- Last 7 days
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arxiv.org arxiv.org
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Tao, Terence. “What Is Good Mathematics?,” February 13, 2007. http://arxiv.org/abs/math/0702396.
Variations of this can also be applied to other fields, like history. What makes good history, good historians, good history teachers, etc.?
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- Oct 2022
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If you give a title to your notes, "claim notes" are simply notes with a verb. They invite you to say: "Prove it!" - "The positive impact of PKM" (not a claim) - "PKM has a positive impact in improving writer's block" (claim) A small change with positive mindset consequences
<script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>If you give a title to your notes, "claim notes" are simply notes with a verb.<br><br>They invite you to say: "Prove it!"<br><br>- "The positive impact of PKM" (not a claim)<br>- "PKM has a positive impact in improving writer's block" (claim)<br><br>A small change with positive mindset consequences
— Bianca Pereira | PKM Coach and Researcher (@bianca_oli_per) October 6, 2022Bianca Pereira coins the ideas of "concept notes" versus "claim notes". Claim notes are framings similar to the theorem or claim portion of the mathematical framing of definition/theorem(claim)/proof. This set up provides the driving impetus of most of mathematics. One defines objects about which one then advances claims for which proofs are provided to make them theorems.
Framing one's notes as claims invites one to provide supporting proof for them to determine how strong they may or may not be. Otherwise, ideas may just state concepts which are far less interesting or active. What is one to do with them? They require more active work to advance or improve upon in more passive framings.
link to: - Maggie Delano's reading framing: https://hypothes.is/a/4xBvpE2TEe2ZmWfoCX_HyQ
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- Feb 2022
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Local file Local file
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his suggests that successful problem solvingmay be a function of flexible strategy application in relation to taskdemands.” (Vartanian 2009, 57)
Successful problem solving requires having the ability to adaptively and flexibly focus one's attention with respect to the demands of the work. Having a toolbelt of potential methods and combinatorially working through them can be incredibly helpful and we too often forget to explicitly think about doing or how to do that.
This is particularly important in mathematics where students forget to look over at their toolbox of methods. What are the different means of proof? Some mathematicians will use direct proof during the day and indirect forms of proof at night. Look for examples and counter-examples. Why not look at a problem from disparate areas of mathematical thought? If topology isn't revealing any results, why not look at an algebraic or combinatoric approach?
How can you put a problem into a different context and leverage that to your benefit?
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