Detect the fallacy here

The first thing that comes to my mind is that the reasoning assumes that the goals of examinations are the same as the goals of performing operations, trials, or construction.

In the former case, examinations (I assume we're talking about examinations to test knowledge) are designed to determine how well a candidate remembers certain pieces of knowledge or how well a candidate can relate information from one area to another area.

In the latter case, operations, trials, and construction are practical exercises in which information is presented or skill applied with a goal to getting the best possible result.  

When a doctor is being assessed to determine her licensability, I'm happy to (at least in part) assess that candidates memory of all things medical; when going under that doctor's knife, I'm not relying on memory but on skill supported as much as it can be ... by others to assist and by whatever guides, manuals, plans, and scripts are available.

If we put the initial paragraph in the form of more formal logic, it might look something like this:

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  • Practitioners (surgeons, lawyers, carpenters, etc.) use reference material to guide them as they complete their tasks to produce the best possible outcome.
  
  
  • The practical work of applying skills to completing physical tasks is essentially the same process as demonstrating knowledge on a written exam.
  
  
  • Therefore, exam candidates should be allowed reference material during exams.
  
  
  
  

That argument seems logically valid, to me; however, I really have to question the second premise.  I see a demonstration of knowledge as being significantly different from producing the best possible outcome.

Then, of course, there's a second flaw in that the initial paragraph implies that students can't look at reference material during examinations.  I've completed many examinations in which I've been able to use (and needed!) reference material.  It started way back in high school when many trigonometry exams involved referring to those neat little tables with lots and lots of columns of numbers.  As well, operators of complex equipment are routinely tested on their ability to use the regularly-available reference material – since their real world will involve consulting manuals to resolve problems.

As Jim pointed out, the purpose of examinations is different from the purpose of operations, trials, and construction. Exams are supposed to test the ability to recall learned knowledge, and problem solving skills. Allowing students to access notes would defeat the point.

Operations, trials and construction are more complex matters that require specific details (e.g. the state of a patient's organs, relevant case facts, and building dimensions in the case of a blueprint). Thus, surgeons, lawyers and architects have guides to assist them in their work.

This is a false equivalence argument.

An examination is unique in the respect that it tests learned knowledge (therefore if you use a textbook, that content is not learned), whereas the other scenarios are not tests, but performances.

Well, they are given a guide in a way. It’s called multiple-choice.