A writer I work with keeps using the phrase "wonder the question" -- as in, "Scientists have wondered this question for years." It totally rubs me the wrong way, perhaps because it's contrary to the normal use of "wonder" and the phrase "ponder the question", but is it truly an improper use of "wonder"?
This is not a proper use of "wonder."
When used as a transitive verb, "wonder" takes an interrogative clause ("if," "whether," or the "wh-" words) as a direct object, but not a noun phrase such as "the/this question."
Relevant excerpts from the Oxford Manual of English Grammar:
184.108.40.206.2 The pattern ‘WONDER [ clause whether/if/wh -phrase …]’ This pattern involves subordinate interrogative and exclamative clauses functioning as Direct Object. As we have seen, closed interrogative clauses are introduced by whether or if , whereas open interrogative clauses are introduced by a wh -phrase which is headed by a wh -word… Subordinate interrogative clauses differ from main interrogative clauses in lacking Subject–auxiliary inversion.
Also, as a contrasting example:
220.127.116.11 Free relative clauses
100 I wondered [interrogative clause what he said].
101 I rejected [free relative clause what he said].
Because WONDER does not normally take an NP as Complement, and because free relative clauses resemble noun phrases in their distribution, the bracketed string in (100) must be an interrogative clause. Conversely, because REJECT cannot take a regular clause as Complement, but does take an NP as Complement (e.g. he rejected the proposal ), the bracketed string in (101) must be a free relative clause.
One exception would be the use of a pronoun to represent the clause (e.g. "I myself wondered this"), but that is also not the same construction as your colleague is using.