Which Proof Format Is Easier to Grade: A or B?

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Discussion Overview

The discussion centers on the preferred format for presenting mathematical proofs in grading contexts, specifically whether format A or format B is easier to grade. The focus is on the clarity and organization of reasoning in proofs.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants argue that format B, which states the conclusion first, is easier to read and grade because it clarifies the author's goal from the outset.
  • Others support the idea that format B organizes reasoning better and reduces the need for the grader to guess the direction of the proof.
  • A participant notes that many students use format A, which complicates grading for them.
  • There is a general preference expressed for format B among several participants.

Areas of Agreement / Disagreement

Participants generally agree that format B is superior for clarity and grading ease, though there is no consensus on the effectiveness of format A.

1MileCrash
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To those of you who may grade proofs in which the result is not stated (ie prove or disprove), which of the following do you think is easier to grade, and a better format:

A) Proof... Therefore the theorem is false/true.

B) The theorem is false/true. To see this, consider the following: Proof...

I think that B is actually easier to read. You have stated your goal prior and so it seems that the proof would be easier to read (you don't have to guess where it is going). I feel like if I were grading these types of assignments, I'd read the conclusion first anyway.
 
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I think the second option is superiour. As you said, it organizes the reasoning from the beginning and makes clear where the author is going.
 
1MileCrash said:
To those of you who may grade proofs in which the result is not stated (ie prove or disprove), which of the following do you think is easier to grade, and a better format:

A) Proof... Therefore the theorem is false/true.

B) The theorem is false/true. To see this, consider the following: Proof...

I think that B is actually easier to read. You have stated your goal prior and so it seems that the proof would be easier to read (you don't have to guess where it is going). I feel like if I were grading these types of assignments, I'd read the conclusion first anyway.

Definitely take the second option. I see many students taking the first option in their exams and it makes it a lot harder for me.
 
Second one, of course.
 

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