What is it about?
We explain the technique of writing proof frameworks to help students start writing proofs. This entails unpacking the statement of the theorem, often worded as an "if-then" statement, into its hypothesis and conclusion. One writes the hypothesis at the top of the page, leaves a space, and writes the conclusion at the bottom of the page. This is a first-level proof framework. After that, one can unpack the conclusion, which is often another "if-then" statement, so one can write another proof framework inside what has already been written.
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Why is it important?
Often university students in a transition-to-proof course, or other proof-based course, when asked to prove a theorem just stare at a blank piece of paper and do not know where to start. This technique at least gets them started.
Perspectives
My husband, John Selden, also a mathematician, and I have been using this technique a long time in our course, Understanding and Constructing Proofs, designed for beginning graduate students who need a little help with proofs
Dr. Annie Selden
New Mexico State University
We have developed and used this in our inquiry-based transition-to-proof course for more than 10 years. We have used it in a proof supplement to a real analysis course that we were asked to teach. The teacher of the real analysis course said that it helped her students write clear proofs, and even if they were not entirely correct, that she was better able to comment on them because they were more organized.
Dr. John Selden
New Mexico State University
Read the Original
This page is a summary of: Proof Frameworks: A Way to Get Started, PRIMUS, November 2017, Taylor & Francis,
DOI: 10.1080/10511970.2017.1355858.
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