How do you do “mental math” with no mental imagery?

DiscussionCategory: QuestionsHow do you do “mental math” with no mental imagery?
Jennifer McDougallJennifer McDougall Staff asked 2 months ago

This has come up in recent social media posts; That many people rely on visual techniques when solving mathematical equations. How do you do "mental math," when you cannot create mental images? Any tips or strategies to share?

Vee AlexanderVee Alexander replied 2 months ago

I just stumbled on this website today over a math reheated question. I visualize numbers in a set pattern and wondered if anyone else did. This doesn’t help me with math! But I’ve never met anyone who “sees” the digits in lines (heading left, or up in rows or columns but always the same configuration) the way I do. And though I say “see,” the inner screen is black, just like it is for anything I “picture.” I’m 72 and never knew I had aphantasia.

3 Answers
Rachel CicconeRachel C answered 2 months ago

Usually what I do is change the numbers to make the math easier. i.e. adding 7 + 5, I go “okay, add three to 7 from the 5 to make 10, then add the two left over to make 12”.

But for anything REALLY complicated, forget it.

Kat KaneKat Williams replied 2 months ago

That’s what I do. Rounding where necessary to simplify it, and beyond that, I need a calculator – or at least pen and paper. I don’t even try to multiple over 2 digits in my head, it’s not worth the hassle and I won’t trust my answer.

Rachel CicconeRachel C replied 2 months ago

Yeah same!

I watched a coworker the other day add up trees I sampled for my job, and I just stared at him for the mental math he just did on the fly because it did involve multiple two digit numbers.

Granted though, I’ve never had any issues learning math, or even calculus in university.

Jon EvansJon Evans answered 2 months ago

I genuinely don’t understand.u. I just do 68+7= 75… No visualising, just remember the numbers and do the sum.

For bigger sums I just break down the numbers:

3247 = (4710)+(4710)+(4710)+(47*2) = 1504

No idea how mental images are meant to help? But then again, no idea what mental images are…

(Sorry if posted twice, the website/my phone don’t seem to agree)

Kat KaneKat Williams replied 2 months ago

Well firstly, mental math isn’t just sums. It includes division, subtraction, addition and multiplication. Also, you did your 32*47 the same way that Rachel is describing above. You used a trick of breaking down the components into more round numbers, and then merging the smaller equations you broke down.

Though your method requires holding on to multiple mini-equations in your head to reach the conclusion. My brain tends to mix digits up, so I couldn’t necessarily keep (47*10)*3=1410 in my head while I was doing the 47*2 – especially since I have to do that like I was doing it on paper – 2*7,. carry the 1, etc. Or I have to say, 2*50=100 and then subtract 6. Either way, by the time I’ve done that, the 1410 has become 1401, or was it 1140? . That you can break it down in that way, with aphantasia, I find impressive. But again, people seem to have found varying ways to work around this. Some people with aphantasia are even genuinely capable of complex calculus, and while I’m pretty good at algebra, I hit brick walls in geometry.

As for the role visualization plays – many normal visualizers are taught to do mental math by seeing the numbers written out and manipulating them in that vision. And people who can do extremely complex math problems in their mind, like multiplying or dividing numbers which are several digits long, say that it’s all done via visualization. The same applies to most memory techniques that are taught; they usually involve utilizing visualization in some way, to accentuate your recall of dates, words, and other facts.

You also don’t have to have mental images to know what they are. Just watch any movie or TV show where they’re shown. Hell, watch an episode of The Librarians where Cassandra is “doing math” and you’ll get a great depiction of what mental images are, for not just people with vivid visual images but those with synesthesia too. Though as I understand it, even among people who have full access to visual imagery, some can superimpose that imagery over their physical sight and some are only capable of visualizing properly when they close their eyes.

Rachel CicconeRachel C replied 2 months ago

I didn’t even know you can also do multiplication that way too! Which shows how good I am at mental math lol

The thing is, I don’t remember how I was specifically taught to do mental math as a child. Mixing the numbers is how I’ve always done it. And I’ve seen online in a few places that people with ADHD sometimes do the same thing for mental math as well.

Frances SmithFrances Smith answered 1 month ago

It’s not as if there are loads of people out there who are super good at mental maths. I’ve come across a lot of people far worse at it than me, but if I do have to calculate something I do it using my memory, and calculate as I would if I were using pen and paper, rather than a calculator. I have an imaginary notebook in my head for this purpose.

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