Visual Thinkers: How can visual skills be applied to maths?

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I'm a visual thinker and I was wondering how I could apply my skills to maths when solving problems. How do you other visual thinkers do it? I'm looking for insight , tips and experience really.

For me it usually requires coming up with a concrete visual analogy in my head. To give a specific example would require me to know the type of mathematical problem you're interested in.

For me it was always counting and taking away numbers and memorization. Then it got harder for me to remember to do it all and understand how to do it as it got more complex for me. I never had a visual need for this. I was taught to do it with hands and using scratch marks my teacher called sticks.

Geometry is even taught in a very visually way. But not the rest of math.

Though Ido remember that board on the wall -somewhere back in elementary school - that showed all of the numbers from one to 100 arranged in a square-starting with one through ten on the top row.

It drove home the idea that 100 is ten "squared"- thus the whole idea of square roots- and cube roots.

I do math visually, and am great at mental math.

I use a "sum of the parts" approach to almost everything I do, and the basic idea I explain to people is when I calculate tips and am accurate to the penny (most times...)

Bill is $100
tip is 20%

I see a diamond shape in my head with the $100 on top

$100
$10 $10
$120

I calcuate 10% of the total 2x with the 10%'s on the outer part of the diamond
the result is the bottom of the diamond

Statistics is my absolute favorite type of math because it is purely visual - Bell curves are a graphical representation of a HUGE data set. Statistics changed my life, honestly... Just think about the implications of statistics! It makes seemingly complex ideas very simple to understand. Excuse me while I stim over the excitement of thinking about stats

It depends on the type of math/math problem.

For me, visual thinking is the mathematics. Without being too specific, I can draw &/or visualise a 3D object and then extrapolate measurements if I have scaled it 1st.

I'm in the sciences and although I'm not super-skilled in mathematics, I do have an understanding of numbers.

Take a class in physics. Math by itself can be too abstract to make visual. Physics will give you some concrete examples to start applying the equations too. If you get the links between the equation and the reality everything will start to click.

I have a hard time with mental math but I tend to associate my math problems with objects. I'm also a programmer so the concept of variables and expressions come a little easier to me to where I don't have to think too much about them. I wish I could help more but this is a problem I actively struggle with as well.

I love physics, I'm really good at it because of my visual skills.

I'd like to improve my math skill using visual techniques, my general ones of seeing individual entities standing in for 1's, 10's, 100's etc. and applying memorized adding/subtracting/dividing/multiplying do not always work beyond a basic problem. I've seen very complicated ones involving rotating objects and lines, etc. standing in for calculations, but I don't really grasp them. I'll have to look into statistics and physics, I never took them in high school due to a hatred of math. Does anyone know of any good books on math visualization techniques or dyscalculia?

Incorporate special interests

I'm curious as to why what you did is visual maths? Is it the fact you used a shape or just the fact you saw the numbers in your head and manipulated them as if looking at a computer screen - isn't this what everyone does ?

I'm going to go out on a limb here and probably leave myself open to ridicule and explain how I do maths. Me & my GF just compared the visual process involved in working out a very simple maths problem i.e. 15 -7

We both saw the numbers in our heads and visually manipulated them as if looking at a calculator but that's where the differences end.


She took the 15 and made it an even number by subtracting 1 = 14 , she then divided 14 by 2 to get 7 , then added the subtracted 1 to the 7 to get 8.

My approach was to visually see it as a sum written down with the 7 under the 15. I subtracted 5 from both numbers to give an easier sum 10 - 2 = 8.

Let the trashing commence

In chemistry, we have a set of symmetry operations (mirror planes, axis of rotation, screw planes, centers of inversion, etc.) that can be applied to molecules and/or crystal systems. Each of these symmetry operations has a corresponding linear algebra matrix that can be applied to the initial system matrix (ie. how the molecule is laid out in space). By applying the symmetry operation, it will often change the position of individual atoms within the molecule. If you work with these operations enough times, you can start to visualize both the physical and the mathematical relationships at the same time.

This concept is extremely important in single crystal x-ray crystallography. The diffraction pattern of the x-rays from the crystal is dependent upon how the crystal is packed. I have used this technique to help prove the existence of new molecules in certain synthesis reactions for my PhD.

Blimey , only the last sentence made sense to me. Did you get to name the molecules?

Yes, I did get to name them in a way. I used a shorthand form to nickname them rather than to follow the formal IUPAC naming scheme in my dissertation. In this case, the IUPAC name for each compound would be the length of a long sentence. My PhD committee members thanked me for using the short version in naming them.