NO. You are talking about modern day general purpose microprocessors. Microcontrollers are totally different things than microprocessors. MCUs have only one task to do most of the time. Your requirement needs a 80386 or better. Maybe a more powerful MCU like those in tablets can do task switching or privileges or both.
You could add delay(1000); in your code to delay 1 second before taking the next measurement and print to serial.
Let's think we have a faucet, water flows out of the faucet. An analog person comes in, turns the faucet smoothly so the flow rate increase all the way from 0 to 1023 assuming every single value in between because the analog person has that smooth hand. The status of faucet has so many values, from 0, to 1023. Now a digital person comes in, he turns the faucet all the way on, or all the way off. There are only two statuses of the faucet, all the way on, or 1, and all the way off, or 0.
A button apparently belongs to a digital input since it either conducts current (just like water in the example) or it conducts no current so it should be connected to a digital pin. If you have a potentiometer that you can use to change current smoothly (thus voltage), then you need an analog input. Using a button on an analog input is like you can sense so many different stages but your button only provides two. Connecting a potentiometer to a digital input is like you can provide so many different stages but your can only sense on or off. Both cases are to be avoided unless you have some special need.
Haha, as a kid I was fed lots of communism crap (never believed a thing they said) but the communists back then were pretty straight with science. It was atheism and evolution all the way. So I was quite alright with math and science although I had different names for Poynting vector since the commies suspected that Mr. Poynting was a capitalist and erased his name from his own vector, like the hats trick in Soviet Union. After living so many years in capitalist country, I start to realize old Carl Max might have gotten a few things right. I can't say too much about his "followers" though. People in my part of the world have low standards in math Even eyeballing numbers and doing approximations will make you a tough prof.
I would suggest you use my phi_prompt library to display a menu. It automatically updates displays menu items as you press up and down to browse the menu and returns the item selected if you press OK. There's a lot more to it that you may want to use, like input a number, as you're making a math game. There is also going to be features that will auto scroll contents that are too long.