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10 votes
Accepted

A formula for the area of a rectangle

First copy your rectangle like this to make a big square of side-length m with a square of side-length d drawn inside it. The big square minus the small square leaves four half-rectangles (coloured ...
DavidButlerUofA's user avatar
6 votes

Styles of visualization in geometry

It seems the Stanford Encyclopedia of Philosophy has a useful article that at least tangentially addresses your interesting question: "Can visual thinking lead to discovery of an idea for a proof ...
Joseph O'Rourke's user avatar
4 votes

Are there mathematical proof info-graphics?

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-...
Nate Bade's user avatar
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4 votes

A formula for the area of a rectangle

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Ben Kovitz's user avatar
4 votes

Styles of visualization in geometry

You might find the essay by Marjorie Senechal, "Visualization and visual thinking." Geometry's Future (1991): 15-21, published by the Consortium for Mathematics (COMAP), of interest. In particular she ...
Joseph Malkevitch's user avatar
4 votes

Visual Pythagorean demonstration

Maybe you can do President Garfield's proof and combine it with a history lesson. page 161 of the New-England Journal of Education, April 1, 1876 (image from Google Books) Note: M. C. = Member of ...
Gerald Edgar's user avatar
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3 votes

Plainly by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{dodgerblue}{|\vec{b}| - |\vec{r}|}$?

No one diagram is going to help every student actually absorb this idea. In fact, the mistake reminds me a bit of students thinking $\sqrt{a^{2}+b^{2}}=a+b$. They are "simplifying" in a way ...
Sue VanHattum's user avatar
  • 21k
3 votes

Are there mathematical proof info-graphics?

"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 ...
amWhy's user avatar
  • 2,095
3 votes

Visual aids for understanding group theory

John Jones has a great visualization tool for a nice selection of finite group tables. It allows you to do things like select a subgroup, and see the group table colored according to the cosets. ...
Steven Gubkin's user avatar
3 votes

Visual aids for understanding group theory

The book Visual Group Theory by Nathan Carter seems to be a rich source of the kind of materials that you are looking for.
Jochen Glueck's user avatar
3 votes
Accepted

The Fundamental Theorem of Calculus and Vegetables

I am grateful to Mark Conger for finding a video of this presentation and getting the University of Michigan to digitize it. It isn't produced in the style of math youtube content, because that was ...
Chris Cunningham's user avatar
2 votes

Given a 3 4 5 triangle, how do you know that it is a right triangle?

If you want to convince someone that certain triples are the side lengths of a right triangle, you can exhibit pictures like the following, which show the $(4,3,5)$, $(12,5,13)$, and $(8,15,17)$ right ...
Will Orrick's user avatar
  • 1,122
2 votes

Visual Pythagorean demonstration

This was in my math folder, I don't know its source. It was shown as 'not needing any further explanation', but of course, for lower level students, I connect the 3 points on the circle's perimeter ...
JTP - Apologise to Monica's user avatar
2 votes

What would you recommend for the math thinking course for school?

Have them work through a few chunks of Euclid's Elements. Then they are doing proof, rather than reading about logic in a theoretical way, which is probably too abstract for kids in the age group you'...
Ben Dunlap's user avatar
2 votes
Accepted

Plainly by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{dodgerblue}{|\vec{b}| - |\vec{r}|}$?

I would tell students that absolute value bars represent distance, and distance is indicated by a line segment without an arrow. This rule of thumb is very intuitive: students should already know ...
Justin Skycak's user avatar
1 vote

Plainly by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{dodgerblue}{|\vec{b}| - |\vec{r}|}$?

My first reaction is to doubt the problem is that they somehow can't see the difference (how could you miss the vertical lines?), but rather that labeling only one vector with its length is throwing ...
Thierry's user avatar
  • 1,527
1 vote

Visual aids for understanding group theory

The Cayley Graph is visually appealing. Here is the dihedral group $D_4$ on two generators $a$ and $b$: (Wikipedia image)
Joseph O'Rourke's user avatar
1 vote

Visual Pythagorean demonstration

The proof by similarity (by finding scaled versions of the triangle within itself) is one option
Venkata Karthik Bandaru's user avatar

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