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Questions tagged [proofs]

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For questions about mathematical proofs in an educational context.

208 questions
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6 votes
1 answer
210 views

In my experience, students who are new to writing their own proofs can get confused about the difference between: truth tables related to if-then statements; e.g., defining when "if p, then q&...
Mark's user avatar
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2 votes
0 answers
113 views

This is something I often wonder about whenever I turn to a book or video to understand a proof. I’m aware that everyone, at some point, has been unable to complete a proof on their own and has had to ...
Jesus Medina's user avatar
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4 votes
4 answers
461 views

I recently started learning more computer science, and I find that the language we use there can be used to give succinct descriptions of many of the phenomena that come up in proofs. For example, if ...
Clemens Bartholdy's user avatar
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1 vote
0 answers
80 views

I’ve been working on a new instructional framework for modern math based on irreducible route units and roadmaps, where logical steps are explicitly justified and anchored to familiar concepts and ...
Mathman's user avatar
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1 vote
0 answers
126 views

How can the Method of Contradiction be formally classified into distinct types of proofs—such as proof by infinite descent—and in what ways does each category apply to different classes of ...
Janaka Rodrigo's user avatar
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3 votes
3 answers
987 views

I have seen many students struggling with the concept of topological vector spaces. They get stuck with the proofs of quite trivial results even though they feel it is true. However, the main problem ...
Kishalay Sarkar's user avatar
  • 133
4 votes
7 answers
3k views

I work as a math intervention teacher with high school sophomores who are currently taking geometry. The sequence of instruction is as followed (so far this year): Introduction to geometry - naming ...
RDrelli's user avatar
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14 votes
7 answers
2k views

To prove that $a \Rightarrow b$, we can equivalently prove $\neg{b} \Rightarrow \neg{a}$. Q. How can we best explain this to the student? Here's my attempt. Suppose we prove that $\neg{b} \...
Joseph O'Rourke's user avatar
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4 votes
3 answers
538 views

I am studying Mathematics/Statistics at university, and realizing how important formal mathematical writing is—not just for assignments and papers, but as a general means of communicating ideas. ...
Tony Theo's user avatar
  • 141
0 votes
1 answer
237 views

Would it help to introduce students to methods of proof more basic than induction, e.g. how to structure a simple proof with a premise and a conclusion, how to generalize, etc.? Maybe start with ...
Dan Christensen's user avatar
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1 vote
1 answer
159 views

I know taking a while to solving a problem matters and that I'd need to consider where I feel I'm lacking or lagging behind on a problem to know which to focus on. But if I were to tackle conceptual ...
Overflow's user avatar
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4 votes
1 answer
2k views

I would appreciate ideas on good practice in the use of AI among mathematics and statistics students to improve their critical thinking in the development of mathematical proofs. I am wondering about ...
user20503's user avatar
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8 votes
4 answers
3k views

I’m thinking about creating an online platform to teach college-level math subjects like abstract algebra, real analysis, topology, and other proof-heavy areas. A key challenge I’m facing is how to ...
Erin's user avatar
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5 votes
4 answers
349 views

Define $e-1$ as the yearly compound interest obtained from a one dollar investment with 100% gross annual interest: $$ e := \lim_{n\to\infty} (1+1/n)^n =: \lim_{n\to\infty} a_n $$ Nine year olds can ...
Bananach's user avatar
  • 275
11 votes
5 answers
2k views

The question Teaching students to find and correct their own errors and its answers address mainly calculation problems of the types typically found in secondary school and the lower levels of ...
J W's user avatar
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