The presumption that students have memorised the formulae allows you to build more complex tests with confidence that they will tease out understanding and not just computation.
In my highschool physics exam, about 2/3rds was of questions based on memorised formulae. For example, the bouncing ball problem, with a series of questions to tease out our application of calculus, memorisation of compression rules and so on.
Then comes the final question. I remember it well because at first, I did not know which formula to apply. Water wells into a pool at rate X per hour, falls over a waterfall into a second pool below, which drains at rate Y per hour. When it falls over the edge of the waterfall, the water is at temperature A; at the start of the problem the temperature in the bottom pool is C.
After an hour, what will the temperature in the second pool be?
To solve this problem you actually need to consider the thermic effect of water falling. You need to build a single equation to accounts for acceleration due to gravity and the beginning temperatures of each pool. Then you need some calculus to transform it into an equation that will spit out the final numerical answer.
The only reason I was able to attempt and solve this problem was because I had memorised the equations. There simply would not have been enough time to try to reverse-engineer a bunch of anonymous letters in-flight.
Similarly, when I studied law, all exams were open-book. This is because, as a law professor told me, "it lets us ask harder questions". There's simply no way to synthesise thousands of pages of material in an exam setting. Either you learnt it beforehand, including a whole bunch of flat out memorisation of details of cases, or you didn't. Having your casebooks for reference is useful, but only to check a detail or reuse a quote.
I'm no physicist, but even if the typical physicist has internalized tons of relationships expressed in formulas, students who have a cheat sheet of tons of formulas still have to frame the problem and then choose the right relationships to solve it, and hence they learn and grow the way we want them to. Maybe I'm wrong, but as a software developer, memorizing syntax speeds me up a little, but when it comes to the entire development lifecycle, the quality and length of time will depend much more on whether I framed the problem correctly and used the right relationships than whether I quickly recalled syntax. It's not totally apples to apples, but it seems like in the 21st century we can get so much more done if we focus on knowing where to look up information and have learned how to use it, much like how I look up APIs and design patterns as a routine part of my job and don't think it really slows me down to have to do that.
In my highschool physics exam, about 2/3rds was of questions based on memorised formulae. For example, the bouncing ball problem, with a series of questions to tease out our application of calculus, memorisation of compression rules and so on.
Then comes the final question. I remember it well because at first, I did not know which formula to apply. Water wells into a pool at rate X per hour, falls over a waterfall into a second pool below, which drains at rate Y per hour. When it falls over the edge of the waterfall, the water is at temperature A; at the start of the problem the temperature in the bottom pool is C.
After an hour, what will the temperature in the second pool be?
To solve this problem you actually need to consider the thermic effect of water falling. You need to build a single equation to accounts for acceleration due to gravity and the beginning temperatures of each pool. Then you need some calculus to transform it into an equation that will spit out the final numerical answer.
The only reason I was able to attempt and solve this problem was because I had memorised the equations. There simply would not have been enough time to try to reverse-engineer a bunch of anonymous letters in-flight.
Similarly, when I studied law, all exams were open-book. This is because, as a law professor told me, "it lets us ask harder questions". There's simply no way to synthesise thousands of pages of material in an exam setting. Either you learnt it beforehand, including a whole bunch of flat out memorisation of details of cases, or you didn't. Having your casebooks for reference is useful, but only to check a detail or reuse a quote.