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I HATED "show your work". You want a proof, ask me for a proof. It's not my fault I can solve your problem in my head. Especially horrifying is if you want m

by Eliezer 10y ago

I HATED "show your work". You want a proof, ask me for a proof. It's not my fault I can solve your problem in my head. Especially horrifying is if you want me to solve the problem a particular way. There is no better way of turning the fun and freedom of math into drudgework. You are licensed to ask me to arrive at the correct answer, or to prove a theorem from premises; telling me how to do it is mathematical abuse.

yequalsx 10y ago
The answer is not important. What is important is that one knows a process for solving the general situation. Knowing how to get the answer in a problem with easy numbers is not the point. Demonstrating how to find it no matter what numbers I used is the point. There is also the fact that I'm not just teaching the student so they can pass this class. I'm teaching them so that they can pass the next class too. In beginning algebra, our lowest level course, we start with basic problems. For instance, you drive for 3 hours and travel 150 miles. What's your average speed. Almost every person gets this right. But many can't do this problem. You drive a car for 4/3 an hour and travel 100/6 miles. What is your average speed? Now many can't do this problem. They ask, which way does the division occur? Our goal is that they know and understand a general process. We are setting them up to solve more advanced problems. Problems that can't be done in their head. If you can't write the steps out in the simple case you'll never understand the harder problems. Problems that involve quadratic functions or trig functions. Mathematics is a human activity and communication is part of it. Knowing how to communicate what is in your brain to another person in a way that they can understand is very valuable. I give the students nice numbers and in exchange they are expected to tell me a general way of solving that type of problem. Instead of feeding them for a day I want to teach them how to fish. I strongly disagree with your belief that this mathematical abuse.
- analog31 10y ago
  Interestingly, I think many of your points would seem obvious if couched in computer programming terms. For instance, how do you write a program that's correct, but that another human can understand and adapt? What happens when a program gets too big to understand all at once in your head? How do you know that you've found all of the possible outputs?
- webmaven 10y ago
  > Knowing how to get the answer in a problem with easy numbers is not the point. So, don't use easy numbers? > I give the students nice numbers and in exchange they are expected to tell me a general way of solving that type of problem. If this quid-pro-quo is explicit, that seems fair. But I still don't see why "nice numbers" are necessary.
  - yequalsx 10y ago
    In this case nice numbers are not necessary. In other types of problems they are. One does not want to burden students with needlessly complicated calculations when the main point is a simple one.
yequalsx 10y ago
I should point out that I'm not licensed by the state or anyone else. At the college level we don't have licenses. My contract states that instructors are solely responsible for grading and assigning grades. In the system that I teach in it is my prerogative, more or less, to grade as I see fit. This is where experience and professional judgment come into play.
Ar-Curunir 10y ago
It is your fault if you can't explain how you solved the problem; anybody can look over someone's shoulder and copy the final answer. Producing the steps allows the teacher to verify that most likely you did the problem yourself.
- waterhouse 10y ago
  In first or second grade, I believe I was asked to "show my work" for "2 x 3 = ?". I believe the teacher didn't accept "But I don't have any work to show" as an answer. I don't think most adults would have any work to show either, nor should they—if they actually repeatedly add 2 to itself, or do anything other than a memory lookup, then there's probably something wrong with their prior math education. In general, if the step that I took to solve a problem was "I looked up a memorized fact in my brain", then that is the truth, and writing down anything else to "show my work" is a lie. As other people have said, a proper way to ask that question is "Show a derivation of the answer to [problem]." Bonus points if you specify what assumptions they're allowed (e.g., in the above example, "addition").

by Eliezer 10y ago

yequalsx 10y ago

The answer is not important. What is important is that one knows a process for solving the general situation. Knowing how to get the answer in a problem with easy numbers is not the point. Demonstrating how to find it no matter what numbers I used is the point. There is also the fact that I'm not just teaching the student so they can pass this class. I'm teaching them so that they can pass the next class too. In beginning algebra, our lowest level course, we start with basic problems. For instance, you drive for 3 hours and travel 150 miles. What's your average speed. Almost every person gets this right. But many can't do this problem. You drive a car for 4/3 an hour and travel 100/6 miles. What is your average speed? Now many can't do this problem. They ask, which way does the division occur? Our goal is that they know and understand a general process. We are setting them up to solve more advanced problems. Problems that can't be done in their head. If you can't write the steps out in the simple case you'll never understand the harder problems. Problems that involve quadratic functions or trig functions. Mathematics is a human activity and communication is part of it. Knowing how to communicate what is in your brain to another person in a way that they can understand is very valuable. I give the students nice numbers and in exchange they are expected to tell me a general way of solving that type of problem. Instead of feeding them for a day I want to teach them how to fish. I strongly disagree with your belief that this mathematical abuse.

analog31 10y ago
Interestingly, I think many of your points would seem obvious if couched in computer programming terms. For instance, how do you write a program that's correct, but that another human can understand and adapt? What happens when a program gets too big to understand all at once in your head? How do you know that you've found all of the possible outputs?
webmaven 10y ago
> Knowing how to get the answer in a problem with easy numbers is not the point. So, don't use easy numbers? > I give the students nice numbers and in exchange they are expected to tell me a general way of solving that type of problem. If this quid-pro-quo is explicit, that seems fair. But I still don't see why "nice numbers" are necessary.
- yequalsx 10y ago
  In this case nice numbers are not necessary. In other types of problems they are. One does not want to burden students with needlessly complicated calculations when the main point is a simple one.

yequalsx 10y ago

I should point out that I'm not licensed by the state or anyone else. At the college level we don't have licenses. My contract states that instructors are solely responsible for grading and assigning grades. In the system that I teach in it is my prerogative, more or less, to grade as I see fit. This is where experience and professional judgment come into play.

Ar-Curunir 10y ago

It is your fault if you can't explain how you solved the problem; anybody can look over someone's shoulder and copy the final answer. Producing the steps allows the teacher to verify that most likely you did the problem yourself.

waterhouse 10y ago
In first or second grade, I believe I was asked to "show my work" for "2 x 3 = ?". I believe the teacher didn't accept "But I don't have any work to show" as an answer. I don't think most adults would have any work to show either, nor should they—if they actually repeatedly add 2 to itself, or do anything other than a memory lookup, then there's probably something wrong with their prior math education. In general, if the step that I took to solve a problem was "I looked up a memorized fact in my brain", then that is the truth, and writing down anything else to "show my work" is a lie. As other people have said, a proper way to ask that question is "Show a derivation of the answer to [problem]." Bonus points if you specify what assumptions they're allowed (e.g., in the above example, "addition").