August 20th, 2017, 04:11 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79  What Do You Think of Trial and Error?
This does not have to do with Geometry, but the general forums don't get many posts, so I'm posting it here. What do you think of these instructions given by New York? "Trial and error is a valid method for solving an equation or a problem. However, you must clearly write the equation you are using along with at least three guesses with an appropriate check. Even if your first guess is correct, demonstrate that you understand the method by showing work for two incorrect guesses and the checks." 
August 20th, 2017, 07:00 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 857 Thanks: 348 
I agree that trial and error is ONE logically valid method for solving problems, but it is very seldom an efficient method absent obvious constraints on the possible set of solutions. If your first guess works, then there is no logical need to try other guesses. If, however, you are trying to determine whether someone grasps how trial and error works, I can see requiring that someone to try a different guess and to explain why that is wrong. Replicating that effort is makework. 
August 20th, 2017, 07:14 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,660 Thanks: 427 
Iterated trial and error is the heart of all approximation techniques such as Newton's method. Make a guess, see if it works, adjust your guess in the appropriate direction, repeat till you're close enough for your purposes. I can't really comment on what the state of New York tells high school students. The paragraph quoted is vague and confusing. Why three guesses? Is this from the regent's exam? Last edited by Maschke; August 20th, 2017 at 07:17 PM. 
August 20th, 2017, 08:59 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339  
August 21st, 2017, 07:06 AM  #5  
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79  Quote:
Last edited by EvanJ; August 21st, 2017 at 07:08 AM.  
August 22nd, 2017, 08:56 AM  #6  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,081 Thanks: 698 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
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August 22nd, 2017, 02:26 PM  #7 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79 
My guess is the reason that three guesses are required is that if a student was correct with his or her first guess, he or she would have shown less work than students who knew the procedure, and therefore the correct guess without other guesses should not be worth full credit.

August 22nd, 2017, 02:32 PM  #8  
Senior Member Joined: Aug 2012 Posts: 1,660 Thanks: 427  Quote:
Your own question is vague. Are you asking us to say that the Regents suck because they clearly are just bs'ing their way through this topic and it actually does not make a lick of sense? Frankly that would be my take, not being a fan of the educrats, particularly when it comes to the teaching of math. Or are you asking about our opinions of the method of trial and error? Either way it's a valid question, I'm just not sure which one you're asking.  
August 22nd, 2017, 03:15 PM  #9 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 573 Thanks: 79 
I'm asking about your opinions of the method of trial and error. Who here has taught math, graded a test, and seen trial and error used?

August 22nd, 2017, 04:56 PM  #10  
Senior Member Joined: Aug 2012 Posts: 1,660 Thanks: 427  Quote:
Well the trick is that you are guessing, but you are making "educated" guesses according to some heuristic which you might not even be aware of. It's the development of that educated guessing facility that we want to teach or inspire in the students. Telling them to make three guesses and show their work is a bureaucrat's understanding of mathematical insight. It's hopeless. This is the problem with the Regents test and with Common Core in general. Ignorant bureaucrats are trying to formalize something they don't really understand. Namely, mathematical intuition and insight. Making a guess that's the right guess. And if you get it on the first shot, and it works, you've got it. Other times you need to make a thousand guesses. All approximation techniques are variations on iterated guessing, and the world runs on computational approximations of mathematical functions. So there's a lot that can be said about mathematical guessing. You could write an essay on the subject or a book But the Regents, being government bureaucrats, are utterly incapable of expressing or teaching it, since they don't have math sense themselves. Their version is "Make three guesses and show your work." Now you tell me. How can that possibly impart anything in the students other than dislike of math? Why three times? Why show your equations if it's a guess? What are they talking about at all? tl;dr: Mathematical guessing is literally the heart of math, in many different ways. The Regents clearly have no idea what it's about. They're bureaucrats teaching math badly. Last edited by Maschke; August 22nd, 2017 at 05:01 PM.  

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