carr; etc.
"Can you give the negative Form of these sentences? I eat ice-cream; I live in the USA; I study music; etc. I don�t eat ice-cream; I don�t live in the USA; I don�t study music; etc.
I think that jfaraujo makes some valid points.
I hope that these remarks are of help to you.
But other Members, with a deeper knowledge of productive questions, may offer better advice.
Les Douglas