If they saw combinations of, say, implicit differentiation, product rule and chain rule before, and they know when to use logarithmic differentiation, then it is certainly OK to combine them, especially if you give a hint to that effect.
So where is the line? Can you maybe give examples of what would seem to be unacceptable degrees of making connections for an exam in an intro level course?
I once had a physics professor (with a reputation for being tough) give an exam problem which required some slightly unusual calculus trick which—though surely covered in a prerequisite math course—had never been used anywhere else in the physics course. [I unfortunately don’t remember the details; this would have been ~2004.] It was something I think most people in the class would not have had a problem with in isolation. But in the context of the exam, under time pressure, it just wasn’t something that came to mind to try. The professor subsequently expressed confusion about why everybody in the class bombed that question, since it only involved doing things which—in isolation—we should all have been able to do.
I don’t think I’d call the question “unacceptable”, but I think the professor’s mystification reflected an unfortunate misjudgment about how hard it is to think creatively under time pressure.
If they saw combinations of, say, implicit differentiation, product rule and chain rule before, and they know when to use logarithmic differentiation, then it is certainly OK to combine them, especially if you give a hint to that effect.
So where is the line? Can you maybe give examples of what would seem to be unacceptable degrees of making connections for an exam in an intro level course?
I once had a physics professor (with a reputation for being tough) give an exam problem which required some slightly unusual calculus trick which—though surely covered in a prerequisite math course—had never been used anywhere else in the physics course. [I unfortunately don’t remember the details; this would have been ~2004.] It was something I think most people in the class would not have had a problem with in isolation. But in the context of the exam, under time pressure, it just wasn’t something that came to mind to try. The professor subsequently expressed confusion about why everybody in the class bombed that question, since it only involved doing things which—in isolation—we should all have been able to do.
I don’t think I’d call the question “unacceptable”, but I think the professor’s mystification reflected an unfortunate misjudgment about how hard it is to think creatively under time pressure.