Rubric for Proofs
September 11, 2014
The rubric for proofs is separated into five different areas.
1. Overall Correctness of Proof : this area considers whether or not the
proof is valid. Deductions are do to the following:
• the proof is invalid due to problems with logical reasoning and/or
mathematical content
• the argument is missing steps
• −2 points if the argument is incomplete.
2. Logical Reasoning: are the rules of logic being followed? The point
total is out of 4, with point deductions for any of the following:
• the same variable name is used to refer to different mathematical
entities.
• incorrect usage of quantifiers (student is using existential quantifiers
when they should be using universal quantifiers).
• the student performs a logical deduction that is not valid (normally
this is called ‘jumping to conclusions’).
• the student uses a logical equivalence, without stating that they are
doing so.
• 0 points if the argument is completely incoherent.
3. Mathematical Content: Does the proof demonstrate understanding of
mathematical definitions? Point deductions for:
• applying a definition incorrectly (for instance, saying n = 2k when n
is odd).
• applying a definition that is not appropriate (applying the definition
of even number when working with an even function).
• employing unnecessary content in a proof
• failing to prove the result, due to misunderstanding the terminology
which appears in the result.
• 0 points if the argument only involves examples.
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4. Proof writing conventions and organization: Is the proof written in
the standard proof writing style? Is the proof well-organized? There are
deductions when:
• −1 point: the proof is missing some standard proof-writing conventions, or has some organizational issues.
• −2 points: the proof is missing many proof-writing conventions, or
the proof is poorly organized.
5. Grammar and professionalism:
• 4 points: the proof is well-written
• 3 points: the proof has some simple grammar errors, but is still
readable.
• 2 points: the proof is unprofessional, and has sentences crossed out.
The proof looks like a rough draft.
• 1 point: the proof suffers from major grammatical mistakes.
• 0 points: the proof is completely illegible, or is missing.
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