The willingness v. ability to learn

IQ testing, as I understand the process, does not consider the will of the subject being tested. Suppose two different people take an IQ test. One of them wants to take the test while the other doesn’t want to take the test. The willing test taker will probably score higher than the unwilling test taker. However, does this mean that the willing test taker will outperform the unwilling test taker even in areas or occupations that the high IQ scorer is not willing to pursue?

When I was a child student, I could not learn grammar.  I could not understand what a verb or a pronoun was or why I would ever need to know. I felt like I wasn’t smart enough to know. Perhaps my IQ wasn’t high enough. Later, when I was a young adult, I wanted to learn how to speak Spanish. So I bought a course, consisting of cassette tapes and a book. But the book taught grammar, and I knew I would have to learn the general concepts of grammar if I wanted to learn Spanish. I did learn Spanish, and as a result, I learned the general concepts of grammar. I believe this learning experience has greatly affected my English communication skills.

Whereas I could not learn grammar when I did not want to learn it, I had no problem learning it when I did want to learn it. Maybe IQs are dependent on willingness.