Jack3 wrote:

"High school science students shouldn't be compelled to memorize theorems and chemical equations. They should be allowed to refer the textbooks during the exam"

Thoughts?

No. They should memorize core equations and then be required to derive other equations from them. Or they will have no idea of the relationships and concepts being expressed.

I do periodic astronomy outreach with our local U's Astronomy 101 students. They have to observe and then fill out sheets recording their experience. One requirement is to write down the magnification of the viewing for each scope. Almost none can tell me that the magnification of an astronomical telescope is calculated by dividing the focal length of the telescope by the focal length of the eyepiece. Even when I tell them how to calculate it, and, often with cellphone calculator in hand, they cannot do that simple mathematical exercise. And, that, with the formula written on their exercise sheet. I refuse to do it for them. It is not surprising for some to haltingly work their way through that simple division, get the correct answer, and then ask me if it is correct. I usually agree, if it is.

The important practical concept is to understand that magnification of a telescope varies with the focal length of the eyepiece. That requires a derivation of the formula to answer the question, "If I want such and such magnification on this here telescope, what eyepiece would I choose?"

So, even with the book open, as the formula is written on the exercise sheet, the average student cannot calculate the magnification ... because they have o idea of the simple relationship.