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I am teaching mathematical proof to kids (10th grade) and am of the opinion that proofs of theorems are a good place to start, where almost all of mathematics' important players come together.

On one side, we have logical structures like propositions, consequence, rules of inferences, propositional logic/calculus, etc.

Then we have formal system, axiomatic system of natural numbers say, on the other side, which has structures of math like axioms, primitive notions/functions, theorems, lemmas etc.

And then we have proof itself where there are various techniques like direct proof/ indirect proof, reasoning (deductive reasoning), using various axioms, theorems etc.

Kids usually struggle with every one of these concepts, let alone all of them together. It is difficult to get the whole picture and all the moving parts. So this place (proof) seems like a good place to show all of this in action. I could make infographics myself, but it would take some time. So I wanted to know whether someone already has done such and is willing to share?

Also, if I were to create such an infographic, how do you suggest I begin, and what, in your opinion, must it include?

[Edit]: I uploaded an initial version of infographic to github, please click here to see. I VERY EAGERLY wait for your INVALUABLE feedback/suggestions to improve this infographic...

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    $\begingroup$ It seems to me that most of the listed ideas are best illustrated, the more so for novices, by specific, well chosen examples, rather than as parts of some grand scheme that will almost necessarily be completely opaque to someone without experience. Start with some simple statements that illustrate something simple, such as that although A imply B, B need not imply A. $\endgroup$
    – Dan Fox
    Sep 30, 2019 at 7:55
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    $\begingroup$ Can you post the age of the kids, rather than a reference to an unspecified country's education system? I have no idea how old a 10th grader is. $\endgroup$
    – Sean Reid
    Sep 30, 2019 at 14:55
  • $\begingroup$ 10th graders in the U.S. are usually about 15 years old. $\endgroup$
    – Sue VanHattum ♦
    Oct 1, 2019 at 4:34
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    $\begingroup$ I guess that's about the age for 10th grader all around the world. I am surprised there are people who don't know the age of 10th graders... $\endgroup$
    – Ashish Shukla
    Oct 1, 2019 at 17:16
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    $\begingroup$ @AshishShukla: Different countries start primary education at different ages. Also, not all countries use the terminology "grade". $\endgroup$
    – J W
    Oct 1, 2019 at 18:51

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Math With Bad Drawing has some images that approach an info-graph (and in general is just a great website for math education), for example:

https://mathwithbaddrawings.com/2015/07/01/infinity-plus-one-please-check-your-intuitions-at-the-front-desk/

There are some good geometry ones, especially around old compass and straight-edge constructions but that wont really give you rules of inference. For instance

http://www.noborubitoy.com/?p=119

Finally, you could look into flowchart proofs, but I haven't found many graphically nice examples. Here is an example:

https://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/teaching-and-learning/flowcharting-proofs

I'll be following this question, I've been looking for some decent proof visualizations as well.

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  • $\begingroup$ Thanks for the links but I am not looking for proof of any particular theorem. I am looking to put all the moving part of the "Proof" itself in an infographic, like what Proof contains Proof Technique(Direct/Indirect), Reasoning vs Logic, various Inference rules etc. such that kids gets to see All the ingredients of a Proof. $\endgroup$
    – Ashish Shukla
    Oct 1, 2019 at 3:15
  • $\begingroup$ I uploaded the infographic in github. Please have a look, link in Question's edited section. Your feedback and suggestions are highly appreciated... $\endgroup$
    – Ashish Shukla
    Oct 30, 2019 at 6:32
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"Kids usually struggle with every one of these concepts, let alone all of them together. It is difficult to get the whole picture and all the moving parts. So this place (proof) seems like a good place to show all of this in action."

I'm afraid there is no "complete picture" of all the facets of logic and proof that you mention, interrelating in one infograph.

Here are some examples of infographs for some components you'd like to include in a combined infograph:

Laws of logic

Math and Logic Thinking

Logical fallacies

logic diagram flowcharts

If you decide to work on this project yourself, here are some tools for creating infographs.

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  • $\begingroup$ Information is beautiful is a great source for infographics. $\endgroup$
    – Nate Bade
    Oct 1, 2019 at 1:57
  • $\begingroup$ Thanks for the links but I am not looking for proof of any particular theorem. I am looking to put all the moving part of the "Proof" itself in an infographic, like what Proof contains Proof Technique(Direct/Indirect), Reasoning vs Logic, various Inference rules etc. such that kids gets to see All the ingredients of a Proof. $\endgroup$
    – Ashish Shukla
    Oct 1, 2019 at 3:14
  • $\begingroup$ Please see these cautionary sites which speak exactly to my point in my previous comment: 7 Mistakes to Avoid When You Create an Infograph; infographic warning signs $\endgroup$
    – amWhy
    Oct 1, 2019 at 20:22
  • $\begingroup$ Infographic Tools for Educators $\endgroup$
    – amWhy
    Oct 1, 2019 at 20:36
  • $\begingroup$ @Namaste I uploaded an initial version of Infographic on github. I have provided link in the "Edit" section of the question. I request you to have a look and provide your invaluable feedback and suggestions... $\endgroup$
    – Ashish Shukla
    Oct 30, 2019 at 6:29

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